{"id":58224,"date":"2025-08-16T06:59:46","date_gmt":"2025-08-15T22:59:46","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/58224.html"},"modified":"2025-08-16T06:59:46","modified_gmt":"2025-08-15T22:59:46","slug":"%e6%97%a0%e7%ba%bf%e9%80%9a%e4%bf%a1%e5%9f%ba%e7%a1%80%ef%bc%9a%e8%b0%83%e5%88%b6%e4%b8%8e%e8%a7%a3%e8%b0%83%e6%8a%80%e6%9c%af_%ef%bc%8844%ef%bc%89-7-4%e6%ad%a3%e4%ba%a4%e5%b9%85%e5%ba%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/58224.html","title":{"rendered":"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03)"},"content":{"rendered":"

7.4 \u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03 (QAM\u89e3\u8c03)<\/h4>\n

\u5728\u65e0\u7ebf\u901a\u4fe1\u7cfb\u7edf\u4e2d，\u6b63\u4ea4\u5e45\u5ea6\u8c03\u5236（Quadrature Amplitude Modulation, QAM）\u662f\u4e00\u79cd\u5e38\u7528\u7684\u591a\u8fdb\u5236\u8c03\u5236\u6280\u672f，\u5b83\u901a\u8fc7\u540c\u65f6\u6539\u53d8\u8f7d\u6ce2\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u6765\u4f20\u8f93\u4fe1\u606f\u3002QAM\u89e3\u8c03\u5219\u662f\u5c06\u63a5\u6536\u5230\u7684QAM\u4fe1\u53f7\u6062\u590d\u6210\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u7684\u8fc7\u7a0b\u3002\u672c\u8282\u5c06\u8be6\u7ec6\u63a2\u8ba8QAM\u89e3\u8c03\u7684\u539f\u7406\u3001\u6b65\u9aa4\u4ee5\u53ca\u5177\u4f53\u5b9e\u73b0\u65b9\u6cd5，\u5e76\u901a\u8fc7\u5b9e\u4f8b\u8fdb\u884c\u8bf4\u660e\u3002<\/p>\n

7.4.1 QAM\u89e3\u8c03\u7684\u57fa\u672c\u539f\u7406<\/h5>\n

QAM\u89e3\u8c03\u7684\u57fa\u672c\u539f\u7406\u662f\u901a\u8fc7\u68c0\u6d4b\u63a5\u6536\u5230\u7684\u4fe1\u53f7\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u6765\u6062\u590d\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002QAM\u4fe1\u53f7\u53ef\u4ee5\u770b\u4f5c\u662f\u4e24\u4e2a\u6b63\u4ea4\u7684\u8f7d\u6ce2\u4fe1\u53f7\u7684\u53e0\u52a0，\u6bcf\u4e2a\u8f7d\u6ce2\u4fe1\u53f7\u5206\u522b\u643a\u5e26\u4e86\u4e0d\u540c\u7684\u4fe1\u606f\u3002\u5177\u4f53\u6765\u8bf4，QAM\u4fe1\u53f7\u53ef\u4ee5\u8868\u793a\u4e3a：<\/p>\n

s(t)=I(t)cos\u2061(2\u03c0fct)+Q(t)sin\u2061(2\u03c0fct) s(t) = I(t) \\\\cos(2\\\\pi f_c t) + Q(t) \\\\sin(2\\\\pi f_c t) <\/span><\/span>s<\/span>(<\/span>t<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>I<\/span>(<\/span>t<\/span>)<\/span><\/span>cos<\/span>(<\/span>2<\/span>\u03c0<\/span>f<\/span><\/span>c<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>Q<\/span>(<\/span>t<\/span>)<\/span><\/span>sin<\/span>(<\/span>2<\/span>\u03c0<\/span>f<\/span><\/span>c<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d，I(t)I(t)<\/span><\/span>I<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c Q(t)Q(t)<\/span><\/span>Q<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u5206\u522b\u662f\u540c\u76f8\u5206\u91cf\u548c\u6b63\u4ea4\u5206\u91cf，fcf_c<\/span><\/span>f<\/span><\/span>c<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u8f7d\u6ce2\u9891\u7387\u3002\u89e3\u8c03\u7684\u76ee\u6807\u662f\u901a\u8fc7\u5bf9\u63a5\u6536\u5230\u7684\u4fe1\u53f7 r(t)r(t)<\/span><\/span>r<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u5904\u7406，\u6062\u590d\u51fa I(t)I(t)<\/span><\/span>I<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c Q(t)Q(t)<\/span><\/span>Q<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

QAM\u89e3\u8c03\u901a\u5e38\u5305\u62ec\u4ee5\u4e0b\u51e0\u4e2a\u6b65\u9aa4：<\/p>\n

  • \u4e0b\u53d8\u9891：\u5c06\u63a5\u6536\u5230\u7684\u9ad8\u9891\u4fe1\u53f7\u8f6c\u6362\u4e3a\u4f4e\u9891\u4fe1\u53f7\u3002<\/li>\n
  • \u4f4e\u901a\u6ee4\u6ce2：\u6ee4\u9664\u9ad8\u9891\u566a\u58f0，\u4fdd\u7559\u6709\u7528\u4fe1\u53f7\u3002<\/li>\n
  • \u91c7\u6837：\u5728\u5408\u9002\u7684\u65f6\u95f4\u70b9\u5bf9\u4fe1\u53f7\u8fdb\u884c\u91c7\u6837，\u5f97\u5230\u79bb\u6563\u7684I\u548cQ\u5206\u91cf\u3002<\/li>\n
  • \u7b26\u53f7\u68c0\u6d4b：\u6839\u636e\u91c7\u6837\u503c\u5224\u65ad\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002<\/li>\n
    7.4.2 \u4e0b\u53d8\u9891<\/h5>\n

    \u4e0b\u53d8\u9891\u662fQAM\u89e3\u8c03\u7684\u7b2c\u4e00\u6b65，\u5176\u76ee\u7684\u662f\u5c06\u63a5\u6536\u5230\u7684\u9ad8\u9891\u4fe1\u53f7 r(t)r(t)<\/span><\/span>r<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u8f6c\u6362\u4e3a\u4f4e\u9891\u4fe1\u53f7\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4e58\u4ee5\u672c\u5730\u632f\u8361\u5668\u7684\u540c\u76f8\u548c\u6b63\u4ea4\u8f7d\u6ce2\u4fe1\u53f7\u6765\u5b9e\u73b0\u3002\u5047\u8bbe\u63a5\u6536\u5230\u7684\u4fe1\u53f7\u4e3a：<\/p>\n

    r(t)=s(t)+n(t) r(t) = s(t) + n(t) <\/span><\/span>r<\/span>(<\/span>t<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>s<\/span>(<\/span>t<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>n<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5176\u4e2d，n(t)n(t)<\/span><\/span>n<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u662f\u52a0\u6027\u9ad8\u65af\u767d\u566a\u58f0（Additive Gaussian White Noise, AWGN）\u3002\u4e0b\u53d8\u9891\u540e\u7684\u4fe1\u53f7\u53ef\u4ee5\u8868\u793a\u4e3a：<\/p>\n

    rI(t)=r(t)cos\u2061(2\u03c0fct) r_I(t) = r(t) \\\\cos(2\\\\pi f_c t) <\/span><\/span>r<\/span><\/span>I<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>t<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span>(<\/span>t<\/span>)<\/span><\/span>cos<\/span>(<\/span>2<\/span>\u03c0<\/span>f<\/span><\/span>c<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>
    \nrQ(t)=r(t)sin\u2061(2\u03c0fct) r_Q(t) = r(t) \\\\sin(2\\\\pi f_c t) <\/span><\/span>r<\/span><\/span>Q<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>t<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span>(<\/span>t<\/span>)<\/span><\/span>sin<\/span>(<\/span>2<\/span>\u03c0<\/span>f<\/span><\/span>c<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u901a\u8fc7\u8fd9\u4e24\u4e2a\u4e58\u6cd5\u64cd\u4f5c，\u53ef\u4ee5\u5c06\u9ad8\u9891\u4fe1\u53f7 s(t)s(t)<\/span><\/span>s<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e0b\u53d8\u9891\u5230\u57fa\u5e26\u4fe1\u53f7 I(t)I(t)<\/span><\/span>I<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c Q(t)Q(t)<\/span><\/span>Q<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    7.4.3 \u4f4e\u901a\u6ee4\u6ce2<\/h5>\n

    \u4f4e\u901a\u6ee4\u6ce2\u5668\u7528\u4e8e\u6ee4\u9664\u4e0b\u53d8\u9891\u540e\u7684\u9ad8\u9891\u566a\u58f0，\u4fdd\u7559\u57fa\u5e26\u4fe1\u53f7\u3002\u7406\u60f3\u60c5\u51b5\u4e0b，\u4f4e\u901a\u6ee4\u6ce2\u5668\u7684\u622a\u6b62\u9891\u7387\u5e94\u8bbe\u7f6e\u4e3a\u57fa\u5e26\u4fe1\u53f7\u7684\u5e26\u5bbd\u3002\u5e38\u7528\u7684\u4f4e\u901a\u6ee4\u6ce2\u5668\u7c7b\u578b\u5305\u62ec\u5df4\u7279\u6c83\u65af\u6ee4\u6ce2\u5668\u3001\u5207\u6bd4\u96ea\u592b\u6ee4\u6ce2\u5668\u548c\u9ad8\u65af\u6ee4\u6ce2\u5668\u7b49\u3002<\/p>\n

    7.4.4 \u91c7\u6837<\/h5>\n

    \u91c7\u6837\u662f\u5728\u4e0b\u53d8\u9891\u548c\u4f4e\u901a\u6ee4\u6ce2\u540e，\u901a\u8fc7\u5bf9\u57fa\u5e26\u4fe1\u53f7 I(t)I(t)<\/span><\/span>I<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c Q(t)Q(t)<\/span><\/span>Q<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u91c7\u6837，\u5f97\u5230\u79bb\u6563\u7684I\u548cQ\u5206\u91cf\u3002\u91c7\u6837\u9891\u7387\u901a\u5e38\u5e94\u5927\u4e8e\u6216\u7b49\u4e8e\u57fa\u5e26\u4fe1\u53f7\u7684\u5948\u594e\u65af\u7279\u9891\u7387\u3002\u5e38\u89c1\u7684\u91c7\u6837\u65b9\u6cd5\u5305\u62ec\u8fc7\u91c7\u6837\u548c\u6b20\u91c7\u6837\u3002<\/p>\n

    7.4.5 \u7b26\u53f7\u68c0\u6d4b<\/h5>\n

    \u7b26\u53f7\u68c0\u6d4b\u662f\u6839\u636e\u91c7\u6837\u5f97\u5230\u7684I\u548cQ\u5206\u91cf，\u5224\u65ad\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002\u8fd9\u901a\u5e38\u901a\u8fc7\u5c06\u91c7\u6837\u503c\u4e0e\u9884\u5b9a\u4e49\u7684\u661f\u5ea7\u56fe\u8fdb\u884c\u6bd4\u8f83\u6765\u5b9e\u73b0\u3002\u661f\u5ea7\u56fe\u662fQAM\u8c03\u5236\u5668\u548c\u89e3\u8c03\u5668\u4e4b\u95f4\u7684\u4e00\u79cd\u7ea6\u5b9a，\u8868\u793a\u4e86\u6bcf\u4e2a\u7b26\u53f7\u5bf9\u5e94\u7684I\u548cQ\u5206\u91cf\u7684\u7ec4\u5408\u3002<\/p>\n

    7.4.6 QAM\u89e3\u8c03\u7684\u5b9e\u73b0<\/h4>\n

    7.4.6.1 \u4eff\u771f\u73af\u5883\u8bbe\u7f6e<\/h5>\n

    \u5728\u672c\u8282\u4e2d，\u6211\u4eec\u5c06\u4f7f\u7528Python\u548cNumPy\u5e93\u6765\u5b9e\u73b0QAM\u89e3\u8c03\u7684\u4eff\u771f\u3002\u9996\u5148，\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86Python\u548cNumPy\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5，\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5：<\/p>\n

    pip install<\/span> numpy<\/p>\n

    \u63a5\u4e0b\u6765，\u5bfc\u5165\u5fc5\u8981\u7684\u5e93：<\/p>\n

    import<\/span> numpy as<\/span> np
    \nimport<\/span> matplotlib.<\/span>pyplot as<\/span> plt
    \nfrom<\/span> scipy.<\/span>signal import<\/span> butter,<\/span> lfilter<\/p>\n

    7.4.6.2 \u751f\u6210QAM\u4fe1\u53f7<\/h5>\n

    \u4e3a\u4e86\u8fdb\u884cQAM\u89e3\u8c03\u7684\u4eff\u771f，\u6211\u4eec\u9996\u5148\u9700\u8981\u751f\u6210\u4e00\u4e2aQAM\u4fe1\u53f7\u3002\u5047\u8bbe\u6211\u4eec\u4f7f\u752816-QAM\u8c03\u5236，\u751f\u6210\u7684\u4fe1\u53f7\u5982\u4e0b：<\/p>\n

    # \u751f\u621016-QAM\u661f\u5ea7\u56fe<\/span>
    \ndef<\/span> generate_16qam_constellation<\/span>(<\/span>)<\/span>:<\/span>
    \n symbols =<\/span> np.<\/span>array(<\/span>[<\/span>1<\/span>,<\/span> 3<\/span>,<\/span> –<\/span>3<\/span>,<\/span> –<\/span>1<\/span>]<\/span>)<\/span>
    \n constellation =<\/span> [<\/span>]<\/span>
    \n for<\/span> i in<\/span> symbols:<\/span>
    \n for<\/span> q in<\/span> symbols:<\/span>
    \n constellation.<\/span>append(<\/span>(<\/span>i,<\/span> q)<\/span>)<\/span>
    \n return<\/span> np.<\/span>array(<\/span>constellation)<\/span><\/p>\n

    # \u751f\u621016-QAM\u4fe1\u53f7<\/span>
    \ndef<\/span> generate_16qam_signal<\/span>(<\/span>bits,<\/span> constellation,<\/span> carrier_freq,<\/span> sample_rate)<\/span>:<\/span>
    \n symbols =<\/span> constellation[<\/span>bits]<\/span>
    \n t =<\/span> np.<\/span>arange(<\/span>0<\/span>,<\/span> len<\/span>(<\/span>bits)<\/span> \/<\/span> sample_rate,<\/span> 1<\/span> \/<\/span> sample_rate)<\/span>
    \n I =<\/span> symbols[<\/span>:<\/span>,<\/span> 0<\/span>]<\/span>
    \n Q =<\/span> symbols[<\/span>:<\/span>,<\/span> 1<\/span>]<\/span>
    \n s_I =<\/span> I *<\/span> np.<\/span>cos(<\/span>2<\/span> *<\/span> np.<\/span>pi *<\/span> carrier_freq *<\/span> t)<\/span>
    \n s_Q =<\/span> Q *<\/span> np.<\/span>sin(<\/span>2<\/span> *<\/span> np.<\/span>pi *<\/span> carrier_freq *<\/span> t)<\/span>
    \n s =<\/span> s_I +<\/span> s_Q
    \n return<\/span> s,<\/span> t,<\/span> I,<\/span> Q<\/p>\n

    # \u751f\u6210\u968f\u673a\u6bd4\u7279<\/span>
    \nbits =<\/span> np.<\/span>random.<\/span>randint(<\/span>0<\/span>,<\/span> 16<\/span>,<\/span> 100<\/span>)<\/span>
    \nconstellation =<\/span> generate_16qam_constellation(<\/span>)<\/span>
    \ncarrier_freq =<\/span> 1000<\/span> # \u8f7d\u6ce2\u9891\u7387<\/span>
    \nsample_rate =<\/span> 10000<\/span> # \u91c7\u6837\u7387<\/span><\/p>\n

    # \u751f\u6210QAM\u4fe1\u53f7<\/span>
    \nqam_signal,<\/span> t,<\/span> I,<\/span> Q =<\/span> generate_16qam_signal(<\/span>bits,<\/span> constellation,<\/span> carrier_freq,<\/span> sample_rate)<\/span><\/p>\n

    # \u7ed8\u5236QAM\u4fe1\u53f7<\/span>
    \nplt.<\/span>figure(<\/span>figsize=<\/span>(<\/span>12<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
    \nplt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>t,<\/span> qam_signal)<\/span>
    \nplt.<\/span>title(<\/span>"16-QAM Signal"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Time (s)"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Amplitude"<\/span>)<\/span><\/p>\n

    plt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 2<\/span>)<\/span>
    \nplt.<\/span>scatter(<\/span>I,<\/span> Q,<\/span> marker=<\/span>'o'<\/span>,<\/span> color=<\/span>'b'<\/span>)<\/span>
    \nplt.<\/span>title(<\/span>"16-QAM Constellation"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"I"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Q"<\/span>)<\/span>
    \nplt.<\/span>grid(<\/span>True<\/span>)<\/span>
    \nplt.<\/span>show(<\/span>)<\/span><\/p>\n

    7.4.6.3 \u4e0b\u53d8\u9891<\/h5>\n

    \u63a5\u4e0b\u6765，\u6211\u4eec\u5c06\u5bf9\u63a5\u6536\u5230\u7684QAM\u4fe1\u53f7\u8fdb\u884c\u4e0b\u53d8\u9891\u5904\u7406\u3002\u5047\u8bbe\u63a5\u6536\u5230\u7684\u4fe1\u53f7\u5df2\u7ecf\u5305\u542b\u4e86\u4e00\u4e9b\u566a\u58f0：<\/p>\n

    # \u52a0\u5165AWGN\u566a\u58f0<\/span>
    \ndef<\/span> add_awgn_noise<\/span>(<\/span>signal,<\/span> snr)<\/span>:<\/span>
    \n signal_power =<\/span> np.<\/span>mean(<\/span>np.<\/span>abs<\/span>(<\/span>signal)<\/span> **<\/span> 2<\/span>)<\/span>
    \n noise_power =<\/span> signal_power \/<\/span> 10<\/span> **<\/span> (<\/span>snr \/<\/span> 10<\/span>)<\/span>
    \n noise =<\/span> np.<\/span>sqrt(<\/span>noise_power)<\/span> *<\/span> np.<\/span>random.<\/span>normal(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> len<\/span>(<\/span>signal)<\/span>)<\/span>
    \n return<\/span> signal +<\/span> noise<\/p>\n

    # \u751f\u6210\u5e26\u566a\u58f0\u7684QAM\u4fe1\u53f7<\/span>
    \nsnr =<\/span> 20<\/span> # \u4fe1\u566a\u6bd4<\/span>
    \nnoisy_signal =<\/span> add_awgn_noise(<\/span>qam_signal,<\/span> snr)<\/span><\/p>\n

    # \u4e0b\u53d8\u9891<\/span>
    \ndef<\/span> downconvert<\/span>(<\/span>signal,<\/span> carrier_freq,<\/span> sample_rate)<\/span>:<\/span>
    \n t =<\/span> np.<\/span>arange(<\/span>0<\/span>,<\/span> len<\/span>(<\/span>signal)<\/span> \/<\/span> sample_rate,<\/span> 1<\/span> \/<\/span> sample_rate)<\/span>
    \n r_I =<\/span> signal *<\/span> np.<\/span>cos(<\/span>2<\/span> *<\/span> np.<\/span>pi *<\/span> carrier_freq *<\/span> t)<\/span>
    \n r_Q =<\/span> signal *<\/span> np.<\/span>sin(<\/span>2<\/span> *<\/span> np.<\/span>pi *<\/span> carrier_freq *<\/span> t)<\/span>
    \n return<\/span> r_I,<\/span> r_Q<\/p>\n

    # \u4e0b\u53d8\u9891\u540e\u7684\u4fe1\u53f7<\/span>
    \nr_I,<\/span> r_Q =<\/span> downconvert(<\/span>noisy_signal,<\/span> carrier_freq,<\/span> sample_rate)<\/span><\/p>\n

    # \u7ed8\u5236\u4e0b\u53d8\u9891\u540e\u7684\u4fe1\u53f7<\/span>
    \nplt.<\/span>figure(<\/span>figsize=<\/span>(<\/span>12<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
    \nplt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>t,<\/span> r_I)<\/span>
    \nplt.<\/span>title(<\/span>"Downconverted In-Phase Signal"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Time (s)"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Amplitude"<\/span>)<\/span><\/p>\n

    plt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 2<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>t,<\/span> r_Q)<\/span>
    \nplt.<\/span>title(<\/span>"Downconverted Quadrature Signal"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Time (s)"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Amplitude"<\/span>)<\/span>
    \nplt.<\/span>show(<\/span>)<\/span><\/p>\n

    7.4.6.4 \u4f4e\u901a\u6ee4\u6ce2<\/h5>\n

    \u4e0b\u53d8\u9891\u540e\u7684\u4fe1\u53f7\u9700\u8981\u901a\u8fc7\u4f4e\u901a\u6ee4\u6ce2\u5668\u6765\u6ee4\u9664\u9ad8\u9891\u566a\u58f0\u3002\u8fd9\u91cc\u6211\u4eec\u4f7f\u7528\u5df4\u7279\u6c83\u65af\u6ee4\u6ce2\u5668：<\/p>\n

    # \u8bbe\u8ba1\u5df4\u7279\u6c83\u65af\u4f4e\u901a\u6ee4\u6ce2\u5668<\/span>
    \ndef<\/span> design_butter_lowpass_filter<\/span>(<\/span>cutoff,<\/span> fs,<\/span> order=<\/span>5<\/span>)<\/span>:<\/span>
    \n nyquist =<\/span> 0.5<\/span> *<\/span> fs
    \n normal_cutoff =<\/span> cutoff \/<\/span> nyquist
    \n b,<\/span> a =<\/span> butter(<\/span>order,<\/span> normal_cutoff,<\/span> btype=<\/span>'low'<\/span>,<\/span> analog=<\/span>False<\/span>)<\/span>
    \n return<\/span> b,<\/span> a<\/p>\n

    # \u5e94\u7528\u4f4e\u901a\u6ee4\u6ce2\u5668<\/span>
    \ndef<\/span> apply_lowpass_filter<\/span>(<\/span>signal,<\/span> b,<\/span> a)<\/span>:<\/span>
    \n return<\/span> lfilter(<\/span>b,<\/span> a,<\/span> signal)<\/span><\/p>\n

    # \u6ee4\u6ce2\u53c2\u6570<\/span>
    \ncutoff =<\/span> 500<\/span> # \u622a\u6b62\u9891\u7387<\/span>
    \nfs =<\/span> sample_rate # \u91c7\u6837\u7387<\/span>
    \nb,<\/span> a =<\/span> design_butter_lowpass_filter(<\/span>cutoff,<\/span> fs)<\/span><\/p>\n

    # \u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7<\/span>
    \nfiltered_r_I =<\/span> apply_lowpass_filter(<\/span>r_I,<\/span> b,<\/span> a)<\/span>
    \nfiltered_r_Q =<\/span> apply_lowpass_filter(<\/span>r_Q,<\/span> b,<\/span> a)<\/span><\/p>\n

    # \u7ed8\u5236\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7<\/span>
    \nplt.<\/span>figure(<\/span>figsize=<\/span>(<\/span>12<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
    \nplt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>t,<\/span> filtered_r_I)<\/span>
    \nplt.<\/span>title(<\/span>"Filtered In-Phase Signal"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Time (s)"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Amplitude"<\/span>)<\/span><\/p>\n

    plt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 2<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>t,<\/span> filtered_r_Q)<\/span>
    \nplt.<\/span>title(<\/span>"Filtered Quadrature Signal"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Time (s)"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Amplitude"<\/span>)<\/span>
    \nplt.<\/span>show(<\/span>)<\/span><\/p>\n

    7.4.6.5 \u91c7\u6837<\/h5>\n

    \u5728\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7\u4e2d，\u6211\u4eec\u9700\u8981\u5728\u5408\u9002\u7684\u65f6\u95f4\u70b9\u8fdb\u884c\u91c7\u6837\u3002\u901a\u5e38，\u91c7\u6837\u70b9\u9009\u62e9\u5728\u4fe1\u53f7\u7684\u5cf0\u503c\u9644\u8fd1，\u4ee5\u786e\u4fdd\u91c7\u6837\u7684\u51c6\u786e\u6027\u3002<\/p>\n

    # \u91c7\u6837<\/span>
    \ndef<\/span> sample_signal<\/span>(<\/span>filtered_signal,<\/span> sample_rate,<\/span> symbol_rate)<\/span>:<\/span>
    \n samples_per_symbol =<\/span> sample_rate \/\/<\/span> symbol_rate
    \n sample_points =<\/span> np.<\/span>arange(<\/span>0<\/span>,<\/span> len<\/span>(<\/span>filtered_signal)<\/span>,<\/span> samples_per_symbol)<\/span>
    \n return<\/span> filtered_signal[<\/span>sample_points]<\/span><\/p>\n

    # \u7b26\u53f7\u7387<\/span>
    \nsymbol_rate =<\/span> 100<\/span> # \u7b26\u53f7\u7387<\/span><\/p>\n

    # \u91c7\u6837\u540e\u7684\u4fe1\u53f7<\/span>
    \nsampled_r_I =<\/span> sample_signal(<\/span>filtered_r_I,<\/span> sample_rate,<\/span> symbol_rate)<\/span>
    \nsampled_r_Q =<\/span> sample_signal(<\/span>filtered_r_Q,<\/span> sample_rate,<\/span> symbol_rate)<\/span><\/p>\n

    # \u7ed8\u5236\u91c7\u6837\u540e\u7684\u4fe1\u53f7<\/span>
    \nplt.<\/span>figure(<\/span>figsize=<\/span>(<\/span>12<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
    \nplt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>sampled_r_I,<\/span> label=<\/span>"Sampled I"<\/span>)<\/span>
    \nplt.<\/span>title(<\/span>"Sampled In-Phase Signal"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Sample Index"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Amplitude"<\/span>)<\/span>
    \nplt.<\/span>legend(<\/span>)<\/span><\/p>\n

    plt.<\/span>subplot(<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 2<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>sampled_r_Q,<\/span> label=<\/span>"Sampled Q"<\/span>)<\/span>
    \nplt.<\/span>title(<\/span>"Sampled Quadrature Signal"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Sample Index"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Amplitude"<\/span>)<\/span>
    \nplt.<\/span>legend(<\/span>)<\/span>
    \nplt.<\/span>show(<\/span>)<\/span><\/p>\n

    7.4.6.6 \u7b26\u53f7\u68c0\u6d4b<\/h5>\n

    \u6700\u540e，\u6211\u4eec\u5c06\u91c7\u6837\u540e\u7684I\u548cQ\u5206\u91cf\u4e0e\u9884\u5b9a\u4e49\u7684\u661f\u5ea7\u56fe\u8fdb\u884c\u6bd4\u8f83，\u6062\u590d\u51fa\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002<\/p>\n

    # \u7b26\u53f7\u68c0\u6d4b<\/span>
    \ndef<\/span> symbol_detection<\/span>(<\/span>sampled_I,<\/span> sampled_Q,<\/span> constellation)<\/span>:<\/span>
    \n detected_bits =<\/span> [<\/span>]<\/span>
    \n for<\/span> i,<\/span> q in<\/span> zip<\/span>(<\/span>sampled_I,<\/span> sampled_Q)<\/span>:<\/span>
    \n min_idx =<\/span> np.<\/span>argmin(<\/span>np.<\/span>abs<\/span>(<\/span>constellation –<\/span> (<\/span>i,<\/span> q)<\/span>)<\/span>)<\/span>
    \n detected_bits.<\/span>append(<\/span>min_idx)<\/span>
    \n return<\/span> np.<\/span>array(<\/span>detected_bits)<\/span><\/p>\n

    # \u6062\u590d\u539f\u59cb\u6bd4\u7279<\/span>
    \ndetected_bits =<\/span> symbol_detection(<\/span>sampled_r_I,<\/span> sampled_r_Q,<\/span> constellation)<\/span><\/p>\n

    # \u7ed8\u5236\u6062\u590d\u7684\u6bd4\u7279\u5e8f\u5217<\/span>
    \nplt.<\/span>figure(<\/span>figsize=<\/span>(<\/span>12<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
    \nplt.<\/span>plot(<\/span>detected_bits,<\/span> label=<\/span>"Detected Bits"<\/span>)<\/span>
    \nplt.<\/span>title(<\/span>"Detected Bit Sequence"<\/span>)<\/span>
    \nplt.<\/span>xlabel(<\/span>"Sample Index"<\/span>)<\/span>
    \nplt.<\/span>ylabel(<\/span>"Bit Value"<\/span>)<\/span>
    \nplt.<\/span>legend(<\/span>)<\/span>
    \nplt.<\/span>show(<\/span>)<\/span><\/p>\n

    7.4.7 QAM\u89e3\u8c03\u7684\u6027\u80fd\u8bc4\u4f30<\/h4>\n

    \u4e3a\u4e86\u8bc4\u4f30QAM\u89e3\u8c03\u7684\u6027\u80fd，\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u8bef\u7801\u7387（Bit Error Rate, BER）\u3002\u8bef\u7801\u7387\u662f\u89e3\u8c03\u540e\u6062\u590d\u7684\u6bd4\u7279\u5e8f\u5217\u4e0e\u539f\u59cb\u6bd4\u7279\u5e8f\u5217\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n

    # \u8ba1\u7b97\u8bef\u7801\u7387<\/span>
    \ndef<\/span> calculate_ber<\/span>(<\/span>original_bits,<\/span> detected_bits)<\/span>:<\/span>
    \n errors =<\/span> np.<\/span>sum<\/span>(<\/span>original_bits !=<\/span> detected_bits)<\/span>
    \n ber =<\/span> errors \/<\/span> len<\/span>(<\/span>original_bits)<\/span>
    \n return<\/span> ber<\/p>\n

    # \u8ba1\u7b97\u8bef\u7801\u7387<\/span>
    \nber =<\/span> calculate_ber(<\/span>bits,<\/span> detected_bits)<\/span>
    \nprint<\/span>(<\/span>f"Bit Error Rate (BER): <\/span>{<\/span>ber}<\/span><\/span>"<\/span><\/span>)<\/span><\/p>\n

    \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb121\u6b21\u3002QAM\u89e3\u8c03\u5219\u662f\u5c06\u63a5\u6536\u5230\u7684QAM\u4fe1\u53f7\u6062\u590d\u6210\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u7684\u8fc7\u7a0b\u3002QAM\u89e3\u8c03\u7684\u57fa\u672c\u539f\u7406\u662f\u901a\u8fc7\u68c0\u6d4b\u63a5\u6536\u5230\u7684\u4fe1\u53f7\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u6765\u6062\u590d\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002QAM\u4fe1\u53f7\u53ef\u4ee5\u770b\u4f5c\u662f\u4e24\u4e2a\u6b63\u4ea4\u7684\u8f7d\u6ce2\u4fe1\u53f7\u7684\u53e0\u52a0\uff0c\u6bcf\u4e2a\u8f7d\u6ce2\u4fe1\u53f7\u5206\u522b\u643a\u5e26\u4e86\u4e0d\u540c\u7684\u4fe1\u606f\u3002\u661f\u5ea7\u56fe\u662fQAM\u8c03\u5236\u5668\u548c\u89e3\u8c03\u5668\u4e4b\u95f4\u7684\u4e00\u79cd\u7ea6\u5b9a\uff0c\u8868\u793a\u4e86\u6bcf\u4e2a\u7b26\u53f7\u5bf9\u5e94\u7684I\u548cQ\u5206\u91cf\u7684\u7ec4\u5408\u3002\u901a\u5e38\uff0c\u91c7\u6837\u70b9\u9009\u62e9\u5728\u4fe1\u53f7\u7684\u5cf0\u503c\u9644\u8fd1\uff0c\u4ee5\u786e\u4fdd\u91c7\u6837\u7684\u51c6\u786e\u6027\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u91c7\u6837\u540e\u7684I\u548cQ\u5206\u91cf\u4e0e\u9884\u5b9a\u4e49\u7684\u661f\u5ea7\u56fe\u8fdb\u884c\u6bd4\u8f83\uff0c\u6062\u590d\u51fa\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002\u4e0b\u53d8\u9891\u662fQAM\u89e3\u8c03\u7684\u7b2c\u4e00\u6b65\uff0c\u5176\u76ee\u7684\u662f\u5c06\u63a5\u6536\u5230\u7684\u9ad8\u9891\u4fe1\u53f7\u3002<\/p>\n","protected":false},"author":2,"featured_media":58223,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[5138,2710,43,78,44],"topic":[],"class_list":["post-58224","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-5138","tag-2710","tag-43","tag-78","tag-44"],"yoast_head":"\n\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/58224.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb121\u6b21\u3002QAM\u89e3\u8c03\u5219\u662f\u5c06\u63a5\u6536\u5230\u7684QAM\u4fe1\u53f7\u6062\u590d\u6210\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u7684\u8fc7\u7a0b\u3002QAM\u89e3\u8c03\u7684\u57fa\u672c\u539f\u7406\u662f\u901a\u8fc7\u68c0\u6d4b\u63a5\u6536\u5230\u7684\u4fe1\u53f7\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u6765\u6062\u590d\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002QAM\u4fe1\u53f7\u53ef\u4ee5\u770b\u4f5c\u662f\u4e24\u4e2a\u6b63\u4ea4\u7684\u8f7d\u6ce2\u4fe1\u53f7\u7684\u53e0\u52a0\uff0c\u6bcf\u4e2a\u8f7d\u6ce2\u4fe1\u53f7\u5206\u522b\u643a\u5e26\u4e86\u4e0d\u540c\u7684\u4fe1\u606f\u3002\u661f\u5ea7\u56fe\u662fQAM\u8c03\u5236\u5668\u548c\u89e3\u8c03\u5668\u4e4b\u95f4\u7684\u4e00\u79cd\u7ea6\u5b9a\uff0c\u8868\u793a\u4e86\u6bcf\u4e2a\u7b26\u53f7\u5bf9\u5e94\u7684I\u548cQ\u5206\u91cf\u7684\u7ec4\u5408\u3002\u901a\u5e38\uff0c\u91c7\u6837\u70b9\u9009\u62e9\u5728\u4fe1\u53f7\u7684\u5cf0\u503c\u9644\u8fd1\uff0c\u4ee5\u786e\u4fdd\u91c7\u6837\u7684\u51c6\u786e\u6027\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u91c7\u6837\u540e\u7684I\u548cQ\u5206\u91cf\u4e0e\u9884\u5b9a\u4e49\u7684\u661f\u5ea7\u56fe\u8fdb\u884c\u6bd4\u8f83\uff0c\u6062\u590d\u51fa\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002\u4e0b\u53d8\u9891\u662fQAM\u89e3\u8c03\u7684\u7b2c\u4e00\u6b65\uff0c\u5176\u76ee\u7684\u662f\u5c06\u63a5\u6536\u5230\u7684\u9ad8\u9891\u4fe1\u53f7\u3002\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/58224.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2025-08-15T22:59:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815225944-689fbbe062334.jpg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/58224.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/58224.html\",\"name\":\"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2025-08-15T22:59:46+00:00\",\"dateModified\":\"2025-08-15T22:59:46+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/58224.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/58224.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/58224.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/58224.html","og_locale":"zh_CN","og_type":"article","og_title":"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb121\u6b21\u3002QAM\u89e3\u8c03\u5219\u662f\u5c06\u63a5\u6536\u5230\u7684QAM\u4fe1\u53f7\u6062\u590d\u6210\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u7684\u8fc7\u7a0b\u3002QAM\u89e3\u8c03\u7684\u57fa\u672c\u539f\u7406\u662f\u901a\u8fc7\u68c0\u6d4b\u63a5\u6536\u5230\u7684\u4fe1\u53f7\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u6765\u6062\u590d\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002QAM\u4fe1\u53f7\u53ef\u4ee5\u770b\u4f5c\u662f\u4e24\u4e2a\u6b63\u4ea4\u7684\u8f7d\u6ce2\u4fe1\u53f7\u7684\u53e0\u52a0\uff0c\u6bcf\u4e2a\u8f7d\u6ce2\u4fe1\u53f7\u5206\u522b\u643a\u5e26\u4e86\u4e0d\u540c\u7684\u4fe1\u606f\u3002\u661f\u5ea7\u56fe\u662fQAM\u8c03\u5236\u5668\u548c\u89e3\u8c03\u5668\u4e4b\u95f4\u7684\u4e00\u79cd\u7ea6\u5b9a\uff0c\u8868\u793a\u4e86\u6bcf\u4e2a\u7b26\u53f7\u5bf9\u5e94\u7684I\u548cQ\u5206\u91cf\u7684\u7ec4\u5408\u3002\u901a\u5e38\uff0c\u91c7\u6837\u70b9\u9009\u62e9\u5728\u4fe1\u53f7\u7684\u5cf0\u503c\u9644\u8fd1\uff0c\u4ee5\u786e\u4fdd\u91c7\u6837\u7684\u51c6\u786e\u6027\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u91c7\u6837\u540e\u7684I\u548cQ\u5206\u91cf\u4e0e\u9884\u5b9a\u4e49\u7684\u661f\u5ea7\u56fe\u8fdb\u884c\u6bd4\u8f83\uff0c\u6062\u590d\u51fa\u539f\u59cb\u7684\u6570\u5b57\u4fe1\u606f\u3002\u4e0b\u53d8\u9891\u662fQAM\u89e3\u8c03\u7684\u7b2c\u4e00\u6b65\uff0c\u5176\u76ee\u7684\u662f\u5c06\u63a5\u6536\u5230\u7684\u9ad8\u9891\u4fe1\u53f7\u3002","og_url":"https:\/\/www.wsisp.com\/helps\/58224.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2025-08-15T22:59:46+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815225944-689fbbe062334.jpg"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"5 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/58224.html","url":"https:\/\/www.wsisp.com\/helps\/58224.html","name":"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2025-08-15T22:59:46+00:00","dateModified":"2025-08-15T22:59:46+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/58224.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/58224.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/58224.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"\u65e0\u7ebf\u901a\u4fe1\u57fa\u7840\uff1a\u8c03\u5236\u4e0e\u89e3\u8c03\u6280\u672f_\uff0844\uff09.7.4\u6b63\u4ea4\u5e45\u5ea6\u89e3\u8c03(QAM\u89e3\u8c03)"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/58224","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=58224"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/58224\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/58223"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=58224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=58224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=58224"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=58224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}