{"id":100992,"date":"2026-09-05T22:01:00","date_gmt":"2026-09-05T14:01:00","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/100992.html"},"modified":"2026-09-05T22:01:00","modified_gmt":"2026-09-05T14:01:00","slug":"qpsk%e5%bc%80%e7%8e%af%e9%a2%91%e5%81%8f%e4%bc%b0%e8%ae%a1%ef%bc%9a4%e6%ac%a1%e6%96%b9fft%e9%a2%91%e5%81%8f%e6%a3%80%e6%b5%8b%e4%b8%8e%e6%a0%a1%e6%ad%a3%e5%8e%9f%e7%90%86%e5%8f%8amatlab%e4%bb%bf","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/100992.html","title":{"rendered":"QPSK\u5f00\u73af\u9891\u504f\u4f30\u8ba1\uff1a4\u6b21\u65b9+FFT\u9891\u504f\u68c0\u6d4b\u4e0e\u6821\u6b63\u539f\u7406\u53caMatlab\u4eff\u771f"},"content":{"rendered":"<h2>QPSK\u5f00\u73af\u9891\u504f\u4f30\u8ba1&#xff1a;4\u6b21\u65b9&#043;FFT\u9891\u504f\u68c0\u6d4b\u4e0e\u6821\u6b63\u539f\u7406\u53caMatlab\u4eff\u771f<\/h2>\n<h3>\u6458\u8981<\/h3>\n<p>QPSK\u901a\u4fe1\u7cfb\u7edf\u4e2d&#xff0c;\u6676\u632f\u504f\u5dee\u3001\u591a\u666e\u52d2\u6548\u5e94\u4f1a\u5f15\u5165\u8f7d\u6ce2\u9891\u504f\u3002\u9891\u504f\u8f83\u5927\u65f6Costas\u95ed\u73af\u8f7d\u6ce2\u540c\u6b65\u4f1a\u8d85\u51fa\u6355\u83b7\u8303\u56f4&#xff0c;\u51fa\u73b0\u65e0\u6cd5\u9501\u76f8\u3001\u661f\u5ea7\u6301\u7eed\u65cb\u8f6c\u95ee\u9898\u3002\u672c\u6587\u8bb2\u89e3\u57fa\u4e8e4\u6b21\u65b9\u8fd0\u7b97&#043;FFT\u7684\u5f00\u73af\u9891\u504f\u4f30\u8ba1\u7b97\u6cd5&#xff0c;\u5bf9\u5b9a\u65f6\u540c\u6b65\u540e\u7684\u57fa\u5e26\u590d\u4fe1\u53f7\u505a4\u6b21\u65b9\u8fd0\u7b97\u6d88\u9664\u8c03\u5236\u4fe1\u606f&#xff0c;\u901a\u8fc7FFT\u9891\u8c31\u5cf0\u503c\u641c\u7d22\u5f97\u5230\u7c97\u9891\u504f\u4f30\u8ba1&#xff1b;\u5229\u7528\u4f30\u8ba1\u503c\u5bf9\u63a5\u6536\u4fe1\u53f7\u5b8c\u6210\u9884\u6821\u6b63&#xff0c;\u5c06\u6b8b\u4f59\u9891\u504f\u538b\u7f29\u5230Costas\u73af\u6355\u83b7\u8303\u56f4\u5185&#xff0c;\u518d\u4ea4\u7531\u95ed\u73af\u73af\u8def\u505a\u7cbe\u7ec6\u76f8\u4f4d\u8ddf\u8e2a\u3002\u7b97\u6cd5\u53ef\u76f4\u63a5\u63a5\u5165\u73b0\u6709QPSK\u63a5\u6536\u673a\u94fe\u8def&#xff0c;\u9644\u5e26\u5b8c\u6574Matlab\u4eff\u771f\u5b9e\u73b0\u3002<\/p>\n<h3>\u4e00\u3001\u524d\u8a00<\/h3>\n<p>\u524d\u9762\u7cfb\u5217\u6587\u7ae0\u5b8c\u6210QPSK\u63a5\u6536\u673a&#xff1a;\u5b9a\u65f6\u540c\u6b65\u3001\u8f7d\u6ce2\u540c\u6b65\u3001\u96c6\u4e2d\u5bfc\u9891\u6d88\u9664\u76f8\u4f4d\u6a21\u7cca\u3002<\/p>\n<p>\u4f46Costas\u73af\u5c5e\u4e8e\u95ed\u73af\u8ddf\u8e2a&#xff0c;\u4f18\u70b9\u662f\u566a\u58f0\u6761\u4ef6\u4e0b\u76f8\u4f4d\u8ddf\u8e2a\u7cbe\u5ea6\u9ad8&#xff0c;\u4f46\u5b58\u5728\u56fa\u6709\u77ed\u677f&#xff1a;\u6355\u83b7\u8303\u56f4\u6709\u9650\u3002\u5f53\u5b9e\u9645\u8f7d\u6ce2\u9891\u504f\u5927\u4e8e\u73af\u8def\u6700\u5927\u6355\u83b7\u9891\u504f\u65f6&#xff0c;\u73af\u8def\u65e0\u6cd5\u5165\u9501&#xff0c;\u661f\u5ea7\u4e00\u76f4\u65cb\u8f6c&#xff0c;\u89e3\u8c03\u5b8c\u5168\u5931\u6548\u3002<\/p>\n<p>\u5de5\u7a0b\u63a5\u6536\u673a\u5e38\u7528\u7ec4\u5408\u67b6\u6784&#xff1a;<\/p>\n<p>\u5f00\u73af\u7c97\u9891\u504f\u4f30\u8ba1 \u2192 \u9891\u504f\u9884\u6821\u6b63 \u2192 Costas\u95ed\u73af\u7cbe\u7ec6\u8f7d\u6ce2\u540c\u6b65<\/p>\n<p>\u5f00\u73af\u7b97\u6cd5\u8d1f\u8d23\u628a\u5927\u9891\u504f\u538b\u7f29\u53d8\u5c0f&#xff0c;\u95ed\u73af\u73af\u8def\u8d1f\u8d23\u9ad8\u7cbe\u5ea6\u76f8\u4f4d\u8ddf\u8e2a\u3002\u9488\u5bf9QPSK\u8c03\u5236&#xff0c;\u4e3b\u6d41\u65b9\u6848\u5c31\u662f4\u6b21\u65b9&#043;FFT\u9891\u504f\u4f30\u8ba1\u3002BPSK\u4f7f\u75282\u6b21\u65b9&#xff0c;M\u2011PSK\u901a\u7528M\u6b21\u65b9\u3002<\/p>\n<h3>\u4e8c\u3001\u6570\u5b66\u539f\u7406<\/h3>\n<p>\u7ecf\u8fc7\u5b9a\u65f6\u540c\u6b65\u91c7\u6837\u4e4b\u540e\u7684\u590d\u57fa\u5e26\u63a5\u6536\u4fe1\u53f7&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">r(k)&#061;A\u22c5s(k)\u22c5ej(2\u03c0\u0394f\u22c5kTs&#043;\u03b8)&#043;n(k)r(k)&#061;A\\\\cdot s(k)\\\\cdot e^{j(2\\\\pi\\\\Delta f \\\\cdot k T_s&#043;\\\\theta)}&#043;n(k)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0213em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.938em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.1389em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">s(k)s(k)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;QPSK\u53d1\u9001\u7b26\u53f7&#xff0c;\u53d6\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">{\u00b11\u00b1j}\\\\{\\\\pm1\\\\pm j\\\\}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">\u00b1<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00b1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u0394f\\\\Delta f<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u5f85\u4f30\u8ba1\u8f7d\u6ce2\u9891\u504f<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TsT_s<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u7b26\u53f7\u5468\u671f<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8\\\\theta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u521d\u59cb\u8f7d\u6ce2\u76f8\u504f<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">n(k)n(k)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u590d\u9ad8\u65af\u566a\u58f0<\/li>\n<\/ul>\n<p>QPSK\u7b26\u53f7\u6ee1\u8db3&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">s4(k)&#061;(\u00b11\u00b1j)4&#061;\u22124s^4(k)&#061;\\\\big(\\\\pm1\\\\pm j\\\\big)^4&#061;-4<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2em;vertical-align: -0.35em\"><\/span><span class=\"mord\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00b1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00b1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.404em;vertical-align: -0.35em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mord\"><span class=\"mord\"><span class=\"delimsizing size1\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.054em\"><span class=\"\" style=\"top: -3.3029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7b26\u53f7\u4fe1\u606f\u7ecf\u8fc74\u6b21\u65b9\u8fd0\u7b97\u4e4b\u540e\u53d8\u6210\u5e38\u6570&#xff0c;\u8c03\u5236\u4fe1\u606f\u88ab\u6d88\u9664\u3002<\/p>\n<p>\u5bf9\u63a5\u6536\u4fe1\u53f7\u505a4\u6b21\u65b9&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">r4(k)&#061;A4\u22c5s4(k)\u22c5ej4(2\u03c0\u0394f\u22c5kTs&#043;\u03b8)&#043;n\u2032(k)&#061;C\u22c5ej(2\u03c0\u22c54\u0394f\u22c5kTs&#043;4\u03b8)&#043;n\u2032(k) r^4(k)&#061;A^4 \\\\cdot s^4(k) \\\\cdot e^{j4(2\\\\pi\\\\Delta f \\\\cdot k T_s&#043;\\\\theta)}&#043;n&#039;(k) &#061; C \\\\cdot e^{j\\\\left(2\\\\pi \\\\cdot 4\\\\Delta f \\\\cdot k T_s &#043;4\\\\theta\\\\right)}&#043;n&#039;(k)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8641em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0213em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.938em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mord mtight\">4<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.1389em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0519em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0213em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.938em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"minner mtight\"><span class=\"mopen mtight delimcenter\" style=\"top: 0em\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mtight\">4\u0394<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.1389em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">4<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose mtight delimcenter\" style=\"top: 0em\"><span class=\"mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0519em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5173\u952e\u73b0\u8c61&#xff1a;<\/p>\n<li>\u539f\u59cb\u8c03\u5236\u7b26\u53f7<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">s(k)\u200bs(k)\u200b<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\u200b<\/span><\/span><\/span><\/span><\/span>\u6d88\u5931&#xff0c;\u53d8\u4e3a\u5e38\u6570C&#xff1b;<\/li>\n<li>\u9891\u504f\u88ab\u653e\u59274\u500d&#xff0c;\u9891\u8c31\u4e0a\u51fa\u73b0\u5355\u6839\u8c31\u7ebf&#xff0c;\u9891\u7387\u4f4d\u7f6e\u7b49\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">4\u0394f4\\\\Delta f<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">4\u0394<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span>&#xff1b;<\/li>\n<li>\u76f8\u504f\u540c\u65f6\u653e\u59274\u500d&#xff1b;<\/li>\n<li>\u566a\u58f0\u9879\u88ab\u653e\u5927\u3002<\/li>\n<p>\u5bf9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">r4(k)r^4(k)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u505aFFT&#xff0c;\u5bfb\u627e\u9891\u8c31\u5e45\u5ea6\u6700\u5927\u503c\u5bf9\u5e94\u7684\u9891\u7387\u70b9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fpeakf_{peak}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">ak<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5219&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u0394f^&#061;fpeak4\\\\hat{\\\\Delta f}&#061; \\\\frac{f_{peak}}{4}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1523em;vertical-align: -0.1944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9579em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2634em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">4<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">ak<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5373\u53ef\u5f97\u5230\u539f\u59cb\u8f7d\u6ce2\u9891\u504f\u7684\u7c97\u4f30\u8ba1\u503c\u3002<\/p>\n<p>\u4ece\u4e0a\u5f0f\u7684\u516c\u5f0f\u4e2d\u53ef\u4ee5\u770b\u5230&#xff0c;\u9891\u504f\u4f30\u8ba1\u7684\u7cbe\u5ea6\u53d7FFT\u8ba1\u7b97\u7684\u6700\u5927\u503c\u5bf9\u5e94\u9891\u7387\u70b9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fpeakf_{peak}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"mord mathnormal mtight\">e<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">ak<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5f71\u54cd&#xff0c;\u5176\u53d7\u6570\u636e\u957f\u5ea6\u9650\u5236&#xff0c;\u5b58\u5728\u6805\u680f\u6548\u5e94\u3002<\/p>\n<h3>\u4e09\u3001\u9891\u504f\u6821\u6b63<\/h3>\n<p>\u5f97\u5230\u9891\u504f\u4f30\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u0394f^\\\\hat{\\\\Delta f}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1523em;vertical-align: -0.1944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9579em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2634em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u540e&#xff0c;\u5bf9\u539f\u59cb\u63a5\u6536\u57fa\u5e26\u4fe1\u53f7\u505a\u9891\u504f\u8865\u507f&#xff0c;\u4e58\u4ee5\u8865\u507f\u65cb\u8f6c\u56e0\u5b50&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">rcomp(k)&#061;r(k)\u22c5e\u2212j\u22c52\u03c0\u0394f^\u22c5kTsr_{\\\\text{comp}}(k)&#061;r(k)\\\\cdot e^{-j\\\\cdot 2\\\\pi \\\\hat{\\\\Delta f}\\\\cdot k T_s}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">comp<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0835em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0835em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9579em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9634em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord mtight\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.1389em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7ecf\u8fc7\u6821\u6b63\u4e4b\u540e&#xff0c;\u4fe1\u53f7\u53ea\u5269\u4e0b\u6b8b\u4f59\u5c0f\u9891\u504f\u4e0e\u56fa\u5b9a\u76f8\u504f&#xff0c;\u6b8b\u4f59\u9891\u504f\u4e00\u822c\u843d\u5165Costas\u73af\u6355\u83b7\u8303\u56f4&#xff0c;\u540e\u7eed\u9001\u5165Costas\u73af\u505a\u7cbe\u7ec6\u76f8\u4f4d\u8ddf\u8e2a\u3002<\/p>\n<h3>\u56db\u3001Matlab\u6838\u5fc3\u4eff\u771f\u4ee3\u7801<\/h3>\n<p>\u5b8c\u6574\u4ee3\u7801\u653e\u5728\u4e0b\u9762\u94fe\u63a5\u4e86&#xff1a;<br \/>\nhttps:\/\/download.csdn.net\/download\/wobiaosha2753\/93394687<\/p>\n<p><span class=\"token comment\">%% \u9891\u504f\u4f30\u8ba1\u52a0\u7ea0\u6b63<\/span><br \/>\nN_fft <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">512<\/span><span class=\"token punctuation\">;<\/span>          <span class=\"token comment\">% FFT\u70b9\u6570<\/span><br \/>\nr4 <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">rx_ds<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token operator\">:<\/span>N_fft<span class=\"token punctuation\">)<\/span><span class=\"token operator\">.^<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">% \u53d6\u524dN_fft\u70b9\u505a4\u6b21\u65b9\u8fd0\u7b97<\/span><br \/>\nfft_r4 <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">fftshift<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">fft<\/span><span class=\"token punctuation\">(<\/span>r4<span class=\"token punctuation\">,<\/span>N_fft<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">[<\/span><span class=\"token operator\">~<\/span><span class=\"token punctuation\">,<\/span>max_idx<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">abs<\/span><span class=\"token punctuation\">(<\/span>fft_r4<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">% \u5bfb\u627e\u9891\u8c31\u5cf0\u503c\u4f4d\u7f6e<\/span><br \/>\n<span class=\"token comment\">% figure,plot(abs(fft_r4));<\/span><br \/>\n<span class=\"token comment\">% FFT\u9891\u7387\u8f74<\/span><br \/>\nf_axis <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8211;<\/span>N_fft<span class=\"token operator\">\/<\/span><span class=\"token number\">2<\/span><span class=\"token operator\">:<\/span>N_fft<span class=\"token operator\">\/<\/span><span class=\"token number\">2<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">\/<\/span>N_fft <span class=\"token operator\">*<\/span> data_rata<span class=\"token punctuation\">;<\/span><br \/>\nf4_peak <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">f_axis<\/span><span class=\"token punctuation\">(<\/span>max_idx<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\ndelta_f_hat <span class=\"token operator\">&#061;<\/span> f4_peak <span class=\"token operator\">\/<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">% \u6062\u590d\u771f\u5b9e\u9891\u504f\u4f30\u8ba1\u503c<\/span><\/p>\n<p><span class=\"token comment\">%\u9891\u504f\u9884\u6821\u6b63<\/span><br \/>\nk <span class=\"token operator\">&#061;<\/span> 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alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u53ef\u4ee5\u770b\u5230&#xff0c;\u5f53\u524d\u7f6e\u7684\u9891\u504f\u7ea0\u6b63\u6a21\u5757\u628a\u8f83\u5927\u9891\u504f\u7ea0\u6b63\u540e&#xff0c;\u7ec6\u5c0f\u9891\u504f\u548c\u76f8\u504f\u53ef\u901a\u8fc7\u9501\u76f8\u73af\u8ddf\u8e2a\u3002\u6700\u7ec8\u661f\u5ea7\u56fe\u6b63\u786e\u3002<\/p>\n<h4>\u9891\u504f\u4f30\u8ba1\u8bef\u5dee&#xff1a;<\/h4>\n<p>\u6b63\u6a21\u5757\u628a\u8f83\u5927\u9891\u504f\u7ea0\u6b63\u540e&#xff0c;\u7ec6\u5c0f\u9891\u504f\u548c\u76f8\u504f\u53ef\u901a\u8fc7\u9501\u76f8\u73af\u8ddf\u8e2a\u3002\u6700\u7ec8\u661f\u5ea7\u56fe\u6b63\u786e\u3002<\/p>\n<h4>\u9891\u504f\u4f30\u8ba1\u8bef\u5dee&#xff1a;<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260905140059-6a9c209b2c00d.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" 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