{"id":123663,"date":"2026-11-08T00:16:46","date_gmt":"2026-11-07T16:16:46","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/123663.html"},"modified":"2026-11-08T00:16:46","modified_gmt":"2026-11-07T16:16:46","slug":"ofdm-%e6%a2%b3%e7%8a%b6%e5%af%bc%e9%a2%91%e8%83%bd%e4%b8%8d%e8%83%bd%e6%97%a0%e6%b7%b7%e5%8f%a0%e6%81%a2%e5%a4%8d%e5%a4%9a%e5%be%84%e4%bf%a1%e9%81%93%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/123663.html","title":{"rendered":"OFDM \u68b3\u72b6\u5bfc\u9891\u80fd\u4e0d\u80fd\u65e0\u6df7\u53e0\u6062\u590d\u591a\u5f84\u4fe1\u9053\uff1f"},"content":{"rendered":"

\/* MD \/ \u5bcc\u6587\u672c\u4e2d\u7684 .toc\uff08\u542b\u535a\u5ba2\u56ed\u642c\u5bb6\u7b49\u5d4c\u5957\u7ed3\u6784\uff09\uff1b.toc-box \u5728\u4fa7\u680f\uff0c\u4e0d\u53d7\u5f71\u54cd *\/
\n #content_views .toc,
\n \/* \u7f16\u8f91\u5668\u5e38\u5728\u76ee\u5f55\u524d\u540e\u63d2\u5165\u7a7a p\uff08:empty \u4ecd\u5360 20px\uff09\uff0c\u4e00\u5e76\u53bb\u6389\u907f\u514d\u9876\u7a7a\u9699 *\/
\n #content_views.markdown_views > p:empty:has(+ .toc),
\n #content_views.markdown_views > .toc + p:empty,
\n \/* \u5bcc\u6587\u672c\u65e7\u7248\u76ee\u5f55\u6807\u8bb0 *\/
\n #content_views.htmledit_views #main-toc,
\n #content_views.htmledit_views #hr-toc,
\n #content_views.htmledit_views p[id*=\\”-toc\\”] {
\n display: none !important;
\n }
\n \/* \u76ee\u5f55\u53bb\u6389\u540e\uff0c\u7d27\u8ddf\u7684\u9996\u4e2a\u6807\u9898\u4e0d\u518d\u591a\u51fa\u4e00\u5757\u4e0a\u8fb9\u8ddd *\/
\n #content_views.markdown_views > .toc + h1,
\n #content_views.markdown_views > .toc + h2,
\n #content_views.markdown_views > .toc + h3,
\n #content_views.markdown_views > .toc + h4,
\n #content_views.markdown_views > .toc + p:empty + h1,
\n #content_views.markdown_views > .toc + p:empty + h2,
\n #content_views.markdown_views > .toc + p:empty + h3,
\n #content_views.markdown_views > .toc + p:empty + h4 {
\n margin-top: 0 !important;
\n }<\/p>\n

\u7b2c\u4e00\u7ae0 \u68b3\u72b6\u5bfc\u9891\u4e0e\u4fe1\u9053\u4f30\u8ba1<\/h3>\n

1.1 OFDM \u9891\u57df\u6a21\u578b<\/h4>\n

\u5728\u5ffd\u7565\u566a\u58f0\u3001\u9891\u504f\u3001\u5b9a\u65f6\u8bef\u5dee，\u4e14\u5faa\u73af\u524d\u7f00\u4e0d\u77ed\u4e8e\u591a\u5f84\u65f6\u5ef6\u7684\u524d\u63d0\u4e0b，OFDM \u7b2c <\/p>\n

k<\/p>\n

k<\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5b50\u8f7d\u6ce2\u4e0a\u7684\u63a5\u6536\u7b26\u53f7\u4e3a<\/p>\n

<\/p>\n

Y<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

=<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

X<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

,<\/p>\n

k<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

1<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

N<\/p>\n

\u2212<\/p>\n

1<\/p>\n

Y[k]=H[k]X[k],\\\\qquad k=0,1,\\\\dots,N-1<\/p>\n

<\/span><\/span>Y<\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span>X<\/span>[<\/span>k<\/span>]<\/span>,<\/span><\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>N<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d <\/p>\n

X<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

X[k]<\/p>\n

<\/span><\/span>X<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u662f\u53d1\u5c04\u7b26\u53f7，<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

H[k]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u662f\u4fe1\u9053\u9891\u7387\u54cd\u5e94\u3002\u8bbe\u4fe1\u9053\u51b2\u6fc0\u54cd\u5e94\u4e3a<\/p>\n

<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

,<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

1<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

L<\/p>\n

\u2212<\/p>\n

1<\/p>\n

h[l],\\\\quad l=0,1,\\\\dots,L-1<\/p>\n

<\/span><\/span>h<\/span>[<\/span>l<\/span>]<\/span>,<\/span><\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>L<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5373\u6700\u5927\u65f6\u5ef6\u5bf9\u5e94 <\/p>\n

L<\/p>\n

\u2212<\/p>\n

1<\/p>\n

L-1<\/p>\n

<\/span><\/span>L<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u4e2a\u91c7\u6837\u70b9，\u5219<\/p>\n

<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

=<\/p>\n

\u2211<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

L<\/p>\n

\u2212<\/p>\n

1<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

]
\n \u2009<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

k<\/p>\n

l<\/p>\n

\/<\/p>\n

N<\/p>\n

H[k]=\\\\sum_{l=0}^{L-1}h[l]\\\\,e^{-j2\\\\pi kl\/N}<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>l<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>L<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span>]<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>k<\/span>l<\/span>\/<\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u91cc\u7684 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u662f FFT \u70b9\u6570，<\/p>\n

L<\/p>\n

L<\/p>\n

<\/span><\/span>L<\/span><\/span><\/span><\/span><\/span> \u662f\u4fe1\u9053\u6709\u6548\u62bd\u5934\u6570\u3002<\/p>\n

\u4e3e\u4e2a\u4f8b\u5b50：\u53d6 <\/p>\n

N<\/p>\n

=<\/p>\n

8<\/p>\n

N=8<\/p>\n

<\/span><\/span>N<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

h<\/p>\n

=<\/p>\n

[<\/p>\n

1<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.5<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.2<\/p>\n

]<\/p>\n

h=[1,\\\\ 0.5,\\\\ 0.2]<\/p>\n

<\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>0.5<\/span>,<\/span>\u00a0<\/span><\/span>0.2<\/span>]<\/span><\/span><\/span><\/span><\/span>（<\/p>\n

L<\/p>\n

=<\/p>\n

3<\/p>\n

L=3<\/p>\n

<\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>）\u3002\u771f\u5b9e\u4fe1\u9053\u9891\u7387\u54cd\u5e94\u4e3a<\/p>\n

<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

=<\/p>\n

1<\/p>\n

+<\/p>\n

0.5<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

k<\/p>\n

\/<\/p>\n

8<\/p>\n

+<\/p>\n

0.2<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

4<\/p>\n

\u03c0<\/p>\n

k<\/p>\n

\/<\/p>\n

8<\/p>\n

H[k]=1+0.5e^{-j2\\\\pi k\/8}+0.2e^{-j4\\\\pi k\/8}<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>0.5<\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>k<\/span>\/8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>0.2<\/span>e<\/span><\/span>\u2212<\/span>j<\/span>4<\/span>\u03c0<\/span>k<\/span>\/8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8ba1\u7b97\u5f97：<\/p>\n\n<\/p>\n

k<\/p>\n

k<\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>01234567<\/tr>\n

\n\n
<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

H[k]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.7000<\/p>\n

+<\/p>\n

j<\/p>\n

0.0000<\/p>\n

1.7000+j0.0000<\/p>\n

<\/span><\/span>1.7000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.3536<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5536<\/p>\n

1.3536-j0.5536<\/p>\n

<\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000-j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.6464<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.1536<\/p>\n

0.6464-j0.1536<\/p>\n

<\/span><\/span>0.6464<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.7000<\/p>\n

+<\/p>\n

j<\/p>\n

0.0000<\/p>\n

0.7000+j0.0000<\/p>\n

<\/span><\/span>0.7000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.6464<\/p>\n

+<\/p>\n

j<\/p>\n

0.1536<\/p>\n

0.6464+j0.1536<\/p>\n

<\/span><\/span>0.6464<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

+<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000+j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.3536<\/p>\n

+<\/p>\n

j<\/p>\n

0.5536<\/p>\n

1.3536+j0.5536<\/p>\n

<\/span><\/span>1.3536<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

1.2 \u68b3\u72b6\u5bfc\u9891<\/h4>\n

\u68b3\u72b6\u5bfc\u9891\u5728\u9891\u57df\u6bcf\u9694 <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5b50\u8f7d\u6ce2\u653e\u7f6e\u4e00\u4e2a\u5df2\u77e5\u7b26\u53f7，\u5bfc\u9891\u5b50\u8f7d\u6ce2\u96c6\u5408\u4e3a<\/p>\n

<\/p>\n

K<\/p>\n

p<\/p>\n

=<\/p>\n

{<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

=<\/p>\n

m<\/p>\n

P<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

m<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

1<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

M<\/p>\n

\u2212<\/p>\n

1<\/p>\n

}<\/p>\n

\\\\mathcal{K}_p=\\\\{k_p(m)=mP,\\\\ m=0,1,\\\\dots,M-1\\\\}<\/p>\n

<\/span><\/span>K<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>P<\/span>,<\/span>\u00a0<\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>M<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>}<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u662f\u5bfc\u9891\u95f4\u9694，<\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u662f\u5bfc\u9891\u4e2a\u6570\u3002\u5f53 <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u65f6，\u5bfc\u9891\u5728\u9891\u57df\u5747\u5300\u5206\u5e03；\u5f53 <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u4e0d\u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u65f6，\u5bfc\u9891\u5206\u5e03\u53d8\u6210\u201c\u51c6\u5747\u5300\u201d，\u9891\u5e26\u8fb9\u7f18\u7684\u95f4\u9694\u4f1a\u4e0e\u4e2d\u95f4\u4e0d\u540c\u3002<\/p>\n

\u8bbe\u5bfc\u9891\u7b26\u53f7\u4e3a\u5df2\u77e5\u7684 <\/p>\n

X<\/p>\n

p<\/p>\n

X_p<\/p>\n

<\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u63a5\u6536\u7aef\u5728\u5bfc\u9891\u4f4d\u7f6e\u505a\u6700\u5c0f\u4e8c\u4e58（LS）\u4f30\u8ba1：<\/p>\n

<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

]<\/p>\n

=<\/p>\n

Y<\/p>\n

[<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

]<\/p>\n

X<\/p>\n

[<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

]<\/p>\n

=<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

]<\/p>\n

X<\/p>\n

p<\/p>\n

X<\/p>\n

p<\/p>\n

=<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

]<\/p>\n

\\\\hat H[k_p(m)] =\\\\frac{Y[k_p(m)]}{X[k_p(m)]} =\\\\frac{H[k_p(m)]X_p}{X_p} =H[k_p(m)]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>X<\/span>[<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Y<\/span>[<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)]<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span>[<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)]<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span>[<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5728\u65e0\u566a\u58f0\u6761\u4ef6\u4e0b，\u5bfc\u9891\u70b9\u4e0a\u7684 LS \u4f30\u8ba1\u662f\u7cbe\u786e\u7684\u3002<\/p>\n

\u4e3e\u4e2a\u4f8b\u5b50：\u628a <\/p>\n

N<\/p>\n

=<\/p>\n

8<\/p>\n

N=8<\/p>\n

<\/span><\/span>N<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span> \u4ee3\u8fdb <\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

=<\/p>\n

m<\/p>\n

P<\/p>\n

k_p(m)=mP<\/p>\n

<\/span><\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>P<\/span><\/span><\/span><\/span><\/span> \u770b\u770b\u3002<\/p>\n

m<\/p>\n

m<\/p>\n

<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4ece 0 \u5f00\u59cb\u9010\u4e2a\u53d6，\u53ea\u8981 <\/p>\n

m<\/p>\n

P<\/p>\n

<<\/p>\n

8<\/p>\n

mP<8<\/p>\n

<\/span><\/span>m<\/span>P<\/span><\/span><<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>，\u8fd9\u4e2a <\/p>\n

m<\/p>\n

P<\/p>\n

mP<\/p>\n

<\/span><\/span>m<\/span>P<\/span><\/span><\/span><\/span><\/span> \u5c31\u8fd8\u5728 8 \u70b9\u7d22\u5f15\u8303\u56f4\u5185，\u662f\u4e00\u4e2a\u6709\u6548\u5bfc\u9891；\u518d\u5f80\u540e\u53d6\u5c31\u8d85\u51fa\u53bb\u4e86\u3002\u56e0\u6b64\u5bfc\u9891\u4e2a\u6570\u662f <\/p>\n

M<\/p>\n

=<\/p>\n

\u2308<\/p>\n

8<\/p>\n

\/<\/p>\n

P<\/p>\n

\u2309<\/p>\n

M=\\\\lceil 8\/P\\\\rceil<\/p>\n

<\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2308<\/span>8\/<\/span>P<\/span>\u2309<\/span><\/span><\/span><\/span><\/span>：<\/p>\n\n<\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span>1234<\/tr>\n

\n\n\n\n
<\/p>\n

K<\/p>\n

p<\/p>\n

\\\\mathcal{K}_p<\/p>\n

<\/span><\/span>K<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

{<\/p>\n

0<\/p>\n

,<\/p>\n

1<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

7<\/p>\n

}<\/p>\n

\\\\{0,1,\\\\dots,7\\\\}<\/p>\n

<\/span><\/span>{<\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>7<\/span>}<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

{<\/p>\n

0<\/p>\n

,<\/p>\n

2<\/p>\n

,<\/p>\n

4<\/p>\n

,<\/p>\n

6<\/p>\n

}<\/p>\n

\\\\{0,2,4,6\\\\}<\/p>\n

<\/span><\/span>{<\/span>0<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>6<\/span>}<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

{<\/p>\n

0<\/p>\n

,<\/p>\n

3<\/p>\n

,<\/p>\n

6<\/p>\n

}<\/p>\n

\\\\{0,3,6\\\\}<\/p>\n

<\/span><\/span>{<\/span>0<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>6<\/span>}<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

{<\/p>\n

0<\/p>\n

,<\/p>\n

4<\/p>\n

}<\/p>\n

\\\\{0,4\\\\}<\/p>\n

<\/span><\/span>{<\/span>0<\/span>,<\/span><\/span>4<\/span>}<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

\u5bfc\u9891\u6570 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span><\/td>\n

8<\/td>\n4<\/td>\n3<\/td>\n2<\/td>\n<\/tr>\n
\u6cbf\u5706\u5468\u7684\u76f8\u90bb\u95f4\u9694<\/td>\n\u5168\u4e3a 1<\/td>\n<\/p>\n

2<\/p>\n

,<\/p>\n

2<\/p>\n

,<\/p>\n

2<\/p>\n

,<\/p>\n

2<\/p>\n

2,2,2,2<\/p>\n

<\/span><\/span>2<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

3<\/p>\n

,<\/p>\n

3<\/p>\n

,<\/p>\n

2<\/p>\n

3,3,2<\/p>\n

<\/span><\/span>3<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

4<\/p>\n

,<\/p>\n

4<\/p>\n

4,4<\/p>\n

<\/span><\/span>4<\/span>,<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/p>\n

P<\/p>\n

=<\/p>\n

1<\/p>\n

P=1<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u662f\u5168\u63d2，8 \u4e2a\u5b50\u8f7d\u6ce2\u5168\u653e\u5bfc\u9891\u3002<\/p>\n

P<\/p>\n

=<\/p>\n

2<\/p>\n

P=2<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

P<\/p>\n

=<\/p>\n

4<\/p>\n

P=4<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span> \u90fd\u6574\u9664 8，\u6700\u540e\u4e00\u4e2a\u5bfc\u9891\u7ed5\u56de <\/p>\n

k<\/p>\n

=<\/p>\n

0<\/p>\n

k=0<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6，\u95f4\u9694\u4ecd\u7136\u662f 2 \u548c 4，\u6574\u5708\u5747\u5300\u3002<\/p>\n

P<\/p>\n

=<\/p>\n

3<\/p>\n

P=3<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u4e0d\u6574\u9664 8：<\/p>\n

m<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

1<\/p>\n

,<\/p>\n

2<\/p>\n

m=0,1,2<\/p>\n

<\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u7ed9\u51fa <\/p>\n

0<\/p>\n

,<\/p>\n

3<\/p>\n

,<\/p>\n

6<\/p>\n

0,3,6<\/p>\n

<\/span><\/span>0<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span>，<\/p>\n

m<\/p>\n

=<\/p>\n

3<\/p>\n

m=3<\/p>\n

<\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f 9，\u8d85\u51fa\u8303\u56f4，\u4e8e\u662f\u5c3e\u90e8 <\/p>\n

6<\/p>\n

\u2192<\/p>\n

0<\/p>\n

6\\\\to0<\/p>\n

<\/span><\/span>6<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u53ea\u5269 <\/p>\n

8<\/p>\n

\u2212<\/p>\n

6<\/p>\n

=<\/p>\n

2<\/p>\n

8-6=2<\/p>\n

<\/span><\/span>8<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>6<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u4e2a\u95f4\u9694，\u6bd4\u4e2d\u95f4\u7684 3 \u77ed，\u8fd9\u5c31\u662f\u524d\u9762\u8bf4\u7684\u201c\u51c6\u5747\u5300\u201d\u3002<\/p>\n

<\/p>\n

0<\/p>\n

\u223c<\/p>\n

7<\/p>\n

0\\\\sim7<\/p>\n

<\/span><\/span>0<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>7<\/span><\/span><\/span><\/span><\/span> \u91cc\u6263\u6389 <\/p>\n

K<\/p>\n

p<\/p>\n

\\\\mathcal{K}_p<\/p>\n

<\/span><\/span>K<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5269\u4e0b\u7684\u5c31\u662f\u975e\u5bfc\u9891\u5b50\u8f7d\u6ce2，\u9700\u8981\u5728\u8fd9\u4e9b\u5b50\u8f7d\u6ce2\u4f4d\u7f6e\u91cd\u5efa\u4fe1\u9053\u4f30\u8ba1\u7ed3\u679c，\u4e0b\u4e00\u8282\u7684\u4e09\u79cd\u91cd\u5efa\u65b9\u5f0f\u8981\u505a\u7684\u5c31\u662f\u5f80\u8fd9\u4e9b\u7a7a\u4f4d\u4e0a\u586b <\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

\\\\hat H[k]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

1.3 \u4ece\u5bfc\u9891\u70b9\u5230\u5168\u9891\u5e26：\u4e09\u79cd\u91cd\u5efa\u65b9\u5f0f<\/h4>\n

\u65b9\u5f0f\u4e00：\u9891\u57df\u7ebf\u6027\u63d2\u503c\u3002 \u5bf9\u76f8\u90bb\u4e24\u4e2a\u5bfc\u9891\u70b9\u4e4b\u95f4\u7684\u5b50\u8f7d\u6ce2，\u6309\u9891\u7387\u8ddd\u79bb\u505a\u7ebf\u6027\u5185\u63d2：<\/p>\n

<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

=<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

0<\/p>\n

]<\/p>\n

+<\/p>\n

k<\/p>\n

\u2212<\/p>\n

k<\/p>\n

0<\/p>\n

k<\/p>\n

1<\/p>\n

\u2212<\/p>\n

k<\/p>\n

0<\/p>\n

(<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

1<\/p>\n

]<\/p>\n

\u2212<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

0<\/p>\n

]<\/p>\n

)<\/p>\n

,<\/p>\n

k<\/p>\n

0<\/p>\n

<<\/p>\n

k<\/p>\n

<<\/p>\n

k<\/p>\n

1<\/p>\n

\\\\hat H[k]=\\\\hat H[k_0]+ \\\\frac{k-k_0}{k_1-k_0} \\\\bigl(\\\\hat H[k_1]-\\\\hat H[k_0]\\\\bigr), \\\\quad k_0<k<k_1<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>k<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span>k<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span>)<\/span><\/span>,<\/span><\/span><\/span>k<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>k<\/span><\/span><<\/span><\/span><\/span><\/span>k<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u9891\u5e26\u4e24\u7aef\u6309\u5faa\u73af\u8fb9\u754c\u5904\u7406\u3002\u7ebf\u6027\u63d2\u503c\u5b9e\u73b0\u7b80\u5355，\u4f46\u771f\u5b9e\u7684 <\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

H[k]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u968f\u9891\u7387\u662f\u5f2f\u7684，\u7528\u76f4\u7ebf\u628a\u76f8\u90bb\u4e24\u4e2a\u5bfc\u9891\u8fde\u8d77\u6765，\u4e2d\u95f4\u7684\u70b9\u5c31\u4f1a\u504f\u79bb\u771f\u503c，\u8fd9\u5c31\u662f\u201c\u66f2\u7387\u8bef\u5dee\u201d，\u5bfc\u9891\u52a0\u5bc6\u53ea\u80fd\u628a\u5b83\u538b\u5c0f\u3002<\/p>\n

\u4e3e\u4e2a\u4f8b\u5b50：\u53d6 <\/p>\n

P<\/p>\n

=<\/p>\n

2<\/p>\n

P=2<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>，\u5bfc\u9891\u96c6\u5408\u4e3a <\/p>\n

{<\/p>\n

0<\/p>\n

,<\/p>\n

2<\/p>\n

,<\/p>\n

4<\/p>\n

,<\/p>\n

6<\/p>\n

}<\/p>\n

\\\\{0,2,4,6\\\\}<\/p>\n

<\/span><\/span>{<\/span>0<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>6<\/span>}<\/span><\/span><\/span><\/span><\/span>\u3002\u6ca1\u6709\u5bfc\u9891\u7684 <\/p>\n

k<\/p>\n

=<\/p>\n

1<\/p>\n

k=1<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5939\u5728 <\/p>\n

k<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

2<\/p>\n

k=0,2<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4，\u6309\u4e0a\u5f0f\u7b97\u5f97 <\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

=<\/p>\n

(<\/p>\n

1.7<\/p>\n

+<\/p>\n

0.8<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

j<\/p>\n

)<\/p>\n

\/<\/p>\n

2<\/p>\n

=<\/p>\n

1.25<\/p>\n

\u2212<\/p>\n

0.25<\/p>\n

j<\/p>\n

\\\\hat H[1]=(1.7+0.8-0.5j)\/2=1.25-0.25j<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>1.7<\/span><\/span>+<\/span><\/span><\/span><\/span>0.8<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.5<\/span>j<\/span>)<\/span>\/2<\/span><\/span>=<\/span><\/span><\/span><\/span>1.25<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.25<\/span>j<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u65b9\u5f0f\u4e8c：DFT \u8865\u96f6\u91cd\u5efa\u3002 \u5f53 <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u65f6，\u5bfc\u9891\u503c <\/p>\n

H<\/p>\n

[<\/p>\n

m<\/p>\n

P<\/p>\n

]<\/p>\n

H[mP]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>m<\/span>P<\/span>]<\/span><\/span><\/span><\/span><\/span> \u6070\u597d\u662f <\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span> \u7684 <\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

N\/P<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span> \u70b9 DFT（<\/p>\n

L<\/p>\n

L<\/p>\n

<\/span><\/span>L<\/span><\/span><\/span><\/span><\/span> \u8d85\u8fc7 <\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

N\/P<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span> \u65f6\u4f1a\u5148\u6298\u53e0，\u89c1 2.1）\u3002\u5bf9\u5bfc\u9891\u5e8f\u5217\u505a <\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

N\/P<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span> \u70b9 IDFT \u5f97\u5230\u65f6\u57df\u4fe1\u9053\u4f30\u8ba1，\u8865\u96f6\u5230 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u70b9\u540e\u518d\u505a <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u70b9 FFT，\u5c31\u5f97\u5230\u5168\u90e8\u5b50\u8f7d\u6ce2\u4e0a\u7684 <\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

\\\\hat H[k]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u4e3e\u4e2a\u4f8b\u5b50：\u6362\u7528 DFT \u8865\u96f6\u65b9\u6cd5\u6c42 <\/p>\n

k<\/p>\n

=<\/p>\n

1<\/p>\n

k=1<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u4e0b\u7684\u9891\u7387\u54cd\u5e94\u3002IDFT \u4e4b\u524d\u7684\u56db\u4e2a\u5bfc\u9891\u503c（\u53d6\u81ea 1.1 \u7684\u8868）\u662f<\/p>\n\n<\/p>\n

k<\/p>\n

p<\/p>\n

k_p<\/p>\n

<\/span><\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0246<\/tr>\n

\n\n
<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

p<\/p>\n

]<\/p>\n

H[k_p]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.7000<\/p>\n

1.7000<\/p>\n

<\/span><\/span>1.7000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000-j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.7000<\/p>\n

0.7000<\/p>\n

<\/span><\/span>0.7000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

+<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000+j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u5bf9\u8fd9\u56db\u4e2a\u503c\u505a 4 \u70b9 IDFT，\u5f97 <\/p>\n

[<\/p>\n

1<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.5<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.2<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0<\/p>\n

]<\/p>\n

[1,\\\\ 0.5,\\\\ 0.2,\\\\ 0]<\/p>\n

<\/span><\/span>[<\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>0.5<\/span>,<\/span>\u00a0<\/span><\/span>0.2<\/span>,<\/span>\u00a0<\/span><\/span>0<\/span>]<\/span><\/span><\/span><\/span><\/span>；\u672b\u5c3e\u8865\u56db\u4e2a\u96f6\u5230 8 \u70b9，\u5f97 <\/p>\n

[<\/p>\n

1<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.5<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.2<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0<\/p>\n

]<\/p>\n

[1,\\\\ 0.5,\\\\ 0.2,\\\\ 0,\\\\ 0,\\\\ 0,\\\\ 0,\\\\ 0]<\/p>\n

<\/span><\/span>[<\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>0.5<\/span>,<\/span>\u00a0<\/span><\/span>0.2<\/span>,<\/span>\u00a0<\/span><\/span>0<\/span>,<\/span>\u00a0<\/span><\/span>0<\/span>,<\/span>\u00a0<\/span><\/span>0<\/span>,<\/span>\u00a0<\/span><\/span>0<\/span>,<\/span>\u00a0<\/span><\/span>0<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002\u518d\u505a 8 \u70b9 FFT：<\/p>\n\n<\/p>\n

k<\/p>\n

k<\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>01234567<\/tr>\n

\n\n
<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

\\\\hat H[k]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.7000<\/p>\n

+<\/p>\n

j<\/p>\n

0.0000<\/p>\n

1.7000+j0.0000<\/p>\n

<\/span><\/span>1.7000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.3536<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5536<\/p>\n

1.3536-j0.5536<\/p>\n

<\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000-j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.6464<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.1536<\/p>\n

0.6464-j0.1536<\/p>\n

<\/span><\/span>0.6464<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.7000<\/p>\n

+<\/p>\n

j<\/p>\n

0.0000<\/p>\n

0.7000+j0.0000<\/p>\n

<\/span><\/span>0.7000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.6464<\/p>\n

+<\/p>\n

j<\/p>\n

0.1536<\/p>\n

0.6464+j0.1536<\/p>\n

<\/span><\/span>0.6464<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

+<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000+j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.3536<\/p>\n

+<\/p>\n

j<\/p>\n

0.5536<\/p>\n

1.3536+j0.5536<\/p>\n

<\/span><\/span>1.3536<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u4e0e 1.1 \u7684\u771f\u5b9e <\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

H[k]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u9010\u70b9\u76f8\u540c，<\/p>\n

k<\/p>\n

=<\/p>\n

1<\/p>\n

k=1<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u4e0a\u5c31\u662f <\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

=<\/p>\n

1.3536<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5536<\/p>\n

\\\\hat H[1]=1.3536-j0.5536<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u65b9\u5f0f\u4e09：\u65f6\u57df LS \u91cd\u5efa\u3002 \u8be5\u65b9\u6cd5\u4e0d\u8981\u6c42 <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span>：\u8bbe\u4fe1\u9053\u62bd\u5934\u6570\u4e0a\u754c\u4e3a <\/p>\n

L<\/p>\n

^<\/p>\n

\\\\hat L<\/p>\n

<\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u6784\u9020\u5bfc\u9891\u4f4d\u7f6e\u7684\u89c2\u6d4b\u77e9\u9635<\/p>\n

<\/p>\n

A<\/p>\n

m<\/p>\n

,<\/p>\n

l<\/p>\n

=<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

l<\/p>\n

\/<\/p>\n

N<\/p>\n

,<\/p>\n

m<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

M<\/p>\n

\u2212<\/p>\n

1<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

L<\/p>\n

^<\/p>\n

\u2212<\/p>\n

1<\/p>\n

A_{m,l}=e^{-j2\\\\pi k_p(m)l\/N}, \\\\quad m=0,\\\\dots,M-1,\\\\ l=0,\\\\dots,\\\\hat L-1<\/p>\n

<\/span><\/span>A<\/span><\/span>m<\/span>,<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)<\/span>l<\/span>\/<\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>M<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u89e3\u6700\u5c0f\u4e8c\u4e58<\/p>\n

<\/p>\n

h<\/p>\n

^<\/p>\n

=<\/p>\n

arg<\/p>\n

\u2061<\/p>\n

min<\/p>\n

\u2061<\/p>\n

h<\/p>\n

\u2225<\/p>\n

A<\/p>\n

h<\/p>\n

\u2212<\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

\u2225<\/p>\n

2<\/p>\n

\\\\hat{h}=\\\\arg\\\\min_{h}\\\\Vert Ah-\\\\hat{H}_p\\\\Vert^2<\/p>\n

<\/span><\/span><\/span>h<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>arg<\/span><\/span><\/span><\/span>h<\/span><\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2225<\/span>A<\/span>h<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2225<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u518d\u7b97<\/p>\n

<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

=<\/p>\n

\u2211<\/p>\n

l<\/p>\n

h<\/p>\n

^<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

k<\/p>\n

l<\/p>\n

\/<\/p>\n

N<\/p>\n

\\\\hat H[k]=\\\\sum_l \\\\hat h[l]e^{-j2\\\\pi kl\/N}<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>l<\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span>]<\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>k<\/span>l<\/span>\/<\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5f53\u5bfc\u9891\u6570 <\/p>\n

M<\/p>\n

\u2265<\/p>\n

L<\/p>\n

^<\/p>\n

M\\\\ge \\\\hat L<\/p>\n

<\/span><\/span>M<\/span><\/span>\u2265<\/span><\/span><\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e14\u5bfc\u9891\u9891\u7387\u70b9\u4e92\u5f02\u65f6，<\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u5217\u6ee1\u79e9，\u65e0\u566a\u58f0\u4e0b\u53ef\u7cbe\u786e\u6062\u590d\u3002<\/p>\n

\u4e3e\u4e2a\u4f8b\u5b50：\u4ecd\u53d6 <\/p>\n

P<\/p>\n

=<\/p>\n

2<\/p>\n

P=2<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u7684\u56db\u4e2a\u5bfc\u9891\u3001\u8bbe <\/p>\n

L<\/p>\n

^<\/p>\n

=<\/p>\n

3<\/p>\n

\\\\hat L=3<\/p>\n

<\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>，\u6309\u4e0a\u9762\u7684\u516c\u5f0f\u628a <\/p>\n

k<\/p>\n

=<\/p>\n

1<\/p>\n

k=1<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5b8c\u6574\u7b97\u4e00\u904d\u3002<\/p>\n

\u7b2c\u4e00\u6b65，\u5217\u51fa\u89c2\u6d4b\u503c\u3002\u5bfc\u9891\u4f4d\u7f6e\u7684 LS \u4f30\u8ba1\u503c\u53d6\u81ea 1.1 \u7684\u8868：<\/p>\n\n<\/p>\n

m<\/p>\n

m<\/p>\n

<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>0123<\/tr>\n

\n\n\n
<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

k_p(m)<\/p>\n

<\/span><\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n

0<\/td>\n2<\/td>\n4<\/td>\n6<\/td>\n<\/tr>\n
<\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

[<\/p>\n

m<\/p>\n

]<\/p>\n

\\\\hat H_p[m]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>m<\/span>]<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1.7000<\/p>\n

1.7000<\/p>\n

<\/span><\/span>1.7000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000-j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.7000<\/p>\n

0.7000<\/p>\n

<\/span><\/span>0.7000<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.8000<\/p>\n

+<\/p>\n

j<\/p>\n

0.5000<\/p>\n

0.8000+j0.5000<\/p>\n

<\/span><\/span>0.8000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u7b2c\u4e8c\u6b65，\u6784\u9020 <\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u3002\u628a <\/p>\n

N<\/p>\n

=<\/p>\n

8<\/p>\n

N=8<\/p>\n

<\/span><\/span>N<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

L<\/p>\n

^<\/p>\n

=<\/p>\n

3<\/p>\n

\\\\hat L=3<\/p>\n

<\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u4ee3\u8fdb <\/p>\n

A<\/p>\n

m<\/p>\n

,<\/p>\n

l<\/p>\n

=<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

k<\/p>\n

p<\/p>\n

(<\/p>\n

m<\/p>\n

)<\/p>\n

l<\/p>\n

\/<\/p>\n

N<\/p>\n

A_{m,l}=e^{-j2\\\\pi k_p(m)l\/N}<\/p>\n

<\/span><\/span>A<\/span><\/span>m<\/span>,<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>m<\/span>)<\/span>l<\/span>\/<\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u56db\u4e2a\u5bfc\u9891\u5bf9\u5e94\u7684\u76f8\u4f4d\u56e0\u5b50\u4f9d\u6b21\u662f <\/p>\n

1<\/p>\n

1<\/p>\n

<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

\u03c0<\/p>\n

l<\/p>\n

\/<\/p>\n

2<\/p>\n

e^{-j\\\\pi l\/2}<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>\u03c0<\/span>l<\/span>\/2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

\u03c0<\/p>\n

l<\/p>\n

e^{-j\\\\pi l}<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>\u03c0<\/span>l<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

3<\/p>\n

\u03c0<\/p>\n

l<\/p>\n

\/<\/p>\n

2<\/p>\n

e^{-j3\\\\pi l\/2}<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>3<\/span>\u03c0<\/span>l<\/span>\/2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>；\u8ba9 <\/p>\n

l<\/p>\n

l<\/p>\n

<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span> \u53d6 <\/p>\n

0<\/p>\n

,<\/p>\n

1<\/p>\n

,<\/p>\n

2<\/p>\n

0,1,2<\/p>\n

<\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>，\u5f97\u5230<\/p>\n

<\/p>\n

A<\/p>\n

=<\/p>\n

[<\/p>\n

1<\/p>\n

1<\/p>\n

1<\/p>\n

1<\/p>\n

\u2212<\/p>\n

j<\/p>\n

\u2212<\/p>\n

1<\/p>\n

1<\/p>\n

\u2212<\/p>\n

1<\/p>\n

1<\/p>\n

1<\/p>\n

j<\/p>\n

\u2212<\/p>\n

1<\/p>\n

]<\/p>\n

,<\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

=<\/p>\n

[<\/p>\n

1.7<\/p>\n

0.8<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

j<\/p>\n

0.7<\/p>\n

0.8<\/p>\n

+<\/p>\n

0.5<\/p>\n

j<\/p>\n

]<\/p>\n

A=\\\\begin{bmatrix}1&1&1\\\\\\\\1&-j&-1\\\\\\\\1&-1&1\\\\\\\\1&j&-1\\\\end{bmatrix},\\\\qquad \\\\hat H_p=\\\\begin{bmatrix}1.7\\\\\\\\0.8-0.5j\\\\\\\\0.7\\\\\\\\0.8+0.5j\\\\end{bmatrix}<\/p>\n

<\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u2212<\/span>j<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span><\/span><\/span>0.8<\/span><\/span>\u2212<\/span><\/span>0.5<\/span>j<\/span><\/span><\/span><\/span>0.7<\/span><\/span><\/span><\/span>0.8<\/span><\/span>+<\/span><\/span>0.5<\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6bd4\u5982\u7b2c\u4e8c\u884c <\/p>\n

k<\/p>\n

p<\/p>\n

=<\/p>\n

2<\/p>\n

k_p=2<\/p>\n

<\/span><\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u7684\u4e24\u4e2a\u76f8\u4f4d\u56e0\u5b50\u662f <\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

\u03c0<\/p>\n

\/<\/p>\n

2<\/p>\n

=<\/p>\n

\u2212<\/p>\n

j<\/p>\n

e^{-j\\\\pi\/2}=-j<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>\u03c0<\/span>\/2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>j<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

\u03c0<\/p>\n

=<\/p>\n

\u2212<\/p>\n

1<\/p>\n

e^{-j\\\\pi}=-1<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>，\u8be5\u884c\u4e58 <\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span> \u5f97 <\/p>\n

1<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

j<\/p>\n

\u2212<\/p>\n

0.2<\/p>\n

=<\/p>\n

0.8<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

j<\/p>\n

1-0.5j-0.2=0.8-0.5j<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.5<\/span>j<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.2<\/span><\/span>=<\/span><\/span><\/span><\/span>0.8<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.5<\/span>j<\/span><\/span><\/span><\/span><\/span>；\u7b2c\u56db\u884c <\/p>\n

k<\/p>\n

p<\/p>\n

=<\/p>\n

6<\/p>\n

k_p=6<\/p>\n

<\/span><\/span>k<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>6<\/span><\/span><\/span><\/span><\/span> \u662f <\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

3<\/p>\n

\u03c0<\/p>\n

\/<\/p>\n

2<\/p>\n

=<\/p>\n

j<\/p>\n

e^{-j3\\\\pi\/2}=j<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>3<\/span>\u03c0<\/span>\/2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>j<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

3<\/p>\n

\u03c0<\/p>\n

=<\/p>\n

\u2212<\/p>\n

1<\/p>\n

e^{-j3\\\\pi}=-1<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>3<\/span>\u03c0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>，\u4e58 <\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span> \u5f97 <\/p>\n

1<\/p>\n

+<\/p>\n

0.5<\/p>\n

j<\/p>\n

\u2212<\/p>\n

0.2<\/p>\n

=<\/p>\n

0.8<\/p>\n

+<\/p>\n

0.5<\/p>\n

j<\/p>\n

1+0.5j-0.2=0.8+0.5j<\/p>\n

<\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>0.5<\/span>j<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.2<\/span><\/span>=<\/span><\/span><\/span><\/span>0.8<\/span><\/span>+<\/span><\/span><\/span><\/span>0.5<\/span>j<\/span><\/span><\/span><\/span><\/span>\u3002\u4e24\u884c\u5206\u522b\u4e0e\u8868\u4e2d\u7684 <\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

\\\\hat H_p[1]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

[<\/p>\n

3<\/p>\n

]<\/p>\n

\\\\hat H_p[3]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>3<\/span>]<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5f97\u4e0a，\u77e9\u9635\u6ca1\u6784\u9020\u9519\u3002<\/p>\n

\u7b2c\u4e09\u6b65，\u89e3\u6700\u5c0f\u4e8c\u4e58\u3002\u8fd9\u91cc <\/p>\n

M<\/p>\n

=<\/p>\n

4<\/p>\n

><\/p>\n

L<\/p>\n

^<\/p>\n

=<\/p>\n

3<\/p>\n

M=4>\\\\hat L=3<\/p>\n

<\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span>><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>，\u65b9\u7a0b\u6bd4\u672a\u77e5\u6570\u591a\u4e00\u4e2a；\u4f46\u65e0\u566a\u58f0\u4e0b <\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

\\\\hat H_p<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6070\u597d\u843d\u5728 <\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u5217\u7a7a\u95f4\u91cc，\u6240\u4ee5\u4ecd\u6709\u7cbe\u786e\u89e3\u3002\u8d70\u6b63\u89c4\u65b9\u7a0b <\/p>\n

A<\/p>\n

H<\/p>\n

A<\/p>\n

h<\/p>\n

^<\/p>\n

=<\/p>\n

A<\/p>\n

H<\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

A^{H}A\\\\hat h=A^{H}\\\\hat H_p<\/p>\n

<\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>h<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>：<\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u4e09\u5217\u4e24\u4e24\u6b63\u4ea4，\u6bcf\u5217\u6a21\u65b9\u90fd\u662f 4，\u6545<\/p>\n

<\/p>\n

A<\/p>\n

H<\/p>\n

A<\/p>\n

=<\/p>\n

4<\/p>\n

I<\/p>\n

,<\/p>\n

A<\/p>\n

H<\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

=<\/p>\n

[<\/p>\n

4<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

2<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.8<\/p>\n

]<\/p>\n

T<\/p>\n

A^{H}A=4I,\\\\qquad A^{H}\\\\hat H_p=[4,\\\\ 2,\\\\ 0.8]^T<\/p>\n

<\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span>I<\/span>,<\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>4<\/span>,<\/span>\u00a0<\/span><\/span>2<\/span>,<\/span>\u00a0<\/span><\/span>0.8<\/span>]<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

h<\/p>\n

^<\/p>\n

=<\/p>\n

(<\/p>\n

A<\/p>\n

H<\/p>\n

A<\/p>\n

)<\/p>\n

\u2212<\/p>\n

1<\/p>\n

A<\/p>\n

H<\/p>\n

H<\/p>\n

^<\/p>\n

p<\/p>\n

=<\/p>\n

1<\/p>\n

4<\/p>\n

[<\/p>\n

4<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

2<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.8<\/p>\n

]<\/p>\n

T<\/p>\n

=<\/p>\n

[<\/p>\n

1<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.5<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.2<\/p>\n

]<\/p>\n

T<\/p>\n

\\\\hat h=(A^{H}A)^{-1}A^{H}\\\\hat H_p=\\\\frac{1}{4}[4,\\\\ 2,\\\\ 0.8]^T=[1,\\\\ 0.5,\\\\ 0.2]^T<\/p>\n

<\/span><\/span><\/span>h<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>4<\/span>,<\/span>\u00a0<\/span><\/span>2<\/span>,<\/span>\u00a0<\/span><\/span>0.8<\/span>]<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>0.5<\/span>,<\/span>\u00a0<\/span><\/span>0.2<\/span>]<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u4e09\u4e2a\u62bd\u5934\u4e0e\u771f\u5b9e <\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span> \u9010\u4e2a\u76f8\u540c\u3002\u8fd9\u91cc\u7684 <\/p>\n

1<\/p>\n

4<\/p>\n

A<\/p>\n

H<\/p>\n

\\\\frac{1}{4}A^{H}<\/p>\n

<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6b63\u662f 4 \u70b9 IDFT \u7684\u524d\u4e09\u884c，\u6240\u4ee5 <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u65f6，\u65b9\u5f0f\u4e09\u89e3\u51fa\u7684\u62bd\u5934\u548c\u65b9\u5f0f\u4e8c 4 \u70b9 IDFT \u5f97\u5230\u7684\u5e8f\u5217\u524d\u4e09\u9879\u662f\u540c\u4e00\u7ec4\u6570\u3002<\/p>\n

\u7b2c\u56db\u6b65，\u4ee3\u56de\u6c42 <\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

\\\\hat H[1]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

k<\/p>\n

=<\/p>\n

1<\/p>\n

k=1<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u65f6 <\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

l<\/p>\n

\/<\/p>\n

8<\/p>\n

e^{-j2\\\\pi l\/8}<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>l<\/span>\/8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728 <\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

1<\/p>\n

,<\/p>\n

2<\/p>\n

l=0,1,2<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u4e0a\u4f9d\u6b21\u662f <\/p>\n

1<\/p>\n

1<\/p>\n

<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

\u03c0<\/p>\n

\/<\/p>\n

4<\/p>\n

=<\/p>\n

0.7071<\/p>\n

\u2212<\/p>\n

0.7071<\/p>\n

j<\/p>\n

e^{-j\\\\pi\/4}=0.7071-0.7071j<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>\u03c0<\/span>\/4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.7071<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.7071<\/span>j<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

\u03c0<\/p>\n

\/<\/p>\n

2<\/p>\n

=<\/p>\n

\u2212<\/p>\n

j<\/p>\n

e^{-j\\\\pi\/2}=-j<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>\u03c0<\/span>\/2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>j<\/span><\/span><\/span><\/span><\/span>，\u4e8e\u662f<\/p>\n

<\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

=<\/p>\n

1<\/p>\n

+<\/p>\n

0.5<\/p>\n

(<\/p>\n

0.7071<\/p>\n

\u2212<\/p>\n

0.7071<\/p>\n

j<\/p>\n

)<\/p>\n

+<\/p>\n

0.2<\/p>\n

(<\/p>\n

\u2212<\/p>\n

j<\/p>\n

)<\/p>\n

=<\/p>\n

1.3536<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5536<\/p>\n

\\\\hat H[1]=1+0.5(0.7071-0.7071j)+0.2(-j)=1.3536-j0.5536<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>0.5<\/span>(<\/span>0.7071<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.7071<\/span>j<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>0.2<\/span>(<\/span>\u2212<\/span>j<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u4e0e 1.1 \u7684\u771f\u5b9e\u503c\u76f8\u540c，\u8bef\u5dee\u4e3a 0\u3002\u5176\u4f59 7 \u4e2a\u5b50\u8f7d\u6ce2\u7167\u6b64\u4ee3\u56de，\u5f97\u5230\u7684 <\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

\\\\hat H[k]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u4e0e\u65b9\u5f0f\u4e8c\u90a3\u5f20\u8868\u9010\u70b9\u76f8\u540c\u3002<\/p>\n

\u771f\u5b9e\u503c <\/p>\n

H<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

=<\/p>\n

1.3536<\/p>\n

\u2212<\/p>\n

j<\/p>\n

0.5536<\/p>\n

H[1]=1.3536-j0.5536<\/p>\n

<\/span><\/span>H<\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span>，\u65b9\u5f0f\u4e8c\u548c\u65b9\u5f0f\u4e09\u7b97\u51fa\u7684 <\/p>\n

H<\/p>\n

^<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

\\\\hat H[1]<\/p>\n

<\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span> \u4e0e\u5b83\u5b8c\u5168\u76f8\u540c，\u65b9\u5f0f\u4e00\u7684\u8bef\u5dee\u6a21\u503c\u662f <\/p>\n

0.3207<\/p>\n

0.3207<\/p>\n

<\/span><\/span>0.3207<\/span><\/span><\/span><\/span><\/span>\u3002\u540c\u4e00\u7ec4\u5bfc\u9891\u3001\u540c\u4e00\u4e2a\u5b50\u8f7d\u6ce2，\u5dee\u522b\u53ea\u6765\u81ea\u91cd\u5efa\u65b9\u5f0f；\u7b2c\u4e09\u7ae0\u4f1a\u7528\u7ebf\u6027\u63d2\u503c\u548c DFT \u8865\u96f6\u628a\u6574\u6761\u9891\u5e26\u4e0a\u7684\u8bef\u5dee\u7edf\u8ba1\u51fa\u6765\u3002<\/p>\n

\n

\u7b2c\u4e8c\u7ae0 \u5bfc\u9891\u95f4\u9694\u4e0e\u4fe1\u9053\u4f30\u8ba1\u7684\u65e0\u6df7\u53e0\u6062\u590d\u6761\u4ef6<\/h3>\n

2.1 \u9891\u57df\u91c7\u6837\u7b49\u4ef7\u4e8e\u65f6\u57df\u5468\u671f\u5ef6\u62d3<\/h4>\n

\u8bbe <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span>，\u8bb0 <\/p>\n

M<\/p>\n

=<\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

M=N\/P<\/p>\n

<\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span>（\u8fd9\u65f6\u5b83\u6b63\u597d\u662f 1.2 \u91cc\u90a3\u4e2a\u5bfc\u9891\u6570），\u53ea\u4fdd\u7559 <\/p>\n

k<\/p>\n

=<\/p>\n

m<\/p>\n

P<\/p>\n

k=mP<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>P<\/span><\/span><\/span><\/span><\/span> \u4e0a\u7684\u9891\u57df\u503c\u3002\u628a <\/p>\n

k<\/p>\n

=<\/p>\n

m<\/p>\n

P<\/p>\n

k=mP<\/p>\n

<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>P<\/span><\/span><\/span><\/span><\/span> \u4ee3\u8fdb 1.1 \u7684\u9891\u7387\u54cd\u5e94\u5f0f：<\/p>\n

<\/p>\n

H<\/p>\n

[<\/p>\n

m<\/p>\n

P<\/p>\n

]<\/p>\n

=<\/p>\n

\u2211<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

L<\/p>\n

\u2212<\/p>\n

1<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

]
\n \u2009<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

P<\/p>\n

l<\/p>\n

\/<\/p>\n

N<\/p>\n

=<\/p>\n

\u2211<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

L<\/p>\n

\u2212<\/p>\n

1<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

]
\n \u2009<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

l<\/p>\n

\/<\/p>\n

M<\/p>\n

H[mP]=\\\\sum_{l=0}^{L-1}h[l]\\\\,e^{-j2\\\\pi mPl\/N}=\\\\sum_{l=0}^{L-1}h[l]\\\\,e^{-j2\\\\pi ml\/M}<\/p>\n

<\/span><\/span>H<\/span>[<\/span>m<\/span>P<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>l<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>L<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span>]<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>P<\/span>l<\/span>\/<\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>l<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>L<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span>]<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>l<\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u628a <\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

N\/P<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span> \u5199\u6210 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u53ea\u662f\u8bb0\u53f7\u3002\u771f\u6b63\u8d77\u4f5c\u7528\u7684\u662f\u6307\u6570\u91cc\u7684 <\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

l<\/p>\n

\/<\/p>\n

M<\/p>\n

e^{-j2\\\\pi ml\/M}<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>l<\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>：\u5b83\u5728 <\/p>\n

l<\/p>\n

l<\/p>\n

<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span> \u4e0a\u52a0 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u7684\u6574\u6570\u500d\u4e0d\u53d8，\u56e0\u4e3a<\/p>\n

<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

(<\/p>\n

l<\/p>\n

+<\/p>\n

M<\/p>\n

)<\/p>\n

\/<\/p>\n

M<\/p>\n

=<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

l<\/p>\n

\/<\/p>\n

M<\/p>\n

\u22c5<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

=<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

l<\/p>\n

\/<\/p>\n

M<\/p>\n

e^{-j2\\\\pi m(l+M)\/M}=e^{-j2\\\\pi ml\/M}\\\\cdot e^{-j2\\\\pi m}=e^{-j2\\\\pi ml\/M}<\/p>\n

<\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>(<\/span>l<\/span>+<\/span>M<\/span>)<\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>l<\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>l<\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u4e5f\u5c31\u662f\u5bf9\u5bfc\u9891\u6765\u8bf4，\u62bd\u5934\u4e0b\u6807 <\/p>\n

l<\/p>\n

l<\/p>\n

<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span> \u53ea\u6709\u9664\u4ee5 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u7684\u4f59\u6570\u6709\u610f\u4e49，<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

l=0<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u4e0e <\/p>\n

l<\/p>\n

=<\/p>\n

M<\/p>\n

l=M<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>M<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

l<\/p>\n

=<\/p>\n

2<\/p>\n

M<\/p>\n

l=2M<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>M<\/span><\/span><\/span><\/span><\/span> \u7ed9\u51fa\u7684\u76f8\u4f4d\u56e0\u5b50\u5b8c\u5168\u4e00\u6837，\u5149\u770b\u5bfc\u9891\u5206\u4e0d\u51fa\u6765\u3002<\/p>\n

\u65e2\u7136\u53ea\u8ba4\u4f59\u6570，\u5c31\u628a\u6bcf\u4e2a\u4e0b\u6807\u5199\u6210 <\/p>\n

l<\/p>\n

=<\/p>\n

l<\/p>\n

\u2032<\/p>\n

+<\/p>\n

q<\/p>\n

M<\/p>\n

l=l'+qM<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span>M<\/span><\/span><\/span><\/span><\/span>（<\/p>\n

0<\/p>\n

\u2264<\/p>\n

l<\/p>\n

\u2032<\/p>\n

<<\/p>\n

M<\/p>\n

0\\\\le l'<M<\/p>\n

<\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>M<\/span><\/span><\/span><\/span><\/span>），\u518d\u628a\u4f59\u6570\u76f8\u540c\u7684\u62bd\u5934\u5e76\u6210\u4e00\u9879：<\/p>\n

<\/p>\n

H<\/p>\n

[<\/p>\n

m<\/p>\n

P<\/p>\n

]<\/p>\n

=<\/p>\n

\u2211<\/p>\n

l<\/p>\n

\u2032<\/p>\n

=<\/p>\n

0<\/p>\n

M<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

\u2211<\/p>\n

q<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

\u2032<\/p>\n

+<\/p>\n

q<\/p>\n

M<\/p>\n

]<\/p>\n

)<\/p>\n

e<\/p>\n

\u2212<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

l<\/p>\n

\u2032<\/p>\n

\/<\/p>\n

M<\/p>\n

H[mP]=\\\\sum_{l'=0}^{M-1}\\\\left(\\\\sum_q h[l'+qM]\\\\right)e^{-j2\\\\pi ml'\/M}<\/p>\n

<\/span><\/span>H<\/span>[<\/span>m<\/span>P<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>M<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span>q<\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span>M<\/span>]<\/span>)<\/span><\/span><\/span><\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u62ec\u53f7\u91cc\u90a3\u4e32 <\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

\u2032<\/p>\n

]<\/p>\n

+<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

\u2032<\/p>\n

+<\/p>\n

M<\/p>\n

]<\/p>\n

+<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

\u2032<\/p>\n

+<\/p>\n

2<\/p>\n

M<\/p>\n

]<\/p>\n

+<\/p>\n

\u22ef<\/p>\n

h[l']+h[l'+M]+h[l'+2M]+\\\\cdots<\/p>\n

<\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>M<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span>M<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f <\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

l<\/p>\n

\u2032<\/p>\n

]<\/p>\n

h_{\\\\text{per}}[l']<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002\u4ee3\u56de\u53bb\u80fd\u770b\u51fa，<\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5bfc\u9891\u503c\u6070\u597d\u662f <\/p>\n

h<\/p>\n

per<\/p>\n

h_{\\\\text{per}}<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u70b9 DFT；\u53cd\u8fc7\u6765，\u5bf9\u5bfc\u9891\u503c\u505a <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u70b9 IDFT，\u62ff\u5230\u7684\u5c31\u662f\u62ec\u53f7\u91cc\u7684\u5e8f\u5217：<\/p>\n

<\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

=<\/p>\n

\u2211<\/p>\n

q<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

+<\/p>\n

q<\/p>\n

M<\/p>\n

]<\/p>\n

=<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

+<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

+<\/p>\n

M<\/p>\n

]<\/p>\n

+<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

+<\/p>\n

2<\/p>\n

M<\/p>\n

]<\/p>\n

+<\/p>\n

\u22ef
\n \u2009<\/p>\n

,<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

M<\/p>\n

\u2212<\/p>\n

1<\/p>\n

h_{\\\\text{per}}[l]=\\\\sum_q h[l+qM]=h[l]+h[l+M]+h[l+2M]+\\\\cdots,\\\\qquad l=0,\\\\dots,M-1<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span>M<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>M<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span>M<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span><\/span>,<\/span><\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>M<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5f0f\u5b50\u5230\u8fd9\u91cc\u5c31\u51fa\u6765\u4e86，\u6765\u8def\u53ea\u6709\u4e24\u6b65：<\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u70b9 DFT \u53ea\u8ba4 <\/p>\n

l<\/p>\n

l<\/p>\n

<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span> \u9664\u4ee5 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u7684\u4f59\u6570，\u4f59\u6570\u76f8\u540c\u7684\u62bd\u5934\u5408\u6210\u4e00\u683c\u3002\u539f\u6765\u7684 <\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span> \u6709 <\/p>\n

L<\/p>\n

L<\/p>\n

<\/span><\/span>L<\/span><\/span><\/span><\/span><\/span> \u4e2a\u62bd\u5934，\u88ab\u644a\u8fdb <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50，\u5404\u6309\u81ea\u5df1\u7684\u4f59\u6570\u5165\u5ea7，\u843d\u8fdb\u540c\u4e00\u683c\u7684\u76f4\u63a5\u76f8\u52a0\u3002<\/p>\n

\u6362\u4e2a\u65b9\u5411\u9a8c\u4e00\u904d\u4e5f\u6210\u7acb：\u628a <\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

l<\/p>\n

\u2032<\/p>\n

]<\/p>\n

=<\/p>\n

1<\/p>\n

M<\/p>\n

\u2211<\/p>\n

m<\/p>\n

=<\/p>\n

0<\/p>\n

M<\/p>\n

\u2212<\/p>\n

1<\/p>\n

H<\/p>\n

[<\/p>\n

m<\/p>\n

P<\/p>\n

]<\/p>\n

e<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

l<\/p>\n

\u2032<\/p>\n

\/<\/p>\n

M<\/p>\n

h_{\\\\text{per}}[l']=\\\\frac{1}{M}\\\\sum_{m=0}^{M-1}H[mP]e^{j2\\\\pi ml'\/M}<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>m<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>M<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span>[<\/span>m<\/span>P<\/span>]<\/span>e<\/span><\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c55\u5f00\u3001\u4ee3\u5165\u4e0a\u9762 <\/p>\n

H<\/p>\n

[<\/p>\n

m<\/p>\n

P<\/p>\n

]<\/p>\n

H[mP]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>m<\/span>P<\/span>]<\/span><\/span><\/span><\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3001\u4ea4\u6362\u6c42\u548c\u6b21\u5e8f，\u5185\u5c42\u5c31\u662f<\/p>\n

<\/p>\n

1<\/p>\n

M<\/p>\n

\u2211<\/p>\n

m<\/p>\n

=<\/p>\n

0<\/p>\n

M<\/p>\n

\u2212<\/p>\n

1<\/p>\n

e<\/p>\n

j<\/p>\n

2<\/p>\n

\u03c0<\/p>\n

m<\/p>\n

(<\/p>\n

l<\/p>\n

\u2032<\/p>\n

\u2212<\/p>\n

l<\/p>\n

)<\/p>\n

\/<\/p>\n

M<\/p>\n

=<\/p>\n

{<\/p>\n

1<\/p>\n

,<\/p>\n

l<\/p>\n

\u2032<\/p>\n

\u2212<\/p>\n

l<\/p>\n

=<\/p>\n

q<\/p>\n

M<\/p>\n

0<\/p>\n

,<\/p>\n

\u5176\u4ed6<\/p>\n

\\\\frac{1}{M}\\\\sum_{m=0}^{M-1}e^{j2\\\\pi m(l'-l)\/M}=\\\\begin{cases}1, & l'-l=qM\\\\\\\\ 0, & \\\\text{\u5176\u4ed6}\\\\end{cases}<\/p>\n

<\/span><\/span><\/span><\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>m<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>M<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>j<\/span>2<\/span>\u03c0<\/span>m<\/span>(<\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>l<\/span>)<\/span>\/<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span><\/span><\/span>1<\/span>,<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>l<\/span><\/span>=<\/span><\/span>q<\/span>M<\/span><\/span><\/span><\/span>\u5176\u4ed6<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5b83\u53ea\u653e\u884c\u4f59\u6570\u76f8\u540c\u7684\u9879，\u5176\u4f59\u5168\u88ab\u62b5\u6d88\u3002\u6bcf\u4e2a\u62bd\u5934 <\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

h[l]<\/p>\n

<\/span><\/span>h<\/span>[<\/span>l<\/span>]<\/span><\/span><\/span><\/span><\/span> \u56e0\u6b64\u53ea\u843d\u8fdb <\/p>\n

l<\/p>\n

\u2032<\/p>\n

l'<\/p>\n

<\/span><\/span>l<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8fd9\u4e00\u683c，\u4e0e\u4e0a\u9762\u7684\u7ed3\u8bba\u4e00\u81f4\u3002<\/p>\n

\u518d\u8bf4\u201c\u5468\u671f\u5ef6\u62d3\u201d\u8fd9\u4e2a\u53eb\u6cd5\u3002\u628a\u4e0a\u5f0f\u91cc\u7684 <\/p>\n

l<\/p>\n

l<\/p>\n

<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span> \u653e\u5f00\u5230\u4efb\u610f\u6574\u6570，\u4ee4 <\/p>\n

h<\/p>\n

p<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

=<\/p>\n

\u2211<\/p>\n

q<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

+<\/p>\n

q<\/p>\n

M<\/p>\n

]<\/p>\n

h_p[l]=\\\\sum_q h[l+qM]<\/p>\n

<\/span><\/span>h<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2211<\/span><\/span>q<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span>M<\/span>]<\/span><\/span><\/span><\/span><\/span>（\u5c31\u662f\u628a <\/p>\n

h<\/p>\n

per<\/p>\n

h_{\\\\text{per}}<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5411\u4e24\u4fa7\u65e0\u9650\u590d\u5236），\u90a3\u4e48 <\/p>\n

h<\/p>\n

p<\/p>\n

[<\/p>\n

l<\/p>\n

+<\/p>\n

M<\/p>\n

]<\/p>\n

=<\/p>\n

h<\/p>\n

p<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

h_p[l+M]=h_p[l]<\/p>\n

<\/span><\/span>h<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>M<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>h<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span>]<\/span><\/span><\/span><\/span><\/span>，<\/p>\n

h<\/p>\n

p<\/p>\n

h_p<\/p>\n

<\/span><\/span>h<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c31\u662f\u4ee5 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5468\u671f\u7684\u5e8f\u5217\u3002<\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u70b9 IDFT \u7ed9\u51fa\u7684\u53ea\u662f\u5b83\u7684\u4e00\u4e2a\u5468\u671f，\u628a\u8fd9\u4e2a\u5468\u671f\u53cd\u590d\u590d\u5236\u94fa\u6ee1\u65f6\u95f4\u8f74\u624d\u662f\u5b8c\u6574\u7684 <\/p>\n

h<\/p>\n

p<\/p>\n

h_p<\/p>\n

<\/span><\/span>h<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>；\u6362\u53e5\u8bdd\u8bf4，<\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span> \u91cc\u6bcf\u4e2a\u62bd\u5934\u90fd\u5728\u76f8\u9694 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u4e2a\u70b9\u7684\u4f4d\u7f6e\u4e0a\u5404\u51fa\u73b0\u4e00\u6b21，\u526f\u672c\u95f4\u8ddd\u5c31\u662f <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

M<\/p>\n

\u2265<\/p>\n

L<\/p>\n

M\\\\ge L<\/p>\n

<\/span><\/span>M<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>L<\/span><\/span><\/span><\/span><\/span> \u65f6\u4e00\u683c\u91cc\u6700\u591a\u843d\u8fdb\u4e00\u4e2a\u62bd\u5934，\u5ef6\u62d3\u7684\u7ed3\u679c\u53ea\u662f\u628a\u62bd\u5934\u632a\u4e86\u4f4d\u7f6e\u3001\u7a7a\u5904\u8865\u96f6；<\/p>\n

M<\/p>\n

<<\/p>\n

L<\/p>\n

M<L<\/p>\n

<\/span><\/span>M<\/span><\/span><<\/span><\/span><\/span><\/span>L<\/span><\/span><\/span><\/span><\/span> \u65f6\u4e00\u683c\u91cc\u6324\u8fdb\u4e24\u4e2a\u4ee5\u4e0a\u62bd\u5934，\u76f8\u52a0\u4e4b\u540e\u518d\u4e5f\u5206\u4e0d\u5f00，\u8fd9\u5c31\u662f\u6df7\u53e0\u3002<\/p>\n

\u4e5f\u5c31\u662f\u8bf4：<\/p>\n

\u9891\u57df\u6bcf\u9694 <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u4e2a\u70b9\u91c7\u6837\u4e00\u6b21，\u7b49\u4ef7\u4e8e\u65f6\u57df\u4ee5 <\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

N\/P<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span> \u4e2a\u91c7\u6837\u70b9\u4e3a\u5468\u671f\u505a\u5468\u671f\u5ef6\u62d3\u3002<\/p>\n

\u4e3e\u4e2a\u4f8b\u5b50：\u4ecd\u53d6 <\/p>\n

N<\/p>\n

=<\/p>\n

8<\/p>\n

N=8<\/p>\n

<\/span><\/span>N<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

h<\/p>\n

=<\/p>\n

[<\/p>\n

1<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.5<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.2<\/p>\n

]<\/p>\n

h=[1,\\\\ 0.5,\\\\ 0.2]<\/p>\n

<\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>0.5<\/span>,<\/span>\u00a0<\/span><\/span>0.2<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002\u5148\u770b <\/p>\n

P<\/p>\n

=<\/p>\n

2<\/p>\n

P=2<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>，\u6b64\u65f6\u5468\u671f <\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

=<\/p>\n

4<\/p>\n

N\/P=4<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span>，\u628a <\/p>\n

H<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

,<\/p>\n

H<\/p>\n

[<\/p>\n

2<\/p>\n

]<\/p>\n

,<\/p>\n

H<\/p>\n

[<\/p>\n

4<\/p>\n

]<\/p>\n

,<\/p>\n

H<\/p>\n

[<\/p>\n

6<\/p>\n

]<\/p>\n

H[0],H[2],H[4],H[6]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>0<\/span>]<\/span>,<\/span><\/span>H<\/span>[<\/span>2<\/span>]<\/span>,<\/span><\/span>H<\/span>[<\/span>4<\/span>]<\/span>,<\/span><\/span>H<\/span>[<\/span>6<\/span>]<\/span><\/span><\/span><\/span><\/span> \u505a 4 \u70b9 IDFT，\u4f8b\u5982<\/p>\n

<\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

=<\/p>\n

1.7<\/p>\n

+<\/p>\n

(<\/p>\n

0.8<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

j<\/p>\n

)<\/p>\n

+<\/p>\n

0.7<\/p>\n

+<\/p>\n

(<\/p>\n

0.8<\/p>\n

+<\/p>\n

0.5<\/p>\n

j<\/p>\n

)<\/p>\n

4<\/p>\n

=<\/p>\n

1<\/p>\n

h_{\\\\text{per}}[0]=\\\\frac{1.7+(0.8-0.5j)+0.7+(0.8+0.5j)}{4}=1<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>0<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span>+<\/span><\/span>(<\/span>0.8<\/span><\/span>\u2212<\/span><\/span>0.5<\/span>j<\/span>)<\/span><\/span>+<\/span><\/span>0.7<\/span><\/span>+<\/span><\/span>(<\/span>0.8<\/span><\/span>+<\/span><\/span>0.5<\/span>j<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

3<\/p>\n

]<\/p>\n

=<\/p>\n

1.7<\/p>\n

+<\/p>\n

(<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

\u2212<\/p>\n

0.8<\/p>\n

j<\/p>\n

)<\/p>\n

\u2212<\/p>\n

0.7<\/p>\n

+<\/p>\n

(<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

+<\/p>\n

0.8<\/p>\n

j<\/p>\n

)<\/p>\n

4<\/p>\n

=<\/p>\n

0<\/p>\n

h_{\\\\text{per}}[3]=\\\\frac{1.7+(-0.5-0.8j)-0.7+(-0.5+0.8j)}{4}=0<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>3<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span>+<\/span><\/span>(<\/span>\u2212<\/span>0.5<\/span><\/span>\u2212<\/span><\/span>0.8<\/span>j<\/span>)<\/span><\/span>\u2212<\/span><\/span>0.7<\/span><\/span>+<\/span><\/span>(<\/span>\u2212<\/span>0.5<\/span><\/span>+<\/span><\/span>0.8<\/span>j<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u56db\u4e2a\u4f4d\u7f6e\u7684\u7ed3\u679c\u662f<\/p>\n\n<\/p>\n

l<\/p>\n

l<\/p>\n

<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span>0123<\/tr>\n

\n\n
<\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

h_{\\\\text{per}}[l]<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span>]<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

1<\/p>\n

1<\/p>\n

<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.5<\/p>\n

0.5<\/p>\n

<\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0.2<\/p>\n

0.2<\/p>\n

<\/span><\/span>0.2<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

0<\/p>\n

0<\/p>\n

<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u8fd9\u5c31\u662f <\/p>\n

h<\/p>\n

=<\/p>\n

[<\/p>\n

1<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.5<\/p>\n

,<\/p>\n

\u00a0<\/p>\n

0.2<\/p>\n

]<\/p>\n

h=[1,\\\\ 0.5,\\\\ 0.2]<\/p>\n

<\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>0.5<\/span>,<\/span>\u00a0<\/span><\/span>0.2<\/span>]<\/span><\/span><\/span><\/span><\/span> \u672b\u5c3e\u8865\u4e00\u4e2a\u96f6\u3002\u56e0\u4e3a <\/p>\n

L<\/p>\n

=<\/p>\n

3<\/p>\n

\u2264<\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

=<\/p>\n

4<\/p>\n

L=3\\\\le N\/P=4<\/p>\n

<\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span>，\u6c42\u548c\u5f0f <\/p>\n

\u2211<\/p>\n

q<\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

+<\/p>\n

q<\/p>\n

\u22c5<\/p>\n

4<\/p>\n

]<\/p>\n

\\\\sum_q h[l+q\\\\cdot4]<\/p>\n

<\/span><\/span>\u2211<\/span><\/span>q<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>4<\/span>]<\/span><\/span><\/span><\/span><\/span> \u91cc\u53ea\u6709 <\/p>\n

q<\/p>\n

=<\/p>\n

0<\/p>\n

q=0<\/p>\n

<\/span><\/span>q<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u90a3\u4e00\u4efd\u975e\u96f6，\u5207\u51fa\u7684\u7b2c\u4e8c\u6bb5\u5168\u662f\u96f6，\u53e0\u4e86\u7b49\u4e8e\u6ca1\u53e0\u3002\u6240\u4ee5\u8fd9\u4e00\u7ec4\u6570\u770b\u7740\u5c31\u662f\u666e\u901a\u8865\u96f6，\u786e\u5b9e\u770b\u4e0d\u51fa\u201c\u5468\u671f\u5ef6\u62d3\u201d\u3002<\/p>\n

\u628a <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u6362\u6210 4，\u5468\u671f\u7f29\u5230 <\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

=<\/p>\n

2<\/p>\n

N\/P=2<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>，\u6bd4 <\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span> \u8fd8\u77ed，\u5ef6\u62d3\u5c31\u85cf\u4e0d\u4f4f\u4e86\u3002\u8fd9\u65f6\u5bfc\u9891\u53ea\u5269 <\/p>\n

H<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

=<\/p>\n

1.7<\/p>\n

H[0]=1.7<\/p>\n

<\/span><\/span>H<\/span>[<\/span>0<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1.7<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

H<\/p>\n

[<\/p>\n

4<\/p>\n

]<\/p>\n

=<\/p>\n

0.7<\/p>\n

H[4]=0.7<\/p>\n

<\/span><\/span>H<\/span>[<\/span>4<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.7<\/span><\/span><\/span><\/span><\/span>，\u505a 2 \u70b9 IDFT：<\/p>\n

<\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

=<\/p>\n

1.7<\/p>\n

+<\/p>\n

0.7<\/p>\n

2<\/p>\n

=<\/p>\n

1.2<\/p>\n

,<\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

=<\/p>\n

1.7<\/p>\n

\u2212<\/p>\n

0.7<\/p>\n

2<\/p>\n

=<\/p>\n

0.5<\/p>\n

h_{\\\\text{per}}[0]=\\\\frac{1.7+0.7}{2}=1.2,\\\\qquad h_{\\\\text{per}}[1]=\\\\frac{1.7-0.7}{2}=0.5<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>0<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span>+<\/span><\/span>0.7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1.2<\/span>,<\/span><\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span>\u2212<\/span><\/span>0.7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5bf9\u7167\u6298\u53e0\u5f0f，<\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

l=0<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u6536\u7684\u662f <\/p>\n

h<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

+<\/p>\n

h<\/p>\n

[<\/p>\n

2<\/p>\n

]<\/p>\n

=<\/p>\n

1<\/p>\n

+<\/p>\n

0.2<\/p>\n

=<\/p>\n

1.2<\/p>\n

h[0]+h[2]=1+0.2=1.2<\/p>\n

<\/span><\/span>h<\/span>[<\/span>0<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>h<\/span>[<\/span>2<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>0.2<\/span><\/span>=<\/span><\/span><\/span><\/span>1.2<\/span><\/span><\/span><\/span><\/span>，<\/p>\n

l<\/p>\n

=<\/p>\n

1<\/p>\n

l=1<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u6536\u7684\u53ea\u6709 <\/p>\n

h<\/p>\n

[<\/p>\n

1<\/p>\n

]<\/p>\n

=<\/p>\n

0.5<\/p>\n

h[1]=0.5<\/p>\n

<\/span><\/span>h<\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span>\u3002\u4e0b\u6807 2 \u5df2\u7ecf\u843d\u5728\u7b2c\u4e8c\u6bb5\u91cc，\u62bd\u5934 <\/p>\n

h<\/p>\n

[<\/p>\n

2<\/p>\n

]<\/p>\n

h[2]<\/p>\n

<\/span><\/span>h<\/span>[<\/span>2<\/span>]<\/span><\/span><\/span><\/span><\/span> \u88ab\u642c\u56de <\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

l=0<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，\u548c <\/p>\n

h<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

h[0]<\/p>\n

<\/span><\/span>h<\/span>[<\/span>0<\/span>]<\/span><\/span><\/span><\/span><\/span> \u52a0\u5728\u4e00\u8d77\u53d8\u6210 <\/p>\n

1.2<\/p>\n

1.2<\/p>\n

<\/span><\/span>1.2<\/span><\/span><\/span><\/span><\/span>，\u8fd9\u4e24\u4e2a\u62bd\u5934\u4ece\u6b64\u518d\u4e5f\u5206\u4e0d\u5f00：\u6362\u6210 <\/p>\n

h<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

=<\/p>\n

0.8<\/p>\n

h[0]=0.8<\/p>\n

<\/span><\/span>h<\/span>[<\/span>0<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.8<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

h<\/p>\n

[<\/p>\n

2<\/p>\n

]<\/p>\n

=<\/p>\n

0.4<\/p>\n

h[2]=0.4<\/p>\n

<\/span><\/span>h<\/span>[<\/span>2<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.4<\/span><\/span><\/span><\/span><\/span>，\u683c 0 \u4ecd\u662f <\/p>\n

0.8<\/p>\n

+<\/p>\n

0.4<\/p>\n

=<\/p>\n

1.2<\/p>\n

0.8+0.4=1.2<\/p>\n

<\/span><\/span>0.8<\/span><\/span>+<\/span><\/span><\/span><\/span>0.4<\/span><\/span>=<\/span><\/span><\/span><\/span>1.2<\/span><\/span><\/span><\/span><\/span>，<\/p>\n

H<\/p>\n

[<\/p>\n

0<\/p>\n

]<\/p>\n

=<\/p>\n

0.8<\/p>\n

+<\/p>\n

0.5<\/p>\n

+<\/p>\n

0.4<\/p>\n

=<\/p>\n

1.7<\/p>\n

H[0]=0.8+0.5+0.4=1.7<\/p>\n

<\/span><\/span>H<\/span>[<\/span>0<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.8<\/span><\/span>+<\/span><\/span><\/span><\/span>0.5<\/span><\/span>+<\/span><\/span><\/span><\/span>0.4<\/span><\/span>=<\/span><\/span><\/span><\/span>1.7<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

H<\/p>\n

[<\/p>\n

4<\/p>\n

]<\/p>\n

=<\/p>\n

0.8<\/p>\n

\u2212<\/p>\n

0.5<\/p>\n

+<\/p>\n

0.4<\/p>\n

=<\/p>\n

0.7<\/p>\n

H[4]=0.8-0.5+0.4=0.7<\/p>\n

<\/span><\/span>H<\/span>[<\/span>4<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.8<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.5<\/span><\/span>+<\/span><\/span><\/span><\/span>0.4<\/span><\/span>=<\/span><\/span><\/span><\/span>0.7<\/span><\/span><\/span><\/span><\/span>，\u4e24\u4e2a\u5bfc\u9891\u503c\u4e00\u4e2a\u90fd\u6ca1\u53d8\u3002\u53ef\u89c1 2 \u70b9 IDFT \u7ed9\u51fa\u7684\u6b63\u662f\u6298\u53e0\u76f8\u52a0\u7684\u7ed3\u679c，\u800c\u4e0d\u662f\u539f\u6765\u7684 <\/p>\n

h<\/p>\n

h<\/p>\n

<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span>\u2014\u2014\u8fd9\u5c31\u662f\u5468\u671f\u5ef6\u62d3\u5e26\u6765\u7684\u6df7\u53e0\u3002<\/p>\n

2.2 \u65e0\u6df7\u53e0\u6761\u4ef6<\/h4>\n

\u771f\u5b9e\u4fe1\u9053\u53ea\u5728 <\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

,<\/p>\n

\u2026<\/p>\n

,<\/p>\n

L<\/p>\n

\u2212<\/p>\n

1<\/p>\n

l=0,\\\\dots,L-1<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>L<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u4e0a\u975e\u96f6\u3002\u8981\u8ba9\u5468\u671f\u5ef6\u62d3\u7684\u5404\u526f\u672c\u4e92\u4e0d\u91cd\u53e0，\u5fc5\u987b<\/p>\n

<\/p>\n

L<\/p>\n

\u2264<\/p>\n

N<\/p>\n

P<\/p>\n

L\\\\le \\\\frac{N}{P}<\/p>\n

<\/span><\/span>L<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7b49\u4ef7\u5730<\/p>\n

<\/p>\n

P<\/p>\n

\u2264<\/p>\n

N<\/p>\n

L<\/p>\n

P\\\\le \\\\frac{N}{L}<\/p>\n

<\/span><\/span>P<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6ee1\u8db3\u8be5\u6761\u4ef6\u65f6，\u4e00\u4e2a\u5468\u671f\u5185\u7684 <\/p>\n

h<\/p>\n

per<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

h_{\\\\text{per}}[l]<\/p>\n

<\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>l<\/span>]<\/span><\/span><\/span><\/span><\/span> \u5c31\u7b49\u4e8e\u539f <\/p>\n

h<\/p>\n

[<\/p>\n

l<\/p>\n

]<\/p>\n

h[l]<\/p>\n

<\/span><\/span>h<\/span>[<\/span>l<\/span>]<\/span><\/span><\/span><\/span><\/span>，\u53ef\u4ee5\u7531\u5bfc\u9891\u503c\u65e0\u5931\u771f\u5730\u6062\u590d\u5168\u90e8 <\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

H[k]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002\u4e0d\u6ee1\u8db3\u65f6，\u4e0d\u540c\u65f6\u5ef6\u62bd\u5934\u4f1a\u6298\u53e0\u5230\u540c\u4e00\u4f4d\u7f6e，\u4ea7\u751f\u6df7\u53e0，\u4efb\u4f55\u63d2\u503c\u90fd\u65e0\u6cd5\u533a\u5206\u3002<\/p>\n

\u5f53 <\/p>\n

L<\/p>\n

=<\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

L=N\/P<\/p>\n

<\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span> \u65f6\u662f\u4e34\u754c\u60c5\u5f62：\u526f\u672c\u9996\u5c3e\u76f8\u63a5\u4f46\u4e0d\u91cd\u53e0，\u7406\u8bba\u4e0a\u4ecd\u53ef\u6062\u590d，\u4f46\u6ca1\u6709\u7559\u4efb\u4f55\u4f59\u91cf\u3002<\/p>\n

\u5bf9\u4e8e <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u4e0d\u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u7684\u60c5\u51b5，\u5747\u5300 DFT \u8865\u96f6\u7684\u5224\u636e\u4e0d\u80fd\u76f4\u63a5\u5957\u7528；\u6b64\u65f6\u8981\u770b\u5bfc\u9891\u6570 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u4e0d\u5c11\u4e8e\u672a\u77e5\u62bd\u5934\u6570，\u4ee5\u53ca\u5bfc\u9891\u9891\u7387\u70b9\u6784\u9020\u7684\u89c2\u6d4b\u77e9\u9635\u662f\u5426\u5217\u6ee1\u79e9\u3002\u82e5 <\/p>\n

M<\/p>\n

<<\/p>\n

L<\/p>\n

M<L<\/p>\n

<\/span><\/span>M<\/span><\/span><<\/span><\/span><\/span><\/span>L<\/span><\/span><\/span><\/span><\/span>，\u5219\u5fc5\u7136\u65e0\u6cd5\u7cbe\u786e\u6062\u590d\u3002<\/p>\n

\u4e3e\u4e2a\u4f8b\u5b50：\u628a <\/p>\n

N<\/p>\n

=<\/p>\n

8<\/p>\n

N=8<\/p>\n

<\/span><\/span>N<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

L<\/p>\n

=<\/p>\n

3<\/p>\n

L=3<\/p>\n

<\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u4ee3\u8fdb <\/p>\n

L<\/p>\n

\u2264<\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

L\\\\le N\/P<\/p>\n

<\/span><\/span>L<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span>：<\/p>\n\n<\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span>124<\/tr>\n

\n\n\n\n
<\/p>\n

N<\/p>\n

\/<\/p>\n

P<\/p>\n

N\/P<\/p>\n

<\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span><\/span><\/span><\/span><\/td>\n

8<\/td>\n4<\/td>\n2<\/td>\n<\/tr>\n
\u4e0e <\/p>\n

L<\/p>\n

=<\/p>\n

3<\/p>\n

L=3<\/p>\n

<\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u6bd4\u8f83<\/td>\n

<\/p>\n

\u2265<\/p>\n

\\\\ge<\/p>\n

<\/span><\/span>\u2265<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

\u2265<\/p>\n

\\\\ge<\/p>\n

<\/span><\/span>\u2265<\/span><\/span><\/span><\/span><\/span><\/td>\n

<\/p>\n

<<\/p>\n

<<\/p>\n

<\/span><\/span><<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

\u526f\u672c\u662f\u5426\u91cd\u53e0<\/td>\n\u5426<\/td>\n\u5426<\/td>\n\u662f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/p>\n

P<\/p>\n

=<\/p>\n

1<\/p>\n

,<\/p>\n

2<\/p>\n

P=1,2<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u90fd\u4e0d\u6df7\u53e0，<\/p>\n

P<\/p>\n

=<\/p>\n

2<\/p>\n

P=2<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u53ea\u7559\u4e00\u4e2a\u62bd\u5934\u7684\u4f59\u91cf；<\/p>\n

P<\/p>\n

=<\/p>\n

4<\/p>\n

P=4<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span> \u65f6\u5468\u671f\u957f\u5ea6\u53ea\u6709 2，\u88c5\u4e0d\u4e0b 3 \u4e2a\u62bd\u5934，<\/p>\n

h<\/p>\n

[<\/p>\n

2<\/p>\n

]<\/p>\n

h[2]<\/p>\n

<\/span><\/span>h<\/span>[<\/span>2<\/span>]<\/span><\/span><\/span><\/span><\/span> \u4f1a\u6298\u5230 <\/p>\n

l<\/p>\n

=<\/p>\n

0<\/p>\n

l=0<\/p>\n

<\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u4e0a（2.1 \u5df2\u7ecf\u7528 2 \u70b9 IDFT \u7b97\u51fa\u6298\u53e0\u540e\u7684 <\/p>\n

1.2<\/p>\n

1.2<\/p>\n

<\/span><\/span>1.2<\/span><\/span><\/span><\/span><\/span>）\u3002<\/p>\n

P<\/p>\n

=<\/p>\n

3<\/p>\n

P=3<\/p>\n

<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u4e0d\u6574\u9664 <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span>，\u8fd9\u5f20\u8868\u5224\u4e0d\u4e86，\u6539\u770b\u5bfc\u9891\u6570：<\/p>\n

M<\/p>\n

=<\/p>\n

3<\/p>\n

M=3<\/p>\n

<\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u4e0d\u5c0f\u4e8e <\/p>\n

L<\/p>\n

=<\/p>\n

3<\/p>\n

L=3<\/p>\n

<\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>，\u4e09\u4e2a\u5bfc\u9891\u9891\u7387\u70b9\u53c8\u4e92\u5f02，\u5269\u4e0b\u7684\u5c31\u662f <\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u5217\u6ee1\u79e9，\u5982\u679c\u6ee1\u79e9\u5219\u53ef\u4ee5\u89e3\u51fa\u4fe1\u9053\u4f30\u8ba1\u7ed3\u679c\u3002<\/p>\n

2.3 \u7ebf\u6027\u63d2\u503c\u4e3a\u4ec0\u4e48\u8fd8\u4f1a\u989d\u5916\u51fa\u9519<\/h4>\n

\u65e0\u6df7\u53e0\u6761\u4ef6\u53ea\u4fdd\u8bc1\u201c\u5b58\u5728\u4e00\u79cd\u7406\u60f3\u91cd\u5efa\u65b9\u5f0f\u53ef\u4ee5\u7cbe\u786e\u6062\u590d\u201d，\u5b83\u5e76\u4e0d\u4fdd\u8bc1\u7ebf\u6027\u63d2\u503c\u7cbe\u786e\u3002\u7ebf\u6027\u63d2\u503c\u53ea\u7528\u4e86\u76f8\u90bb\u4e24\u4e2a\u5bfc\u9891\u70b9，\u76f8\u5f53\u4e8e\u7528\u4e00\u4e2a\u5206\u6bb5\u76f4\u7ebf\u53bb\u903c\u8fd1 <\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

H[k]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u7684\u66f2\u7ebf\u3002<\/p>\n

H<\/p>\n

[<\/p>\n

k<\/p>\n

]<\/p>\n

H[k]<\/p>\n

<\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u662f <\/p>\n

L<\/p>\n

L<\/p>\n

<\/span><\/span>L<\/span><\/span><\/span><\/span><\/span> \u4e2a\u590d\u6307\u6570\u7684\u53e0\u52a0，\u5176\u9891\u7387\u9009\u62e9\u6027\u8d8a\u5f3a，\u66f2\u7ebf\u5f2f\u66f2\u8d8a\u5389\u5bb3，\u7ebf\u6027\u63d2\u503c\u7684\u66f2\u7387\u8bef\u5dee\u5c31\u8d8a\u5927\u3002<\/p>\n

\u56e0\u6b64\u5b9e\u9645\u8bef\u5dee\u7531\u4e24\u90e8\u5206\u7ec4\u6210：<\/p>\n

  • \u6df7\u53e0\u8bef\u5dee：\u5bfc\u9891\u95f4\u9694\u8d85\u8fc7\u65e0\u6df7\u53e0\u8fb9\u754c，\u6216\u5bfc\u9891\u6570\u5c11\u4e8e\u672a\u77e5\u62bd\u5934\u6570\u65f6\u51fa\u73b0；<\/li>\n
  • \u63d2\u503c\u8bef\u5dee：\u5373\u4f7f\u65e0\u6df7\u53e0，\u7ebf\u6027\u63d2\u503c\u4e5f\u59cb\u7ec8\u5b58\u5728\u3002<\/li>\n

    \u76f4\u63a5\u91cf\u4e00\u4e0b <\/p>\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    P=2<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u65f6 <\/p>\n

    H<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    H[k]<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u7684\u5f2f\u66f2\u7a0b\u5ea6\u3002\u7ebf\u6027\u63d2\u503c\u5728 <\/p>\n

    k<\/p>\n

    =<\/p>\n

    1<\/p>\n

    ,<\/p>\n

    3<\/p>\n

    k=1,3<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u5904\u53d6\u7684\u5c31\u662f\u4e24\u7aef\u5bfc\u9891\u7684\u4e2d\u70b9，\u4e0e\u771f\u5b9e\u503c\u76f8\u51cf：<\/p>\n

    <\/p>\n

    H<\/p>\n

    [<\/p>\n

    0<\/p>\n

    ]<\/p>\n

    +<\/p>\n

    H<\/p>\n

    [<\/p>\n

    2<\/p>\n

    ]<\/p>\n

    2<\/p>\n

    \u2212<\/p>\n

    H<\/p>\n

    [<\/p>\n

    1<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    \u2212<\/p>\n

    0.1036<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.3036<\/p>\n

    ,<\/p>\n

    H<\/p>\n

    [<\/p>\n

    2<\/p>\n

    ]<\/p>\n

    +<\/p>\n

    H<\/p>\n

    [<\/p>\n

    4<\/p>\n

    ]<\/p>\n

    2<\/p>\n

    \u2212<\/p>\n

    H<\/p>\n

    [<\/p>\n

    3<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    0.1036<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.0964<\/p>\n

    \\\\frac{H[0]+H[2]}{2}-H[1]=-0.1036+j0.3036,\\\\qquad \\\\frac{H[2]+H[4]}{2}-H[3]=0.1036-j0.0964<\/p>\n

    <\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span>[<\/span>0<\/span>]<\/span><\/span>+<\/span><\/span>H<\/span>[<\/span>2<\/span>]<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>H<\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>0.1036<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.3036<\/span>,<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span>[<\/span>2<\/span>]<\/span><\/span>+<\/span><\/span>H<\/span>[<\/span>4<\/span>]<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>H<\/span>[<\/span>3<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.1036<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.0964<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u6a21\u5206\u522b\u662f <\/p>\n

    0.3207<\/p>\n

    0.3207<\/p>\n

    <\/span><\/span>0.3207<\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

    0.1415<\/p>\n

    0.1415<\/p>\n

    <\/span><\/span>0.1415<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    P=2<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3 <\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    \u2264<\/p>\n

    N<\/p>\n

    \/<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    L=3\\\\le N\/P=4<\/p>\n

    <\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span>，\u672c\u4e0d\u8be5\u6709\u6df7\u53e0，\u53ef\u8fd9\u4e24\u5904\u504f\u5dee\u90fd\u4e0d\u4e3a\u96f6，\u5927\u5c0f\u8fd8\u4e0d\u4e00\u6837\u2014\u2014\u5b83\u4eec\u6b63\u662f\u7ebf\u6027\u63d2\u503c\u4e22\u6389\u7684\u66f2\u7387\u3002\u6362\u7528 DFT \u8865\u96f6，\u8fd9\u4e24\u4e2a\u70b9\u4e0a\u7684 <\/p>\n

    H<\/p>\n

    ^<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    \\\\hat H[k]<\/p>\n

    <\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u4e0e <\/p>\n

    H<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    H[k]<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u9010\u70b9\u76f8\u7b49\u3002\u53ef\u89c1\u8fd9\u90e8\u5206\u8bef\u5dee\u4e0e\u6df7\u53e0\u65e0\u5173，\u52a0\u5bc6\u5bfc\u9891\u53ea\u80fd\u628a\u5b83\u538b\u5c0f，\u53ea\u8981\u8fd8\u6709\u975e\u5bfc\u9891\u70b9\u5c31\u6d88\u4e0d\u5e72\u51c0\u3002<\/p>\n

    \n

    \u7b2c\u4e09\u7ae0 \u8ba1\u7b97\u5b9e\u4f8b<\/h3>\n

    3.1 \u7528\u4e8e\u5bf9\u6bd4\u7684\u4fe1\u9053\u9891\u7387\u54cd\u5e94\u4f8b\u5b50<\/h4>\n

    1.1 \u5df2\u7ecf\u7ed9\u51fa <\/p>\n

    N<\/p>\n

    =<\/p>\n

    8<\/p>\n

    N=8<\/p>\n

    <\/span><\/span>N<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

    h<\/p>\n

    =<\/p>\n

    [<\/p>\n

    1<\/p>\n

    ,<\/p>\n

    \u00a0<\/p>\n

    0.5<\/p>\n

    ,<\/p>\n

    \u00a0<\/p>\n

    0.2<\/p>\n

    ]<\/p>\n

    h=[1,\\\\ 0.5,\\\\ 0.2]<\/p>\n

    <\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>1<\/span>,<\/span>\u00a0<\/span><\/span>0.5<\/span>,<\/span>\u00a0<\/span><\/span>0.2<\/span>]<\/span><\/span><\/span><\/span><\/span>（<\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    L=3<\/p>\n

    <\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>）\u548c 8 \u4e2a <\/p>\n

    H<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    H[k]<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span> \u7684\u5177\u4f53\u6570\u503c，\u8fd9\u91cc\u6cbf\u7528，\u4e0d\u518d\u91cd\u590d\u3002<\/p>\n

    \u7531 Parseval \u5173\u7cfb：<\/p>\n

    <\/p>\n

    \u2211<\/p>\n

    k<\/p>\n

    =<\/p>\n

    0<\/p>\n

    7<\/p>\n

    \u2223<\/p>\n

    H<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    \u2223<\/p>\n

    2<\/p>\n

    =<\/p>\n

    8<\/p>\n

    \u2211<\/p>\n

    l<\/p>\n

    =<\/p>\n

    0<\/p>\n

    2<\/p>\n

    \u2223<\/p>\n

    h<\/p>\n

    [<\/p>\n

    l<\/p>\n

    ]<\/p>\n

    \u2223<\/p>\n

    2<\/p>\n

    =<\/p>\n

    8<\/p>\n

    (<\/p>\n

    1<\/p>\n

    +<\/p>\n

    0.25<\/p>\n

    +<\/p>\n

    0.04<\/p>\n

    )<\/p>\n

    =<\/p>\n

    10.32<\/p>\n

    \\\\sum_{k=0}^{7}\\\\vert H[k]\\\\vert^2=8\\\\sum_{l=0}^{2}\\\\vert h[l]\\\\vert^2=8(1+0.25+0.04)=10.32<\/p>\n

    <\/span><\/span><\/span>k<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>H<\/span>[<\/span>k<\/span>]<\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span>l<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>h<\/span>[<\/span>l<\/span>]<\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>0.25<\/span><\/span>+<\/span><\/span><\/span><\/span>0.04<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>10.32<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u540e\u6587\u5f52\u4e00\u5316 MSE \u5747\u9664\u4ee5 <\/p>\n

    10.32<\/p>\n

    10.32<\/p>\n

    <\/span><\/span>10.32<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    3.2 \u9694 1 \u63d2 1（P=2）：4 \u4e2a\u5bfc\u9891<\/h4>\n

    \u5bfc\u9891\u5728 <\/p>\n

    k<\/p>\n

    =<\/p>\n

    0<\/p>\n

    ,<\/p>\n

    2<\/p>\n

    ,<\/p>\n

    4<\/p>\n

    ,<\/p>\n

    6<\/p>\n

    k=0,2,4,6<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span>，\u975e\u5bfc\u9891\u70b9\u662f <\/p>\n

    k<\/p>\n

    =<\/p>\n

    1<\/p>\n

    ,<\/p>\n

    3<\/p>\n

    ,<\/p>\n

    5<\/p>\n

    ,<\/p>\n

    7<\/p>\n

    k=1,3,5,7<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>5<\/span>,<\/span><\/span>7<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    \u7ebf\u6027\u63d2\u503c： \u975e\u5bfc\u9891\u70b9\u53d6\u76f8\u90bb\u4e24\u4e2a\u5bfc\u9891\u7684\u4e2d\u70b9，\u4f8b\u5982<\/p>\n

    <\/p>\n

    H<\/p>\n

    ^<\/p>\n

    [<\/p>\n

    1<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    H<\/p>\n

    [<\/p>\n

    0<\/p>\n

    ]<\/p>\n

    +<\/p>\n

    H<\/p>\n

    [<\/p>\n

    2<\/p>\n

    ]<\/p>\n

    2<\/p>\n

    =<\/p>\n

    1.7<\/p>\n

    +<\/p>\n

    (<\/p>\n

    0.8<\/p>\n

    \u2212<\/p>\n

    0.5<\/p>\n

    j<\/p>\n

    )<\/p>\n

    2<\/p>\n

    =<\/p>\n

    1.25<\/p>\n

    \u2212<\/p>\n

    0.25<\/p>\n

    j<\/p>\n

    \\\\hat H[1]=\\\\frac{H[0]+H[2]}{2}=\\\\frac{1.7+(0.8-0.5j)}{2}=1.25-0.25j<\/p>\n

    <\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span>[<\/span>0<\/span>]<\/span><\/span>+<\/span><\/span>H<\/span>[<\/span>2<\/span>]<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span>+<\/span><\/span>(<\/span>0.8<\/span><\/span>\u2212<\/span><\/span>0.5<\/span>j<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1.25<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.25<\/span>j<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u771f\u5b9e\u503c <\/p>\n

    H<\/p>\n

    [<\/p>\n

    1<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    1.3536<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.5536<\/p>\n

    H[1]=1.3536-j0.5536<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span>，\u8bef\u5dee\u6a21\u503c\u7ea6 <\/p>\n

    0.3207<\/p>\n

    0.3207<\/p>\n

    <\/span><\/span>0.3207<\/span><\/span><\/span><\/span><\/span>\u3002\u56db\u4e2a\u70b9\u5168\u7b97\u51fa\u6765：<\/p>\n\n<\/p>\n

    k<\/p>\n

    k<\/p>\n

    <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u771f\u5b9e <\/p>\n

    H<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    H[k]<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span>\u7ebf\u6027\u63d2\u503c <\/p>\n

    H<\/p>\n

    ^<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    \\\\hat H[k]<\/p>\n

    <\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u2223<\/p>\n

    e<\/p>\n

    k<\/p>\n

    \u2223<\/p>\n

    \\\\vert e_k \\\\vert<\/p>\n

    <\/span><\/span>\u2223<\/span>e<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span><\/tr>\n

    \n\n\n\n\n
    1<\/td>\n<\/p>\n

    1.3536<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.5536<\/p>\n

    1.3536-j0.5536<\/p>\n

    <\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    1.2500<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.2500<\/p>\n

    1.2500-j0.2500<\/p>\n

    <\/span><\/span>1.2500<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.2500<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.3207<\/td>\n<\/tr>\n
    3<\/td>\n<\/p>\n

    0.6464<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.1536<\/p>\n

    0.6464-j0.1536<\/p>\n

    <\/span><\/span>0.6464<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    0.7500<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.2500<\/p>\n

    0.7500-j0.2500<\/p>\n

    <\/span><\/span>0.7500<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.2500<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.1415<\/td>\n<\/tr>\n
    5<\/td>\n<\/p>\n

    0.6464<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.1536<\/p>\n

    0.6464+j0.1536<\/p>\n

    <\/span><\/span>0.6464<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    0.7500<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.2500<\/p>\n

    0.7500+j0.2500<\/p>\n

    <\/span><\/span>0.7500<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.2500<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.1415<\/td>\n<\/tr>\n
    7<\/td>\n<\/p>\n

    1.3536<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.5536<\/p>\n

    1.3536+j0.5536<\/p>\n

    <\/span><\/span>1.3536<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    1.2500<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.2500<\/p>\n

    1.2500+j0.2500<\/p>\n

    <\/span><\/span>1.2500<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.2500<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.3207<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u8bef\u5dee\u5e73\u65b9\u548c：<\/p>\n

    <\/p>\n

    \u2211<\/p>\n

    \u2223<\/p>\n

    e<\/p>\n

    k<\/p>\n

    \u2223<\/p>\n

    2<\/p>\n

    =<\/p>\n

    0.2458<\/p>\n

    \\\\sum \\\\vert e_k \\\\vert^2=0.2458<\/p>\n

    <\/span><\/span>\u2211<\/span><\/span>\u2223<\/span>e<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.2458<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5f52\u4e00\u5316 MSE：<\/p>\n

    <\/p>\n

    MSE<\/p>\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    ,<\/p>\n

    linear<\/p>\n

    =<\/p>\n

    0.2458<\/p>\n

    10.32<\/p>\n

    =<\/p>\n

    2.38<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    2<\/p>\n

    \\\\text{MSE}_{P=2,\\\\text{linear}} =\\\\frac{0.2458}{10.32} =2.38\\\\times10^{-2}<\/p>\n

    <\/span><\/span>MSE<\/span><\/span><\/span>P<\/span>=<\/span>2<\/span>,<\/span>linear<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>10.32<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.2458<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2.38<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    DFT \u8865\u96f6： \u5bfc\u9891\u503c <\/p>\n

    H<\/p>\n

    [<\/p>\n

    0<\/p>\n

    ]<\/p>\n

    ,<\/p>\n

    H<\/p>\n

    [<\/p>\n

    2<\/p>\n

    ]<\/p>\n

    ,<\/p>\n

    H<\/p>\n

    [<\/p>\n

    4<\/p>\n

    ]<\/p>\n

    ,<\/p>\n

    H<\/p>\n

    [<\/p>\n

    6<\/p>\n

    ]<\/p>\n

    H[0],H[2],H[4],H[6]<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>0<\/span>]<\/span>,<\/span><\/span>H<\/span>[<\/span>2<\/span>]<\/span>,<\/span><\/span>H<\/span>[<\/span>4<\/span>]<\/span>,<\/span><\/span>H<\/span>[<\/span>6<\/span>]<\/span><\/span><\/span><\/span><\/span> \u505a 4 \u70b9 IDFT，\u5f97\u5230 <\/p>\n

    h<\/p>\n

    per<\/p>\n

    [<\/p>\n

    0..3<\/p>\n

    ]<\/p>\n

    h_{\\\\text{per}}[0..3]<\/p>\n

    <\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>0..3<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002\u56e0\u4e3a<\/p>\n

    <\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    \u2264<\/p>\n

    N<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    L=3\\\\le \\\\frac{N}{P}=4<\/p>\n

    <\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5ef6\u62d3\u4e0d\u91cd\u53e0，<\/p>\n

    h<\/p>\n

    per<\/p>\n

    [<\/p>\n

    0..2<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    h<\/p>\n

    [<\/p>\n

    0..2<\/p>\n

    ]<\/p>\n

    h_{\\\\text{per}}[0..2]=h[0..2]<\/p>\n

    <\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>0..2<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>h<\/span>[<\/span>0..2<\/span>]<\/span><\/span><\/span><\/span><\/span>，\u8865\u96f6\u5230 8 \u70b9\u518d\u505a FFT，\u5f97\u5230\u5168\u90e8 <\/p>\n

    H<\/p>\n

    ^<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    \\\\hat H[k]<\/p>\n

    <\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span>，\u4e0e\u771f\u5b9e\u503c\u9010\u70b9\u76f8\u7b49\u3002\u516b\u4e2a\u70b9\u7684\u6570\u503c\u5c31\u662f 1.3 \u65b9\u5f0f\u4e8c\u90a3\u5f20 FFT \u7ed3\u679c\u8868，\u8fd9\u91cc\u4e0d\u518d\u91cd\u5217\u3002<\/p>\n

    <\/p>\n

    MSE<\/p>\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    ,<\/p>\n

    DFT<\/p>\n

    =<\/p>\n

    0<\/p>\n

    \\\\text{MSE}_{P=2,\\\\text{DFT}}=0<\/p>\n

    <\/span><\/span>MSE<\/span><\/span><\/span>P<\/span>=<\/span>2<\/span>,<\/span>DFT<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    3.3 \u9694 3 \u63d2 1（P=4）：2 \u4e2a\u5bfc\u9891<\/h4>\n

    \u5bfc\u9891\u5728 <\/p>\n

    k<\/p>\n

    =<\/p>\n

    0<\/p>\n

    ,<\/p>\n

    4<\/p>\n

    k=0,4<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span>，\u6b64\u65f6<\/p>\n

    <\/p>\n

    M<\/p>\n

    =<\/p>\n

    2<\/p>\n

    <<\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    M=2<L=3<\/p>\n

    <\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><<\/span><\/span><\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u62bd\u5934\u6570\u6bd4\u5bfc\u9891\u6570\u591a，\u6df7\u53e0\u5df2\u7ecf\u65e0\u6cd5\u907f\u514d，\u4e24\u79cd\u65b9\u6cd5\u90fd\u56de\u4e0d\u5230\u96f6\u8bef\u5dee\u3002<\/p>\n

    \u7ebf\u6027\u63d2\u503c： \u5bfc\u9891\u95f4\u8ddd\u662f 4，\u4e24\u6bb5\u90fd\u662f\u8d70 4 \u6b65\u3001\u9ad8\u5ea6\u5dee <\/p>\n

    1.0<\/p>\n

    1.0<\/p>\n

    <\/span><\/span>1.0<\/span><\/span><\/span><\/span><\/span>，\u659c\u7387\u5927\u5c0f\u76f8\u540c\u3001\u7b26\u53f7\u76f8\u53cd：<\/p>\n

    <\/p>\n

    H<\/p>\n

    ^<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    1.7<\/p>\n

    +<\/p>\n

    0.7<\/p>\n

    \u2212<\/p>\n

    1.7<\/p>\n

    4<\/p>\n

    d<\/p>\n

    =<\/p>\n

    1.7<\/p>\n

    \u2212<\/p>\n

    0.25<\/p>\n

    d<\/p>\n

    \\\\hat H[k]=1.7+\\\\frac{0.7-1.7}{4}d =1.7-0.25d<\/p>\n

    <\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1.7<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.7<\/span><\/span>\u2212<\/span><\/span>1.7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>=<\/span><\/span><\/span><\/span>1.7<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.25<\/span>d<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u7b2c\u4e00\u6bb5\u4ee5 <\/p>\n

    k<\/p>\n

    =<\/p>\n

    0<\/p>\n

    k=0<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8d77\u70b9，<\/p>\n

    d<\/p>\n

    d<\/p>\n

    <\/span><\/span>d<\/span><\/span><\/span><\/span><\/span> \u53d6 1 \u5230 3 \u4f9d\u6b21\u662f <\/p>\n

    k<\/p>\n

    =<\/p>\n

    1<\/p>\n

    ,<\/p>\n

    2<\/p>\n

    ,<\/p>\n

    3<\/p>\n

    k=1,2,3<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>；\u7b2c\u4e8c\u6bb5\u4ece <\/p>\n

    k<\/p>\n

    =<\/p>\n

    4<\/p>\n

    k=4<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span> \u7684 <\/p>\n

    0.7<\/p>\n

    0.7<\/p>\n

    <\/span><\/span>0.7<\/span><\/span><\/span><\/span><\/span> \u51fa\u53d1\u5f80\u4e0a\u8d70，<\/p>\n

    d<\/p>\n

    d<\/p>\n

    <\/span><\/span>d<\/span><\/span><\/span><\/span><\/span> \u53d6 1 \u5230 3 \u5bf9\u5e94 <\/p>\n

    k<\/p>\n

    =<\/p>\n

    5<\/p>\n

    ,<\/p>\n

    6<\/p>\n

    ,<\/p>\n

    7<\/p>\n

    k=5,6,7<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>5<\/span>,<\/span><\/span>6<\/span>,<\/span><\/span>7<\/span><\/span><\/span><\/span><\/span>\u3002\u8ba1\u7b97\u5f97：<\/p>\n\n<\/p>\n

    k<\/p>\n

    k<\/p>\n

    <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u771f\u5b9e <\/p>\n

    H<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    H[k]<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span>\u7ebf\u6027\u63d2\u503c <\/p>\n

    H<\/p>\n

    ^<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    \\\\hat H[k]<\/p>\n

    <\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u2223<\/p>\n

    e<\/p>\n

    k<\/p>\n

    \u2223<\/p>\n

    \\\\vert e_k \\\\vert<\/p>\n

    <\/span><\/span>\u2223<\/span>e<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span><\/tr>\n

    \n\n\n\n\n\n\n
    1<\/td>\n<\/p>\n

    1.3536<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.5536<\/p>\n

    1.3536-j0.5536<\/p>\n

    <\/span><\/span>1.3536<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    1.4500<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.0000<\/p>\n

    1.4500+j0.0000<\/p>\n

    <\/span><\/span>1.4500<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.5619<\/td>\n<\/tr>\n
    2<\/td>\n<\/p>\n

    0.8000<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.5000<\/p>\n

    0.8000-j0.5000<\/p>\n

    <\/span><\/span>0.8000<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    1.2000<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.0000<\/p>\n

    1.2000+j0.0000<\/p>\n

    <\/span><\/span>1.2000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.6403<\/td>\n<\/tr>\n
    3<\/td>\n<\/p>\n

    0.6464<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    0.1536<\/p>\n

    0.6464-j0.1536<\/p>\n

    <\/span><\/span>0.6464<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    0.9500<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.0000<\/p>\n

    0.9500+j0.0000<\/p>\n

    <\/span><\/span>0.9500<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.3402<\/td>\n<\/tr>\n
    5<\/td>\n<\/p>\n

    0.6464<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.1536<\/p>\n

    0.6464+j0.1536<\/p>\n

    <\/span><\/span>0.6464<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.1536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    0.9500<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.0000<\/p>\n

    0.9500+j0.0000<\/p>\n

    <\/span><\/span>0.9500<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.3402<\/td>\n<\/tr>\n
    6<\/td>\n<\/p>\n

    0.8000<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.5000<\/p>\n

    0.8000+j0.5000<\/p>\n

    <\/span><\/span>0.8000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    1.2000<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.0000<\/p>\n

    1.2000+j0.0000<\/p>\n

    <\/span><\/span>1.2000<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.6403<\/td>\n<\/tr>\n
    7<\/td>\n<\/p>\n

    1.3536<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.5536<\/p>\n

    1.3536+j0.5536<\/p>\n

    <\/span><\/span>1.3536<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.5536<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    1.4500<\/p>\n

    +<\/p>\n

    j<\/p>\n

    0.0000<\/p>\n

    1.4500+j0.0000<\/p>\n

    <\/span><\/span>1.4500<\/span><\/span>+<\/span><\/span><\/span><\/span>j<\/span>0.0000<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		0.5619<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u8bef\u5dee\u5e73\u65b9\u548c：<\/p>\n

    <\/p>\n

    \u2211<\/p>\n

    \u2223<\/p>\n

    e<\/p>\n

    k<\/p>\n

    \u2223<\/p>\n

    2<\/p>\n

    =<\/p>\n

    1.6829<\/p>\n

    \\\\sum \\\\vert e_k \\\\vert^2=1.6829<\/p>\n

    <\/span><\/span>\u2211<\/span><\/span>\u2223<\/span>e<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1.6829<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5f52\u4e00\u5316 MSE：<\/p>\n

    <\/p>\n

    MSE<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    ,<\/p>\n

    linear<\/p>\n

    =<\/p>\n

    1.6829<\/p>\n

    10.32<\/p>\n

    =<\/p>\n

    1.63<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    1<\/p>\n

    \\\\text{MSE}_{P=4,\\\\text{linear}} =\\\\frac{1.6829}{10.32} =1.63\\\\times10^{-1}<\/p>\n

    <\/span><\/span>MSE<\/span><\/span><\/span>P<\/span>=<\/span>4<\/span>,<\/span>linear<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>10.32<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.6829<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1.63<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    DFT \u8865\u96f6： 2 \u4e2a\u5bfc\u9891\u503c <\/p>\n

    H<\/p>\n

    [<\/p>\n

    0<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    1.7<\/p>\n

    H[0]=1.7<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>0<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1.7<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

    H<\/p>\n

    [<\/p>\n

    4<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    0.7<\/p>\n

    H[4]=0.7<\/p>\n

    <\/span><\/span>H<\/span>[<\/span>4<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.7<\/span><\/span><\/span><\/span><\/span> \u505a 2 \u70b9 IDFT：<\/p>\n

    <\/p>\n

    h<\/p>\n

    per<\/p>\n

    [<\/p>\n

    0<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    1.7<\/p>\n

    +<\/p>\n

    0.7<\/p>\n

    2<\/p>\n

    =<\/p>\n

    1.2<\/p>\n

    ,<\/p>\n

    h<\/p>\n

    per<\/p>\n

    [<\/p>\n

    1<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    1.7<\/p>\n

    \u2212<\/p>\n

    0.7<\/p>\n

    2<\/p>\n

    =<\/p>\n

    0.5<\/p>\n

    h_{\\\\text{per}}[0]=\\\\frac{1.7+0.7}{2}=1.2, \\\\qquad h_{\\\\text{per}}[1]=\\\\frac{1.7-0.7}{2}=0.5<\/p>\n

    <\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>0<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span>+<\/span><\/span>0.7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1.2<\/span>,<\/span><\/span><\/span>h<\/span><\/span>per<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1.7<\/span><\/span>\u2212<\/span><\/span>0.7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u8fd9\u6b63\u662f <\/p>\n

    h<\/p>\n

    [<\/p>\n

    0<\/p>\n

    ]<\/p>\n

    +<\/p>\n

    h<\/p>\n

    [<\/p>\n

    2<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    1<\/p>\n

    +<\/p>\n

    0.2<\/p>\n

    =<\/p>\n

    1.2<\/p>\n

    h[0]+h[2]=1+0.2=1.2<\/p>\n

    <\/span><\/span>h<\/span>[<\/span>0<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>h<\/span>[<\/span>2<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>0.2<\/span><\/span>=<\/span><\/span><\/span><\/span>1.2<\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

    h<\/p>\n

    [<\/p>\n

    1<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    0.5<\/p>\n

    h[1]=0.5<\/p>\n

    <\/span><\/span>h<\/span>[<\/span>1<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span> \u7684\u6df7\u53e0\u7ed3\u679c\u3002\u8865\u96f6\u5230 8 \u70b9\u518d\u505a FFT：<\/p>\n

    <\/p>\n

    H<\/p>\n

    ^<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    1.2<\/p>\n

    +<\/p>\n

    0.5<\/p>\n

    e<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    2<\/p>\n

    \u03c0<\/p>\n

    k<\/p>\n

    \/<\/p>\n

    8<\/p>\n

    \\\\hat H[k]=1.2+0.5e^{-j2\\\\pi k\/8}<\/p>\n

    <\/span><\/span><\/span>H<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>1.2<\/span><\/span>+<\/span><\/span><\/span><\/span>0.5<\/span>e<\/span><\/span>\u2212<\/span>j<\/span>2<\/span>\u03c0<\/span>k<\/span>\/8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u4e0e\u771f\u5b9e\u503c\u7684\u8bef\u5dee\u4e3a<\/p>\n

    <\/p>\n

    e<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    =<\/p>\n

    0.2<\/p>\n

    \u2212<\/p>\n

    0.2<\/p>\n

    e<\/p>\n

    \u2212<\/p>\n

    j<\/p>\n

    \u03c0<\/p>\n

    k<\/p>\n

    \/<\/p>\n

    2<\/p>\n

    e[k]=0.2-0.2e^{-j\\\\pi k\/2}<\/p>\n

    <\/span><\/span>e<\/span>[<\/span>k<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0.2<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.2<\/span>e<\/span><\/span>\u2212<\/span>j<\/span>\u03c0<\/span>k<\/span>\/2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    <\/p>\n

    \u2223<\/p>\n

    e<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    \u2223<\/p>\n

    2<\/p>\n

    =<\/p>\n

    0.08<\/p>\n

    (<\/p>\n

    1<\/p>\n

    \u2212<\/p>\n

    cos<\/p>\n

    \u2061<\/p>\n

    (<\/p>\n

    \u03c0<\/p>\n

    k<\/p>\n

    \/<\/p>\n

    2<\/p>\n

    )<\/p>\n

    )<\/p>\n

    \\\\vert e[k]\\\\vert^2=0.08\\\\bigl(1-\\\\cos(\\\\pi k\/2)\\\\bigr)<\/p>\n

    <\/span><\/span>\u2223<\/span>e<\/span>[<\/span>k<\/span>]<\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.08<\/span>(<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>cos<\/span>(<\/span>\u03c0<\/span>k<\/span>\/2<\/span>)<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5bf9 <\/p>\n

    k<\/p>\n

    =<\/p>\n

    0<\/p>\n

    ,<\/p>\n

    \u2026<\/p>\n

    ,<\/p>\n

    7<\/p>\n

    k=0,\\\\dots,7<\/p>\n

    <\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>7<\/span><\/span><\/span><\/span><\/span> \u6c42\u548c：<\/p>\n

    <\/p>\n

    \u2211<\/p>\n

    \u2223<\/p>\n

    e<\/p>\n

    [<\/p>\n

    k<\/p>\n

    ]<\/p>\n

    \u2223<\/p>\n

    2<\/p>\n

    =<\/p>\n

    0.64<\/p>\n

    \\\\sum \\\\vert e[k]\\\\vert^2=0.64<\/p>\n

    <\/span><\/span>\u2211<\/span><\/span>\u2223<\/span>e<\/span>[<\/span>k<\/span>]<\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.64<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u56e0\u6b64<\/p>\n

    <\/p>\n

    MSE<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    ,<\/p>\n

    DFT<\/p>\n

    =<\/p>\n

    0.64<\/p>\n

    10.32<\/p>\n

    =<\/p>\n

    6.20<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    2<\/p>\n

    \\\\text{MSE}_{P=4,\\\\text{DFT}} =\\\\frac{0.64}{10.32} =6.20\\\\times10^{-2}<\/p>\n

    <\/span><\/span>MSE<\/span><\/span><\/span>P<\/span>=<\/span>4<\/span>,<\/span>DFT<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>10.32<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.64<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>6.20<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u867d\u7136\u6bd4\u7ebf\u6027\u63d2\u503c\u7684 <\/p>\n

    1.63<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    1<\/p>\n

    1.63\\\\times10^{-1}<\/p>\n

    <\/span><\/span>1.63<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u597d，\u4f46\u5df2\u7ecf\u56de\u4e0d\u5230\u96f6\u8bef\u5dee\u3002<\/p>\n

    3.4 \u6c47\u603b\u5bf9\u6bd4<\/h4>\n\n\u5bfc\u9891\u95f4\u9694 <\/p>\n

    P<\/p>\n

    P<\/p>\n

    <\/span><\/span>P<\/span><\/span><\/span><\/span><\/span>\u5bfc\u9891\u4f4d\u7f6e\u5bfc\u9891\u6570 <\/p>\n

    M<\/p>\n

    M<\/p>\n

    <\/span><\/span>M<\/span><\/span><\/span><\/span><\/span>\u7ebf\u6027\u63d2\u503c <\/p>\n

    \u2211<\/p>\n

    \u2223<\/p>\n

    e<\/p>\n

    k<\/p>\n

    \u2223<\/p>\n

    2<\/p>\n

    \\\\sum \\\\vert e_k \\\\vert^2<\/p>\n

    <\/span><\/span>\u2211<\/span><\/span>\u2223<\/span>e<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7ebf\u6027\u63d2\u503c\u5f52\u4e00\u5316 MSEDFT \u8865\u96f6\u5f52\u4e00\u5316 MSE<\/tr>\n

    \n\n\n
    2<\/td>\n<\/p>\n

    0<\/p>\n

    ,<\/p>\n

    2<\/p>\n

    ,<\/p>\n

    4<\/p>\n

    ,<\/p>\n

    6<\/p>\n

    0,2,4,6<\/p>\n

    <\/span><\/span>0<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		4<\/td>\n0.2458<\/td>\n<\/p>\n

    2.38<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    2<\/p>\n

    2.38\\\\times10^{-2}<\/p>\n

    <\/span><\/span>2.38<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    0<\/p>\n

    0<\/p>\n

    <\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

    4<\/td>\n<\/p>\n

    0<\/p>\n

    ,<\/p>\n

    4<\/p>\n

    0,4<\/p>\n

    <\/span><\/span>0<\/span>,<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/td>\n

    		2<\/td>\n1.6829<\/td>\n<\/p>\n

    1.63<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    1<\/p>\n

    1.63\\\\times10^{-1}<\/p>\n

    <\/span><\/span>1.63<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n

    		<\/p>\n

    6.20<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    2<\/p>\n

    6.20\\\\times10^{-2}<\/p>\n

    <\/span><\/span>6.20<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u4e09\u6761\u7ed3\u8bba：<\/p>\n

  • \u5bfc\u9891\u70b9\u672c\u8eab\u6c38\u8fdc\u7cbe\u786e，\u8bef\u5dee\u5168\u90e8\u6765\u81ea\u975e\u5bfc\u9891\u70b9\u91cd\u5efa\u3002<\/li>\n
  • \u7ebf\u6027\u63d2\u503c\u4e24\u79cd\u914d\u7f6e\u90fd\u56de\u4e0d\u5230\u96f6，\u539f\u56e0\u8fd8\u4e0d\u4e00\u6837：\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    P=2<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3\u65e0\u6df7\u53e0\u6761\u4ef6，<\/p>\n

    2.38<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    2<\/p>\n

    2.38\\\\times10^{-2}<\/p>\n

    <\/span><\/span>2.38<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7eaf\u7cb9\u662f\u66f2\u7387\u8bef\u5dee；<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    P=4<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span> \u7684 <\/p>\n

    1.63<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    1<\/p>\n

    1.63\\\\times10^{-1}<\/p>\n

    <\/span><\/span>1.63<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u91cc\u65e2\u6709 <\/p>\n

    M<\/p>\n

    =<\/p>\n

    2<\/p>\n

    <<\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    M=2<L=3<\/p>\n

    <\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><<\/span><\/span><\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u7684\u4fe1\u606f\u7f3a\u53e3，\u4e5f\u6709\u95f4\u8ddd\u4ece 2 \u62c9\u5230 4 \u4e4b\u540e\u66f4\u5389\u5bb3\u7684\u66f2\u7387，\u7ea6\u4e3a <\/p>\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    P=2<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u7684 6.85 \u500d\u3002<\/li>\n

  • DFT \u8865\u96f6\u7684\u8fb9\u754c\u5c31\u662f\u65e0\u6df7\u53e0\u6761\u4ef6：\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    P=2<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u65f6 <\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    \u2264<\/p>\n

    N<\/p>\n

    \/<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    L=3\\\\le N\/P=4<\/p>\n

    <\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span>，\u91cd\u5efa\u7ed3\u679c\u4e0e\u771f\u5b9e\u503c\u9010\u70b9\u76f8\u7b49；<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    P=4<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span> \u65f6 <\/p>\n

    N<\/p>\n

    \/<\/p>\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    <<\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    N\/P=2<L=3<\/p>\n

    <\/span><\/span>N<\/span>\/<\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><<\/span><\/span><\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>，\u62bd\u5934\u5728\u65f6\u57df\u5df2\u7ecf\u6298\u5230\u4e00\u8d77，<\/p>\n

    6.20<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    2<\/p>\n

    6.20\\\\times10^{-2}<\/p>\n

    <\/span><\/span>6.20<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8fd9\u7b14\u8bef\u5dee\u662f\u6df7\u53e0\u7684\u4ee3\u4ef7，\u6362\u54ea\u79cd\u91cd\u5efa\u65b9\u5f0f\u90fd\u6d88\u4e0d\u6389\u3002<\/li>\n

    \u65b9\u5f0f\u4e09（\u65f6\u57df LS）\u6ca1\u6709\u5355\u5217\u8fdb\u6765：<\/p>\n

    P<\/p>\n

    =<\/p>\n

    2<\/p>\n

    P=2<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u65f6 <\/p>\n

    M<\/p>\n

    =<\/p>\n

    4<\/p>\n

    \u2265<\/p>\n

    L<\/p>\n

    ^<\/p>\n

    =<\/p>\n

    3<\/p>\n

    M=4\\\\ge\\\\hat L=3<\/p>\n

    <\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span>\u2265<\/span><\/span><\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>，\u5b83\u89e3\u51fa\u7684\u62bd\u5934\u4e0e DFT \u8865\u96f6\u662f\u540c\u4e00\u7ec4\u6570（1.3 \u5df2\u7ecf\u7b97\u8fc7）；<\/p>\n

    P<\/p>\n

    =<\/p>\n

    4<\/p>\n

    P=4<\/p>\n

    <\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span> \u65f6 <\/p>\n

    M<\/p>\n

    =<\/p>\n

    2<\/p>\n

    <<\/p>\n

    L<\/p>\n

    =<\/p>\n

    3<\/p>\n

    M=2<L=3<\/p>\n

    <\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><<\/span><\/span><\/span><\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>，\u6309 <\/p>\n

    L<\/p>\n

    ^<\/p>\n

    =<\/p>\n

    3<\/p>\n

    \\\\hat L=3<\/p>\n

    <\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u5efa\u7684\u77e9\u9635\u662f 2 \u4e2a\u65b9\u7a0b\u89e3 3 \u4e2a\u672a\u77e5\u6570，\u89e3\u4e0d\u552f\u4e00，\u8bef\u5dee\u4e5f\u6ca1\u6cd5\u548c\u53e6\u5916\u4e24\u79cd\u6446\u5728\u4e00\u8d77\u6bd4\u2014\u2014\u771f\u628a <\/p>\n

    L<\/p>\n

    ^<\/p>\n

    \\\\hat L<\/p>\n

    <\/span><\/span><\/span>L<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u964d\u5230 2，\u5b83\u5c31\u9000\u5316\u6210\u65b9\u5f0f\u4e8c，\u8bef\u5dee\u540c\u6837\u662f <\/p>\n

    6.20<\/p>\n

    \u00d7<\/p>\n

    10<\/p>\n

    \u2212<\/p>\n

    2<\/p>\n

    6.20\\\\times10^{-2}<\/p>\n

    <\/span><\/span>6.20<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    \n

    \u5982\u679c\u672c\u6587\u6070\u597d\u80fd\u5e2e\u5230\u4f60，\u90a3\u662f\u6211\u7684\u8363\u5e78，\u6b22\u8fce\u70b9\u8d5e\u6536\u85cf\u3002<\/p>\n

    \n

    \u76f8\u5173\u9605\u8bfb（\u672c\u4e13\u680f\u7cfb\u5217）<\/h4>\n

    \u672c\u4e13\u680f\u662f\u4e00\u4e2a\u7a0b\u5e8f\u5458\u4ece\u5de5\u7a0b\u5b9e\u8df5\u7684\u89d2\u5ea6\u5bf9\u65e0\u7ebf\u901a\u4fe1\u7269\u7406\u5c42\u539f\u7406\u4ea7\u751f\u7684\u4e00\u4e9b\u601d\u8003：<\/p>\n

  • \u300a\u85cf\u5728\u8eab\u8fb9\u7684\u901a\u4fe1\u539f\u7406\u300b：\u4ece\u751f\u6d3b\u573a\u666f\u8ba4\u8bc6\u53d1\u5c04\u529f\u7387\u3001\u566a\u58f0\u3001\u4fe1\u566a\u6bd4\u548c\u591a\u5f84<\/li>\n
  • \u300a\u7ebf\u6027\u5377\u79ef\u4e0e\u5faa\u73af\u5377\u79ef\u7684\u7231\u6068\u60c5\u4ec7\u300b：\u4e24\u79cd\u5377\u79ef\u600e\u4e48\u7b97，\u4ee5\u53ca\u5b83\u4eec\u7684\u7b49\u4ef7\u6761\u4ef6<\/li>\n
  • \u300a\u6ed1\u52a8\u76f8\u5173\u4e0e\u5faa\u73af\u76f8\u5173\u7684\u7231\u6068\u60c5\u4ec7\u300b：\u7ebf\u6027\u5377\u79ef\u3001\u5faa\u73af\u5377\u79ef\u3001\u6ed1\u52a8\u76f8\u5173\u3001\u5faa\u73af\u76f8\u5173\u4e4b\u95f4\u7684\u533a\u522b\u4e0e\u8054\u7cfb<\/li>\n
  • \u300a\u7ebf\u6027\u5377\u79ef\u4e0e\u6ed1\u52a8\u76f8\u5173\u7684\u5e94\u7528\u2014\u2014\u5339\u914d\u6ee4\u6ce2\u5668\u300b：\u7ebf\u6027\u5377\u79ef\u548c\u6ed1\u52a8\u76f8\u5173\u90fd\u80fd\u5b9e\u73b0\u5339\u914d\u6ee4\u6ce2\u5668<\/li>\n
  • \u300a\u5355\u8f7d\u6ce2 PSK \u8c03\u5236\u4e2d，\u4e3a\u4ec0\u4e48\u5fc5\u987b\u4f7f\u7528\u6210\u578b\u6ee4\u6ce2\u5668\u548c\u5339\u914d\u6ee4\u6ce2\u5668？\u300b：\u6210\u578b\u6ee4\u6ce2\u5668\u548c\u5339\u914d\u6ee4\u6ce2\u5668\u600e\u4e48\u914d\u5408，\u5b9e\u73b0\u9650\u5e26\u3001\u65e0 ISI\u3001\u91c7\u6837\u65f6\u523b\u4fe1\u566a\u6bd4\u6700\u5927<\/li>\n
  • \u300a\u5faa\u73af\u5377\u79ef\u6700\u51fa\u540d\u7684\u5e94\u7528\u2014\u2014OFDM\u7684\u5faa\u73af\u524d\u7f00\u300b：OFDM \u901a\u8fc7\u6dfb\u52a0\u5faa\u73af\u524d\u7f00\u89e3\u51b3\u5747\u8861\u590d\u6742\u5ea6\u548c\u7b26\u53f7\u95f4\u5e72\u6270\u7684\u95ee\u9898<\/li>\n
  • \u300a\u4e00\u4e2a OFDM \u7b26\u53f7\u7ecf\u8fc7\u591a\u5f84\u4fe1\u9053，\u8fd8\u80fd\u4e0d\u80fd\u6062\u590d\u539f\u6837？\u300b：\u8fdb\u4e00\u6b65\u4ecb\u7ecd\u5faa\u73af\u5377\u79ef\u7684\u5e94\u7528：\u7528\u6700\u7b80\u5355\u7684\u4f8b\u5b50\u6765\u7406\u89e3\u591a\u5f84\u4fe1\u9053\u548c\u5747\u8861<\/li>\n
  • \u300a\u4ece5G\u7684PRACH\u4fe1\u9053\u5b66\u4e60\u5faa\u73af\u76f8\u5173\u300b：\u4e3a\u4ec0\u4e48\u57fa\u7ad9\u5bf9\u624b\u673a\u53d1\u5c04\u7684ZC\u5e8f\u5217\u505a\u5faa\u73af\u76f8\u5173<\/li>\n
  • \u300aZC \u5e8f\u5217\u7684\u5faa\u73af\u76f8\u5173，\u4e3a\u4ec0\u4e48\u5c31\u662f\u4fe1\u9053\u4f30\u8ba1\u300b：\u5bf9\u6bd4\u5b66\u4e60ZC\u5e8f\u5217\u7684\u5faa\u73af\u76f8\u5173\u548c\u4fe1\u9053\u4f30\u8ba1\u4e4b\u95f4\u7684\u5173\u7cfb<\/li>\n
  • \u300aOFDM \u68b3\u72b6\u5bfc\u9891\u80fd\u4e0d\u80fd\u65e0\u6df7\u53e0\u6062\u590d\u591a\u5f84\u4fe1\u9053？\u300b:\u6700\u5927\u591a\u5f84\u65f6\u5ef6\u4e0eOFDM\u68b3\u72b6\u5bfc\u9891\u5b50\u8f7d\u6ce2\u95f4\u9694\u7684\u5173\u7cfb<\/li>\n","protected":false},"excerpt":{"rendered":"

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