{"id":6891,"date":"2026-03-05T13:27:26","date_gmt":"2026-03-05T05:27:26","guid":{"rendered":"https:\/\/nullthought.net\/?p=6891"},"modified":"2026-03-05T13:27:28","modified_gmt":"2026-03-05T05:27:28","slug":"%e5%bf%ab%e9%80%9f%e5%82%85%e9%87%8c%e5%8f%b6%e5%8f%98%e6%8d%a2%ef%bc%88fft%ef%bc%89%e8%ae%a1%e7%ae%97%e9%a2%91%e8%b0%b1%e5%88%86%e5%b8%83%ef%bc%8c%e9%81%bf%e5%85%8d%e9%81%97%e6%bc%8f%e7%89%b9","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=6891","title":{"rendered":"\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\uff08FFT\uff09\u8ba1\u7b97\u9891\u8c31\u5206\u5e03\uff0c\u907f\u514d\u9057\u6f0f\u7279\u5f81\u9891\u8c31\u7684\u5904\u7406\u65b9\u5f0f"},"content":{"rendered":"\n<p>\u4e3a\u4e86\u201c\u5c3d\u91cf\u4e0d\u6f0f\u6389\u7279\u5f81\u9891\u8c31\u201d\uff0c\u5173\u952e\u4e0d\u662f\u53ea\u628a FFT \u7b97\u51fa\u6765\uff0c\u800c\u662f\u628a<strong>\u91c7\u6837\u2192\u9884\u5904\u7406\u2192\u8c31\u4f30\u8ba1\u2192\u65f6\u9891\u8865\u5145\u2192\u7279\u5f81\u63d0\u53d6\/\u9a8c\u8bc1<\/strong>\u8fd9\u4e00\u6574\u6761\u94fe\u8def\u505a\u5f97\u66f4\u9c81\u68d2\u3002\u4e0b\u9762\u6309\u5b9e\u6218\u5e38\u7528\u7a0b\u5ea6\u7ed9\u51fa\u4e00\u5957\u201c\u9632\u6f0f\u7279\u5f81\u201d\u7684\u5904\u7406\u65b9\u5f0f\u6e05\u5355\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e00\u3001\u4ece\u6e90\u5934\u907f\u514d\u201c\u770b\u4e0d\u89c1\u201d\uff1a\u91c7\u6837\u4e0e\u9891\u7387\u5206\u8fa8\u7387\u8bbe\u8ba1<\/h4>\n\n\n\n<p><strong>1\uff09\u91c7\u6837\u7387\u4e0e\u6297\u6df7\u53e0\uff08anti-aliasing\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u91c7\u6837\u7387\u8981\u4fdd\u8bc1\uff1a\u611f\u5174\u8da3\u6700\u9ad8\u9891\u7387 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>f<\/mi><mrow><mi>m<\/mi><mi>a<\/mi><mi>x<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">f_{max}<\/annotation><\/semantics><\/math>\u200b \u8fdc\u5c0f\u4e8e <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>f<\/mi><mi>s<\/mi><\/msub><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f_s\/2<\/annotation><\/semantics><\/math>\uff0c\u5e76\u7559\u51fa\u4f59\u91cf\uff08\u5c24\u5176\u6709\u51b2\u51fb\/\u5c16\u5cf0\u65f6\uff0c\u9ad8\u9891\u80fd\u91cf\u4f1a\u5f88\u5bbd\uff09\u3002<\/li>\n\n\n\n<li>\u5fc5\u987b\u6709<strong>\u6a21\u62df\u6297\u6df7\u53e0\u4f4e\u901a<\/strong>\uff08\u6216\u8bbe\u5907\u5185\u7f6e\u540c\u7b49\u80fd\u529b\uff09\uff0c\u5426\u5219\u9ad8\u9891\u6298\u53e0\u5230\u4f4e\u9891\uff0c\u5bb9\u6613\u628a\u201c\u5047\u7279\u5f81\u201d\u5f53\u771f\u7279\u5f81\uff0c\u4e5f\u4f1a\u63a9\u76d6\u771f\u7279\u5f81\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>2\uff09\u9891\u7387\u5206\u8fa8\u7387 \u0394f<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"normal\">\u0394<\/mi><mi>f<\/mi><mo>=<\/mo><msub><mi>f<\/mi><mi>s<\/mi><\/msub><mi mathvariant=\"normal\">\/<\/mi><mi>N<\/mi><mo>=<\/mo><mn>1<\/mn><mi mathvariant=\"normal\">\/<\/mi><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta f = f_s\/N = 1\/T<\/annotation><\/semantics><\/math>\uff08T \u662f\u91c7\u6837\u65f6\u957f\uff09\u3002\u8981\u5206\u5f00\u5f88\u8fd1\u7684\u8c31\u7ebf\uff0c\u5c31\u8981\u66f4\u957f\u7684\u8bb0\u5f55\u957f\u5ea6 T\u3002<\/li>\n\n\n\n<li>\u5e38\u89c1\u201c\u6f0f\u7279\u5f81\u201d\u539f\u56e0\u4e4b\u4e00\uff1a<strong>\u5206\u8fa8\u7387\u4e0d\u591f<\/strong>\u5bfc\u81f4\u4e24\u4e2a\u7279\u5f81\u5cf0\u7c98\u5728\u4e00\u8d77\uff0c\u6216\u5cf0\u88ab\u566a\u58f0\u5e95\u6df9\u6ca1\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>3\uff09\u591a\u6863\u4f4d\u91c7\u96c6\uff08\u5bbd\u5e26\u626b\u4e00\u904d + \u91cd\u70b9\u653e\u5927\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5148\u7528\u8f83\u9ad8\u91c7\u6837\u7387\u505a\u5bbd\u5e26\u666e\u67e5\uff08\u4e0d\u6f0f\u5927\u8303\u56f4\uff09\uff0c\u518d\u5bf9\u53ef\u7591\u9891\u6bb5\u505a<strong>\u66f4\u957f\u65f6\u957f\/\u66f4\u9ad8\u5206\u8fa8\u7387<\/strong>\u7684\u201c\u7cbe\u626b\u201d\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e8c\u3001\u9884\u5904\u7406\uff1a\u51cf\u5c11\u6cc4\u6f0f\u4e0e\u4f4e\u9891\u6c61\u67d3\uff0c\u63d0\u5347\u53ef\u68c0\u51fa\u6027<\/h4>\n\n\n\n<p><strong>4\uff09\u53bb\u76f4\u6d41\/\u53bb\u8d8b\u52bf\uff08de-mean \/ detrend\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u76f4\u6d41\u5206\u91cf\u3001\u6162\u6f02\u79fb\u4f1a\u62ac\u9ad8\u4f4e\u9891\u566a\u58f0\u5e95\uff0c\u63a9\u76d6\u4f4e\u9891\u7279\u5f81\u6216\u5236\u9020\u201c\u5047\u4f4e\u9891\u5cf0\u201d\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>5\uff09\u5408\u7406\u7a97\u51fd\u6570\uff0c\u63a7\u5236\u8c31\u6cc4\u6f0f<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7279\u5f81\u9891\u7387\u4e0d\u4e00\u5b9a\u6b63\u597d\u843d\u5728 FFT \u7684\u9891\u70b9\u4e0a\uff0c\u4f1a\u53d1\u751f<strong>\u8c31\u6cc4\u6f0f<\/strong>\u4e0e<strong>scalloping loss\uff08\u6805\u680f\u6548\u5e94\uff09<\/strong>\u3002<\/li>\n\n\n\n<li>\u7ecf\u9a8c\uff1a\n<ul class=\"wp-block-list\">\n<li><strong>Hann\/Hamming<\/strong>\uff1a\u901a\u7528\uff0c\u6cc4\u6f0f\u8f83\u5c0f\uff0c\u5e45\u503c\u635f\u5931\u53ef\u63a5\u53d7\uff1b<\/li>\n\n\n\n<li><strong>Blackman \/ Blackman-Harris<\/strong>\uff1a\u66f4\u5f3a\u6291\u5236\u65c1\u74e3\uff0c\u9002\u5408\u5f3a\u5f31\u5cf0\u5171\u5b58\uff08\u9ad8\u52a8\u6001\u8303\u56f4\uff09\uff1b<\/li>\n\n\n\n<li><strong>Flat-top<\/strong>\uff1a\u5e45\u503c\u6d4b\u91cf\u66f4\u51c6\uff0c\u4f46\u4e3b\u74e3\u66f4\u5bbd\uff08\u5206\u8fa8\u7387\u53d8\u5dee\uff09\uff0c\u9002\u5408\u201c\u8981\u7cbe\u786e\u5e45\u503c\u201d\u800c\u4e0d\u662f\u201c\u5206\u5f00\u8fd1\u5cf0\u201d\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>6\uff09\u5e45\u503c\u6821\u6b63<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u52a0\u7a97\u540e\u8981\u505a<strong>coherent gain \/ ENBW<\/strong>\u76f8\u5173\u6821\u6b63\uff0c\u5426\u5219\u5cf0\u503c\u5e45\u5ea6\u4f1a\u7cfb\u7edf\u6027\u504f\u5c0f\uff0c\u5f31\u5cf0\u66f4\u5bb9\u6613\u201c\u770b\u8d77\u6765\u4e0d\u5b58\u5728\u201d\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e09\u3001\u8c31\u4f30\u8ba1\u66f4\u7a33\uff1a\u907f\u514d\u201c\u5076\u7136\u6027\u201d\u4e0e\u201c\u566a\u58f0\u5e95\u63a9\u76d6\u201d<\/h4>\n\n\n\n<p><strong>7\uff09Welch \u5206\u6bb5\u5e73\u5747\uff08\u5f3a\u70c8\u63a8\u8350\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u628a\u4fe1\u53f7\u5206\u6bb5\u3001\u52a0\u7a97\u3001\u91cd\u53e0\uff08\u5982 50%~75%\uff09\u3001\u6c42\u529f\u7387\u8c31\u518d\u5e73\u5747\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4f18\u70b9\uff1a\u663e\u8457\u964d\u4f4e\u65b9\u5dee\u3001\u7a33\u5b9a\u566a\u58f0\u5e95\uff0c\u5f31\u5cf0\u66f4\u5bb9\u6613\u5192\u51fa\u6765\uff1b<\/li>\n\n\n\n<li>\u4ee3\u4ef7\uff1a\u9891\u7387\u5206\u8fa8\u7387\u7565\u964d\uff08\u6bcf\u6bb5\u66f4\u77ed\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>8\uff09\u591a\u9525\u7a97 Multi-taper\uff08\u66f4\u201c\u9632\u6f0f\u201d\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u7a84\u5e26\u8c31\u7ebf+\u566a\u58f0\u573a\u666f\u7279\u522b\u597d\uff1a\u7528\u591a\u7ec4\u6b63\u4ea4\u7a97\u5f97\u5230\u591a\u4efd\u8c31\u518d\u5e73\u5747\uff0c<strong>\u6cc4\u6f0f\u66f4\u53ef\u63a7<\/strong>\u3001\u4f30\u8ba1\u65b9\u5dee\u66f4\u4f4e\u3002<\/li>\n\n\n\n<li>\u5728\u201c\u5f3a\u5cf0\u65c1\u8fb9\u627e\u5f31\u5cf0\u201d\u65f6\u975e\u5e38\u6709\u4ef7\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>9\uff09\u65f6\u57df\u540c\u6b65\u5e73\u5747 \/ \u8f6c\u901f\u540c\u6b65\uff08\u82e5\u5b58\u5728\u5468\u671f\u6027\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u673a\u68b0\u7cfb\u7edf\u91cc\u5f88\u591a\u7279\u5f81\u4e0e\u8f6c\u901f\u3001\u5de5\u9891\u3001\u556e\u5408\u9891\u76f8\u5173\uff1a\n<ul class=\"wp-block-list\">\n<li>\u82e5\u8f6c\u901f\u7a33\u5b9a\uff1a\u505a<strong>Time Synchronous Averaging (TSA)<\/strong>\uff0c\u80fd\u628a\u968f\u673a\u566a\u58f0\u538b\u4e0b\u53bb\uff1b<\/li>\n\n\n\n<li>\u82e5\u8f6c\u901f\u6ce2\u52a8\uff1a\u505a<strong>Order Tracking\uff08\u9636\u6b21\u5206\u6790\uff09<\/strong>\uff0c\u628a\u9891\u7387\u8f74\u6362\u6210\u201c\u9636\u6b21\u201d\uff0c\u5426\u5219\u5cf0\u4f1a\u88ab\u201c\u62c9\u5bbd\u201d\u770b\u4e0d\u89c1\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u56db\u3001\u5bf9\u51c6\u9891\u70b9\uff1a\u51cf\u5c11\u201c\u5cf0\u503c\u843d\u5728\u4e24\u4e2a bin \u4e4b\u95f4\u201d\u5bfc\u81f4\u7684\u6f0f\u68c0<\/h4>\n\n\n\n<p><strong>10\uff09\u589e\u52a0\u8bb0\u5f55\u957f\u5ea6\uff08\u6700\u6709\u6548\uff09 vs \u96f6\u586b\u5145\uff08zero-padding\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u589e\u52a0\u8bb0\u5f55\u957f\u5ea6<\/strong>\uff1a\u771f\u6b63\u63d0\u9ad8\u5206\u8fa8\u7387\uff08\u66f4\u4e0d\u6f0f\uff09\u3002<\/li>\n\n\n\n<li><strong>\u96f6\u586b\u5145<\/strong>\uff1a\u4e0d\u63d0\u9ad8\u771f\u5b9e\u5206\u8fa8\u7387\uff0c\u4f46\u80fd\u8ba9\u8c31\u770b\u8d77\u6765\u66f4\u5e73\u6ed1\u3001\u4fbf\u4e8e\u5cf0\u503c\u5b9a\u4f4d\uff08\u5c24\u5176\u914d\u5408\u5cf0\u503c\u63d2\u503c\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>11\uff09\u5cf0\u503c\u63d2\u503c\uff08bin \u95f4\u63d2\u503c\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u68c0\u6d4b\u8c31\u7ebf\u9891\u7387\u5f88\u6709\u7528\uff1a\u5728\u5cf0\u9644\u8fd1\u505a\u629b\u7269\u7ebf\/\u9ad8\u65af\u63d2\u503c\uff0c\u53ef\u663e\u8457\u964d\u4f4e\u201c\u6805\u680f\u6548\u5e94\u201d\u5e26\u6765\u7684\u4f4e\u4f30\u4e0e\u6f0f\u68c0\u98ce\u9669\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>12\uff09Zoom-FFT \/ CZT\uff08Chirp-Z Transform\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5982\u679c\u4f60\u53ea\u5173\u5fc3\u67d0\u4e00\u5c0f\u6bb5\u9891\u5e26\uff1a\u7528 CZT \u6216 Zoom-FFT \u76f4\u63a5\u5bf9\u8be5\u9891\u5e26\u505a\u9ad8\u5206\u8fa8\u7387\u5206\u6790\uff0c\u6bd4\u201c\u5168\u9891\u6bb5\u8d85\u5927 N\u201d\u66f4\u9ad8\u6548\u3001\u66f4\u4e0d\u6f0f\u7ec6\u8282\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e94\u3001\u975e\u5e73\u7a33\/\u77ac\u6001\u7279\u5f81\uff1a\u5355\u6b21 FFT \u6700\u5bb9\u6613\u6f0f\u6389\u7684\u90e8\u5206<\/h4>\n\n\n\n<p>\u5f88\u591a\u6545\u969c\u7279\u5f81\u4e0d\u662f\u201c\u5168\u7a0b\u7a33\u5b9a\u4e00\u6761\u7ebf\u201d\uff0c\u800c\u662f<strong>\u95f4\u6b47\u51fa\u73b0\u3001\u9891\u7387\u6f02\u79fb\u3001\u51b2\u51fb\u8c03\u5236<\/strong>\u3002\u8fd9\u65f6\u201c\u6574\u6bb5 FFT\u201d\u4f1a\u628a\u80fd\u91cf\u644a\u5e73\uff0c\u5bfc\u81f4\u770b\u4e0d\u5230\u5cf0\u3002<\/p>\n\n\n\n<p><strong>13\uff09STFT\uff08\u77ed\u65f6\u5085\u91cc\u53f6\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7528\u6ed1\u52a8\u7a97\u53e3\u770b\u968f\u65f6\u95f4\u53d8\u5316\u7684\u8c31\uff08\u8c31\u56fe\uff09\u3002<\/li>\n\n\n\n<li>\u5bf9\u201c\u95e8\u673a\u52a8\u4f5c\u8fc7\u7a0b\u201d\u201c\u542f\u505c\u77ac\u6001\u201d\u201c\u5076\u53d1\u51b2\u51fb\u201d\u7279\u522b\u6709\u6548\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>14\uff09\u5c0f\u6ce2\/\u8fde\u7eed\u5c0f\u6ce2 CWT<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u51b2\u51fb\u7c7b\u3001\u975e\u5e73\u7a33\u4fe1\u53f7\u66f4\u654f\u611f\uff0c\u65f6\u9891\u5206\u8fa8\u7387\u81ea\u9002\u5e94\uff1b\u5e38\u7528\u6765\u907f\u514d\u6f0f\u6389\u201c\u77ed\u4fc3\u4f46\u5173\u952e\u201d\u7684\u5f02\u5e38\u80fd\u91cf\u5e26\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>15\uff09\u5305\u7edc\u89e3\u8c03\uff08Envelope \/ Demodulation\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8f74\u627f\u3001\u9f7f\u8f6e\u7b49\u5e38\u89c1\u201c\u9ad8\u9891\u5171\u632f\u88ab\u4f4e\u9891\u8c03\u5236\u201d\uff1a\u76f4\u63a5\u770b\u539f\u59cb FFT \u53ef\u80fd\u53ea\u770b\u5230\u4e00\u5768\u5bbd\u5e26\u3002<\/li>\n\n\n\n<li>\u505a\u5e26\u901a\uff08\u6293\u5171\u632f\u5e26\uff09\u2192\u5e0c\u5c14\u4f2f\u7279\u5305\u7edc\u2192\u5bf9\u5305\u7edc\u505a FFT\uff0c\u7ecf\u5e38\u80fd\u628a\u201c\u9690\u85cf\u7684\u8c03\u5236\u9891\u7387\u201d\u62c9\u51fa\u6765\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u516d\u3001\u8ba9\u201c\u5f31\u7279\u5f81\u201d\u4e0d\u88ab\u5f3a\u7279\u5f81\u6df9\u6ca1\uff1a\u52a8\u6001\u8303\u56f4\u4e0e\u53bb\u5e72\u6270<\/h4>\n\n\n\n<p><strong>16\uff09\u5bf9\u6570\u5750\u6807\/\u5206\u6bb5\u663e\u793a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>PSD \u7528 dB \u663e\u793a\uff1b\u6216\u8005\u540c\u4e00\u5f20\u56fe\u505a\u201c\u5168\u9891 + 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\u7b97\u51fa\u6765\uff0c\u800c\u662f\u628a\u91c7\u6837\u2192\u9884\u5904\u7406\u2192\u8c31\u4f30\u8ba1\u2192\u65f6\u9891\u8865\u5145\u2192\u7279\u5f81\u63d0\u53d6\/\u9a8c\u8bc1 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