{"id":286,"date":"2025-05-12T20:52:42","date_gmt":"2025-05-12T11:52:42","guid":{"rendered":"https:\/\/www.shin-ichi.org\/?p=286"},"modified":"2025-07-31T11:25:17","modified_gmt":"2025-07-31T02:25:17","slug":"%e3%80%8e%e9%ab%98%e9%80%9f%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e5%a4%89%e6%8f%9b%ef%bc%88fft%ef%bc%89%e3%81%ae%e5%9f%ba%e7%a4%8e%e3%81%a8%e5%bf%9c%e7%94%a8%e3%80%8f%e3%82%92llm%e3%81%ab%e8%81%9e","status":"publish","type":"post","link":"https:\/\/www.shin-ichi.org\/?p=286","title":{"rendered":"\u300e\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff08fft\uff09\u306e\u57fa\u790e\u3068\u5fdc\u7528\u300f\u3092LLM\u306b\u805e\u3044\u3066\u307f\u305f\u2014AI\u304c\u5c0e\u304f\u7814\u7a76\u30e1\u30e2"},"content":{"rendered":"\n<p>\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff08FFT\uff09\u306f\u73fe\u4ee3\u306e\u30c7\u30b8\u30bf\u30eb\u4fe1\u53f7\u51e6\u7406\u306b\u304a\u3051\u308b\u6700\u3082\u91cd\u8981\u306a\u6280\u8853\u306e\u4e00\u3064\u3067\u3059\u3002\u672c\u30ec\u30dd\u30fc\u30c8\u3067\u306f\u3001FFT\u306e\u57fa\u790e\u6982\u5ff5\u304b\u3089\u5fdc\u7528\u4f8b\u307e\u3067\u5e45\u5e83\u304f\u89e3\u8aac\u3057\u3001\u521d\u5fc3\u8005\u306e\u65b9\u306b\u3082\u7406\u89e3\u3057\u3084\u3059\u3044\u3088\u3046\u5177\u4f53\u4f8b\u3092\u4ea4\u3048\u306a\u304c\u3089\u8aac\u660e\u3057\u307e\u3059\u3002FFT\u306f\u79d1\u5b66\u6280\u8853\u8a08\u7b97\u3084\u4fe1\u53f7\u51e6\u7406\u306e\u5206\u91ce\u3067\u5e83\u304f\u5229\u7528\u3055\u308c\u3001\u65e5\u5e38\u751f\u6d3b\u306b\u304a\u3044\u3066\u3082\u97f3\u58f0\u8a8d\u8b58\u3084\u30b9\u30de\u30fc\u30c8\u30d5\u30a9\u30f3\u306e\u30a2\u30d7\u30ea\u306a\u3069\u8eab\u8fd1\u306a\u3068\u3053\u308d\u3067\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>\u203b\u672c\u30da\u30fc\u30b8\u306f\u3001AI\u306e\u6d3b\u7528\u3084\u7814\u7a76\u306b\u95a2\u9023\u3059\u308b\u539f\u7406\u30fb\u6a5f\u5668\u30fb\u30c7\u30d0\u30a4\u30b9\u306b\u3064\u3044\u3066\u5b66\u3076\u305f\u3081\u306b\u3001\u500b\u4eba\u7684\u306b\u6574\u7406\u30fb\u8a18\u8ff0\u3057\u3066\u3044\u308b\u3082\u306e\u3067\u3059\u3002\u5185\u5bb9\u306b\u306f\u8aa4\u308a\u3084\u898b\u843d\u3068\u3057\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u53ef\u80fd\u6027\u3082\u3042\u308a\u307e\u3059\u306e\u3067\u3001\u3082\u3057\u304a\u6c17\u3065\u304d\u306e\u70b9\u3084\u3054\u52a9\u8a00\u7b49\u3054\u3056\u3044\u307e\u3057\u305f\u3089\u3001\u3054\u9023\u7d61\u3044\u305f\u3060\u3051\u307e\u3059\u3068\u5e78\u3044\u3067\u3059\u3002<\/strong><\/p>\n\n\n\n<p><strong>\u203b\u672c\u30da\u30fc\u30b8\u306e\u5185\u5bb9\u306f\u3001\u500b\u4eba\u7684\u306a\u5b66\u7fd2\u304a\u3088\u3073\u60c5\u5831\u6574\u7406\u3092\u76ee\u7684\u3068\u3057\u3066\u63d0\u4f9b\u3057\u3066\u3044\u308b\u3082\u306e\u3067\u3042\u308a\u3001\u305d\u306e\u6b63\u78ba\u6027\u3001\u5b8c\u5168\u6027\u3001\u6709\u7528\u6027\u7b49\u306b\u3064\u3044\u3066\u3044\u304b\u306a\u308b\u4fdd\u8a3c\u3082\u884c\u3044\u307e\u305b\u3093\u3002\u672c\u30da\u30fc\u30b8\u306e\u60c5\u5831\u3092\u5229\u7528\u3057\u305f\u3053\u3068\u3001\u307e\u305f\u306f\u5229\u7528\u3067\u304d\u306a\u304b\u3063\u305f\u3053\u3068\u306b\u3088\u3063\u3066\u767a\u751f\u3057\u305f\u640d\u5bb3\uff08\u76f4\u63a5\u7684\u30fb\u9593\u63a5\u7684\u30fb\u7279\u5225\u30fb\u5076\u767a\u7684\u30fb\u7d50\u679c\u7684\u640d\u5bb3\u3092\u542b\u307f\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306b\u9650\u308a\u307e\u305b\u3093\uff09\u306b\u3064\u3044\u3066\u3001\u5f53\u65b9\u306f\u4e00\u5207\u8cac\u4efb\u3092\u8ca0\u3044\u307e\u305b\u3093\u3002\u3054\u5229\u7528\u306f\u5229\u7528\u8005\u3054\u81ea\u8eab\u306e\u8cac\u4efb\u3067\u304a\u9858\u3044\u3044\u305f\u3057\u307e\u3059\u3002<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-fft\">1. FFT\u3068\u306f\u4f55\u304b\uff08\u5b9a\u7fa9\u30fb\u6982\u8981\uff09<\/h2>\n\n\n\n<p>FFT\u306f\u300cFast Fourier Transform\uff08\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff09\u300d\u306e\u7565\u79f0\u3067\u3059\u3002\u540d\u524d\u306e\u901a\u308a\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3068\u3044\u3046\u6570\u5b66\u7684\u306a\u5909\u63db\u3092\u9ad8\u901f\u306b\u5b9f\u884c\u3059\u308b\u305f\u3081\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08\u8a08\u7b97\u624b\u9806\uff09\u3067\u3059\u3002\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u305d\u306e\u3082\u306e\u306f\u3001\u6642\u9593\u3068\u3068\u3082\u306b\u5909\u5316\u3059\u308b\u4fe1\u53f7\uff08\u6642\u9593\u9818\u57df\u306e\u4fe1\u53f7\uff09\u3092\u3001\u7570\u306a\u308b\u5468\u6ce2\u6570\u6210\u5206\u306e\u96c6\u307e\u308a\u3068\u3057\u3066\u8868\u73fe\u3059\u308b\uff08\u5468\u6ce2\u6570\u9818\u57df\u306b\u5909\u63db\u3059\u308b\uff09\u6570\u5b66\u7684\u624b\u6cd5\u3067\u3059\u3002<\/p>\n\n\n\n<p>FFT\u306f\u305d\u306e\u540d\u306e\u901a\u308a\u3001\u3053\u306e\u5909\u63db\u3092\u300c\u9ad8\u901f\u306b\u300d\u884c\u3046\u305f\u3081\u306e\u65b9\u6cd5\u3067\u3042\u308a\u3001\u7279\u306b\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3092\u4f7f\u3063\u305f\u8a08\u7b97\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u81ea\u4f53\u306f19\u4e16\u7d00\u521d\u982d\u304b\u3089\u77e5\u3089\u308c\u3066\u3044\u307e\u3057\u305f\u304c\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u52b9\u7387\u3088\u304f\u8a08\u7b97\u3059\u308b\u305f\u3081\u306eFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5e83\u304f\u666e\u53ca\u3057\u305f\u306e\u306f20\u4e16\u7d00\u534a\u3070\u4ee5\u964d\u306e\u3053\u3068\u3067\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\">2<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.1 FFT\u306e\u57fa\u672c\u7684\u306a\u5f79\u5272<\/h3>\n\n\n\n<p>FFT\u306e\u4e3b\u306a\u5f79\u5272\u306f\u3001\u6642\u9593\u7684\u306b\u5909\u5316\u3059\u308b\u4fe1\u53f7\uff08\u4f8b\u3048\u3070\u97f3\u58f0\u6ce2\u5f62\u3084\u632f\u52d5\u30c7\u30fc\u30bf\uff09\u3092\u3001\u305d\u308c\u3092\u69cb\u6210\u3059\u308b\u5468\u6ce2\u6570\u6210\u5206\uff08\u3069\u306e\u3088\u3046\u306a\u97f3\u306e\u9ad8\u3055\u3084\u632f\u52d5\u306e\u901f\u3055\u306e\u6210\u5206\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u304b\uff09\u306b\u5206\u89e3\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u5909\u63db\u306b\u3088\u308a\u3001\u6642\u9593\u9818\u57df\u3067\u306f\u898b\u3048\u306b\u304f\u304b\u3063\u305f\u4fe1\u53f7\u306e\u7279\u5fb4\u304c\u3001\u5468\u6ce2\u6570\u9818\u57df\u3067\u306f\u660e\u78ba\u306b\u73fe\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\">2<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.2 \u30c7\u30b8\u30bf\u30eb\u4e16\u754c\u306b\u304a\u3051\u308bFFT\u306e\u4f4d\u7f6e\u3065\u3051<\/h3>\n\n\n\n<p>\u73fe\u4ee3\u306e\u30c7\u30b8\u30bf\u30eb\u6a5f\u5668\u3067\u306f\u3001\u9023\u7d9a\u7684\u306a\u30a2\u30ca\u30ed\u30b0\u4fe1\u53f7\u3092\u30c7\u30b8\u30bf\u30eb\u5316\uff08\u96e2\u6563\u5316\uff09\u3057\u3066\u51e6\u7406\u3057\u307e\u3059\u3002\u3053\u306e\u30c7\u30b8\u30bf\u30eb\u5316\u3055\u308c\u305f\u4fe1\u53f7\u306b\u5bfe\u3057\u3066\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u884c\u3046\u65b9\u6cd5\u304c\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff08DFT\uff09\u3067\u3042\u308a\u3001FFT\u306f\u3053\u306eDFT\u3092\u52b9\u7387\u3088\u304f\u8a08\u7b97\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u3064\u307e\u308a\u3001FFT\u306fDFT\u306e\u4e00\u7a2e\u306e\u300c\u8a08\u7b97\u65b9\u6cd5\u300d\u3067\u3042\u308a\u3001\u8a08\u7b97\u7d50\u679c\u305d\u306e\u3082\u306e\u306fDFT\u3068\u540c\u3058\u3082\u306e\u306b\u306a\u308a\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/ice-tohtech.jp\/nakagawa\/fourier\/dft1_c1.htm\">3<\/a>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2\">2. \u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3068\u305d\u306e\u610f\u7fa9\uff08\u6642\u9593\u9818\u57df\u3068\u5468\u6ce2\u6570\u9818\u57df\u306e\u5909\u63db\uff09<\/h2>\n\n\n\n<p>\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306e\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u3001\u300c\u3069\u3093\u306a\u306b\u8907\u96d1\u306a\u6ce2\u5f62\u3082\u3001\u5358\u7d14\u306a\u6b63\u5f26\u6ce2\uff08\u30b5\u30a4\u30f3\u6ce2\uff09\u3068\u4f59\u5f26\u6ce2\uff08\u30b3\u30b5\u30a4\u30f3\u6ce2\uff09\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u8868\u73fe\u3067\u304d\u308b\u300d\u3068\u3044\u3046\u3082\u306e\u3067\u3059\u3002\u3053\u308c\u306f\u30d5\u30e9\u30f3\u30b9\u306e\u6570\u5b66\u8005\u30b8\u30e7\u30bc\u30d5\u30fb\u30d5\u30fc\u30ea\u30a8\uff08Joseph Fourier\uff09\u304c19\u4e16\u7d00\u521d\u982d\u306b\u767a\u898b\u3057\u305f\u539f\u7406\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 \u6642\u9593\u9818\u57df\u3068\u5468\u6ce2\u6570\u9818\u57df<\/h3>\n\n\n\n<p>\u4fe1\u53f7\u3092\u8868\u73fe\u3059\u308b\u65b9\u6cd5\u306b\u306f\u5927\u304d\u304f\u5206\u3051\u3066\u4e8c\u3064\u306e\u8996\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6642\u9593\u9818\u57df\uff08Time domain\uff09<\/strong>: \u4fe1\u53f7\u306e\u5f37\u3055\uff08\u632f\u5e45\uff09\u304c\u6642\u9593\u3068\u3068\u3082\u306b\u3069\u3046\u5909\u5316\u3059\u308b\u304b\u3092\u8868\u73fe\u3059\u308b\u65b9\u6cd5<\/li>\n\n\n\n<li><strong>\u5468\u6ce2\u6570\u9818\u57df\uff08Frequency domain\uff09<\/strong>: \u4fe1\u53f7\u304c\u3069\u306e\u3088\u3046\u306a\u5468\u6ce2\u6570\u6210\u5206\u304b\u3089\u306a\u308a\u3001\u305d\u308c\u305e\u308c\u306e\u6210\u5206\u304c\u3069\u308c\u304f\u3089\u3044\u306e\u5f37\u3055\uff08\u632f\u5e45\uff09\u3092\u6301\u3063\u3066\u3044\u308b\u304b\u3092\u8868\u73fe\u3059\u308b\u65b9\u6cd5<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u30d4\u30a2\u30ce\u306e\u300c\u30c9\u300d\u306e\u97f3\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u6642\u9593\u9818\u57df\u3067\u306f\u3001\u7a7a\u6c17\u306e\u5727\u529b\u304c\u6642\u9593\u3068\u5171\u306b\u5909\u5316\u3059\u308b\u30d1\u30bf\u30fc\u30f3\uff08\u6ce2\u5f62\uff09\u3068\u3057\u3066\u8868\u3055\u308c\u307e\u3059\u3002\u4e00\u65b9\u3001\u5468\u6ce2\u6570\u9818\u57df\u3067\u306f\u3001\u57fa\u672c\u5468\u6ce2\u6570\uff08\u4f8b\u3048\u3070\u4e2d\u592e\u306e\u30c9\u306a\u3089261.6Hz\uff09\u3068\u305d\u306e\u500d\u97f3\uff08522Hz\u3001783Hz...\uff09\u304c\u7279\u5b9a\u306e\u5f37\u3055\u3067\u5b58\u5728\u3059\u308b\u3068\u3044\u3046\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\">2<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 \u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306e\u610f\u7fa9<\/h3>\n\n\n\n<p>\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306e\u610f\u7fa9\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u307e\u3068\u3081\u3089\u308c\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4fe1\u53f7\u306e\u5206\u6790<\/strong>: \u8907\u96d1\u306a\u4fe1\u53f7\u304b\u3089\u3069\u306e\u3088\u3046\u306a\u5468\u6ce2\u6570\u6210\u5206\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u304b\u3092\u660e\u3089\u304b\u306b\u3059\u308b<\/li>\n\n\n\n<li><strong>\u7279\u5fb4\u62bd\u51fa<\/strong>: \u6642\u9593\u9818\u57df\u3067\u306f\u898b\u3048\u306b\u304f\u3044\u7279\u5fb4\u3092\u5468\u6ce2\u6570\u9818\u57df\u3067\u6349\u3048\u308b<\/li>\n\n\n\n<li><strong>\u4fe1\u53f7\u51e6\u7406\u306e\u52b9\u7387\u5316<\/strong>: \u6642\u9593\u9818\u57df\u3088\u308a\u3082\u5468\u6ce2\u6570\u9818\u57df\u306e\u65b9\u304c\u51e6\u7406\u304c\u5bb9\u6613\u306a\u5834\u5408\u304c\u3042\u308b<\/li>\n\n\n\n<li><strong>\u30ce\u30a4\u30ba\u9664\u53bb<\/strong>: \u4e0d\u8981\u306a\u5468\u6ce2\u6570\u6210\u5206\u3092\u7279\u5b9a\u3057\u3066\u9664\u53bb\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u5de5\u5834\u306e\u6a5f\u68b0\u304b\u3089\u51fa\u308b\u632f\u52d5\u3092\u6e2c\u5b9a\u3057\u305f\u5834\u5408\u3001\u6642\u9593\u9818\u57df\u306e\u30c7\u30fc\u30bf\u3060\u3051\u3067\u306f\u7570\u5e38\u3092\u691c\u51fa\u3059\u308b\u306e\u304c\u96e3\u3057\u3044\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u4f7f\u3063\u3066\u5468\u6ce2\u6570\u6210\u5206\u3092\u5206\u6790\u3059\u308b\u3068\u3001\u6b63\u5e38\u6642\u306b\u306f\u898b\u3089\u308c\u306a\u3044\u7279\u5b9a\u306e\u5468\u6ce2\u6570\u6210\u5206\u304c\u73fe\u308c\u308b\u3053\u3068\u3067\u3001\u6a5f\u68b0\u306e\u6545\u969c\u306e\u4e88\u5146\u3092\u691c\u51fa\u3067\u304d\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\">2<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\">17<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.3 \u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306e\u5177\u4f53\u4f8b<\/h3>\n\n\n\n<p>\u97f3\u58f0\u4fe1\u53f7\u3092\u4f8b\u306b\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u300c\u3042\u300d\u3068\u300c\u3044\u300d\u3068\u3044\u3046\u6bcd\u97f3\u306f\u3001\u6642\u9593\u9818\u57df\u3067\u306f\u7570\u306a\u308b\u6ce2\u5f62\u3068\u3057\u3066\u73fe\u308c\u307e\u3059\u304c\u3001\u306a\u305c\u805e\u304d\u5206\u3051\u3089\u308c\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u305d\u308c\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u97f3\u304c\u7570\u306a\u308b\u5468\u6ce2\u6570\u6210\u5206\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u304b\u3089\u3067\u3059\u3002\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u4f7f\u3046\u3068\u3001\u300c\u3042\u300d\u3068\u300c\u3044\u300d\u306e\u97f3\u58f0\u4fe1\u53f7\u304b\u3089\u3001\u305d\u308c\u305e\u308c\u7279\u5fb4\u7684\u306a\u5468\u6ce2\u6570\u6210\u5206\uff08\u30d5\u30a9\u30eb\u30de\u30f3\u30c8\u5468\u6ce2\u6570\uff09\u3092\u62bd\u51fa\u3067\u304d\u3001\u3053\u308c\u304c\u97f3\u58f0\u8a8d\u8b58\u6280\u8853\u306e\u57fa\u790e\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-dft\">3. DFT\uff08\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff09\u3068\u306e\u95a2\u4fc2\u3068\u9055\u3044<\/h2>\n\n\n\n<p>FFT\u3092\u7406\u89e3\u3059\u308b\u4e0a\u3067\u91cd\u8981\u306a\u306e\u306f\u3001DFT\uff08Discrete Fourier Transform\u3001\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff09\u3068\u306e\u95a2\u4fc2\u3092\u660e\u78ba\u306b\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 DFT\u306e\u5b9a\u7fa9<\/h3>\n\n\n\n<p>DFT\u306f\u3001\u96e2\u6563\u5316\uff08\u30c7\u30b8\u30bf\u30eb\u5316\uff09\u3055\u308c\u305f\u6709\u9650\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u306b\u5bfe\u3059\u308b\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3067\u3059\u3002\u30a2\u30ca\u30ed\u30b0\u4fe1\u53f7\u3092\u30c7\u30b8\u30bf\u30eb\u5316\uff08\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\uff09\u3059\u308b\u3068\u3001\u9023\u7d9a\u7684\u306a\u4fe1\u53f7\u304c\u96e2\u6563\u7684\u306a\u30c7\u30fc\u30bf\u70b9\u306e\u96c6\u307e\u308a\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u30c7\u30b8\u30bf\u30eb\u5316\u3055\u308c\u305f\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u9069\u7528\u3059\u308b\u65b9\u6cd5\u304cDFT\u3067\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\">7<\/a>\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u30011\u79d2\u9593\u306e\u97f3\u58f0\u4fe1\u53f7\u309244.1kHz\u3067\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b\u3068\u300144,100\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u5f97\u3089\u308c\u307e\u3059\u3002DFT\u306f\u3053\u306e44,100\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u306b\u5bfe\u3057\u3066\u3001\u305d\u308c\u306b\u542b\u307e\u308c\u308b\u5468\u6ce2\u6570\u6210\u5206\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2 FFT\u3068DFT\u306e\u95a2\u4fc2<\/h3>\n\n\n\n<p>FFT\u3068DFT\u306e\u95a2\u4fc2\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u307e\u3068\u3081\u3089\u308c\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u7d50\u679c\u306e\u540c\u4e00\u6027<\/strong>: FFT\u3068DFT\u306f\u8a08\u7b97\u7d50\u679c\u304c\u540c\u3058\u3067\u3059\u3002\u3069\u3061\u3089\u3082\u540c\u3058\u5468\u6ce2\u6570\u30b9\u30da\u30af\u30c8\u30eb\u3092\u751f\u6210\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u8a08\u7b97\u65b9\u6cd5\u306e\u9055\u3044<\/strong>: FFT\u306fDFT\u3092\u9ad8\u901f\u306b\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u3064\u307e\u308a\u3001FFT\u306fDFT\u306e\u4e00\u7a2e\u306e\u300c\u89e3\u6cd5\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5236\u7d04\u306e\u9055\u3044<\/strong>: DFT\u306f\u3069\u306e\u3088\u3046\u306a\u30b5\u30a4\u30ba\u306e\u30c7\u30fc\u30bf\u306b\u3082\u9069\u7528\u3067\u304d\u307e\u3059\u304c\u3001FFT\uff08\u7279\u306b\u57fa\u672c\u7684\u306aCooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff09\u306f\u901a\u5e38\u3001\u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c2\u306e\u3079\u304d\u4e57\uff08256, 512, 1024\u306a\u3069\uff09\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/ice-tohtech.jp\/nakagawa\/fourier\/dft1_c1.htm\" target=\"_blank\" rel=\"noreferrer noopener\">3<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001100\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u306b\u5bfe\u3057\u3066\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u884c\u3046\u5834\u5408\u3001DFT\u306f\u76f4\u63a5\u8a08\u7b97\u3067\u304d\u307e\u3059\u304c\u3001\u57fa\u672c\u7684\u306aFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u9069\u7528\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u5de5\u592b\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.3 \u306a\u305cFFT\u304c\u5fc5\u8981\u306a\u306e\u304b<\/h3>\n\n\n\n<p>DFT\u3092\u7d20\u76f4\u306b\u8a08\u7b97\u3059\u308b\u3068\u3001\u30c7\u30fc\u30bf\u70b9\u306e\u6570\u3092N\u3068\u3057\u305f\u5834\u5408\u3001\u8a08\u7b97\u91cf\u306fO(N\u00b2)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001N\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u305d\u308c\u305e\u308c\u306b\u5bfe\u3057\u3066\u3001N\u56de\u306e\u8907\u7d20\u6570\u8a08\u7b97\u304c\u5fc5\u8981\u306b\u306a\u308b\u305f\u3081\u3067\u3059\u3002\u4f8b\u3048\u3070\u30011,024\u70b9\u306eDFT\u3092\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u3068\u3001\u7d04100\u4e07\u56de\u306e\u8a08\u7b97\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>FFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u3046\u3068\u3001\u8a08\u7b97\u91cf\u3092O(N log N)\u306b\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002\u540c\u30581,024\u70b9\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001FFT\u3067\u306f\u7d0410,000\u56de\u306e\u8a08\u7b97\u3067\u6e08\u307f\u307e\u3059\u3002\u30c7\u30fc\u30bf\u70b9\u304c\u591a\u304f\u306a\u308b\u307b\u3069\u3001FFT\u306e\u52b9\u7387\u306e\u826f\u3055\u304c\u969b\u7acb\u3061\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\">7<\/a>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-fftcooley-tukey\">4. FFT\u306e\u6b74\u53f2\u30fb\u767a\u5c55\uff08\u4ee3\u8868\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7d39\u4ecb\uff1aCooley-Tukey\u306a\u3069\uff09<\/h2>\n\n\n\n<p>FFT\u306e\u6982\u5ff5\u306f\u610f\u5916\u306b\u3082\u53e4\u3044\u6b74\u53f2\u3092\u6301\u3061\u307e\u3059\u304c\u3001\u305d\u306e\u91cd\u8981\u6027\u304c\u5e83\u304f\u8a8d\u8b58\u3055\u308c\u305f\u306e\u306f\u6bd4\u8f03\u7684\u6700\u8fd1\u306e\u3053\u3068\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 \u30ac\u30a6\u30b9\u306b\u3088\u308b\u5148\u99c6\u7684\u7814\u7a76<\/h3>\n\n\n\n<p>\u5b9f\u306f\u3001FFT\u306e\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u306f1805\u5e74\u9803\u306b\u6570\u5b66\u8005\u30ab\u30fc\u30eb\u30fb\u30d5\u30ea\u30fc\u30c9\u30ea\u30d2\u30fb\u30ac\u30a6\u30b9\uff08Carl Friedrich Gauss\uff09\u306b\u3088\u3063\u3066\u767a\u898b\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002\u30ac\u30a6\u30b9\u306f\u5c0f\u60d1\u661f\u30d1\u30e9\u30b9\u3068\u30e6\u30ce\u30fc\u306e\u8ecc\u9053\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u3001\u3053\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u5f7c\u306e\u7814\u7a76\u306f\u30e9\u30c6\u30f3\u8a9e\u3067\u66f8\u304b\u308c\u3001\u5f7c\u306e\u6b7b\u5f8c\u306b\u767a\u8868\u3055\u308c\u305f\u305f\u3081\u3001\u9577\u3044\u9593\u6ce8\u76ee\u3055\u308c\u307e\u305b\u3093\u3067\u3057\u305f<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Cooley%E2%80%93Tukey_FFT_algorithm\">12<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.2 Cooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u767a\u898b<\/h3>\n\n\n\n<p>FFT\u304c\u73fe\u4ee3\u7684\u306a\u610f\u5473\u3067\u91cd\u8981\u306b\u306a\u3063\u305f\u306e\u306f\u30011965\u5e74\u306bIBM\u306e\u30b8\u30a7\u30fc\u30e0\u30ba\u30fb\u30af\u30fc\u30ea\u30fc\uff08James Cooley\uff09\u3068\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u5927\u5b66\u306e\u30b8\u30e7\u30f3\u30fb\u30c6\u30e5\u30fc\u30ad\u30fc\uff08John Tukey\uff09\u304c\u8ad6\u6587\u3092\u767a\u8868\u3057\u3066\u304b\u3089\u3067\u3059\u3002\u5f7c\u3089\u306f\u52b9\u7387\u7684\u306aFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u958b\u767a\u3057\u3001\u305d\u308c\u304c\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4e0a\u3067\u5b9f\u884c\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\u3002\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4eca\u65e5\u3067\u3082\u300cCooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\">2<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Cooley%E2%80%93Tukey_FFT_algorithm\">12<\/a>\u3002<\/p>\n\n\n\n<p>\u8208\u5473\u6df1\u3044\u3053\u3068\u306b\u3001\u30c6\u30e5\u30fc\u30ad\u30fc\u304c\u3053\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u601d\u3044\u3064\u3044\u305f\u306e\u306f\u3001\u30b1\u30cd\u30c7\u30a3\u5927\u7d71\u9818\u306e\u79d1\u5b66\u8aee\u554f\u59d4\u54e1\u4f1a\u306e\u4f1a\u8b70\u4e2d\u3060\u3063\u305f\u3068\u8a00\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u306f\u3001\u30bd\u9023\u306e\u6838\u5b9f\u9a13\u3092\u691c\u51fa\u3059\u308b\u305f\u3081\u306b\u5730\u9707\u8a08\u30c7\u30fc\u30bf\u3092\u5206\u6790\u3059\u308b\u65b9\u6cd5\u304c\u8b70\u8ad6\u3055\u308c\u3066\u3044\u307e\u3057\u305f<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Cooley%E2%80%93Tukey_FFT_algorithm\">12<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.3 FFT\u306e\u666e\u53ca\u3068\u767a\u5c55<\/h3>\n\n\n\n<p>Cooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u767a\u8868\u5f8c\u3001FFT\u306f\u6025\u901f\u306b\u666e\u53ca\u3057\u307e\u3057\u305f\u30021970\u5e74\u4ee3\u306b\u306a\u308b\u3068\u3001FFT\u3092\u5b9f\u88c5\u3057\u305f\u5c02\u7528\u306e\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\uff08FFT\u30a2\u30ca\u30e9\u30a4\u30b6\u30fc\uff09\u3082\u767b\u5834\u3057\u3001\u97f3\u97ff\u30fb\u632f\u52d5\u89e3\u6790\u306a\u3069\u306e\u5206\u91ce\u3067\u5e83\u304f\u5229\u7528\u3055\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u305d\u306e\u5f8c\u3082\u3001\u69d8\u3005\u306a\u6539\u826f\u7248\u306eFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u958b\u767a\u3055\u308c\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u57fa\u65704FFT\uff08Radix-4 FFT\uff09<\/strong>: \u30c7\u30fc\u30bf\u30924\u3064\u305a\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u3066\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/li>\n\n\n\n<li><strong>\u5206\u5272\u57fa\u6570FFT\uff08Split-Radix FFT\uff09<\/strong>: \u57fa\u65702\u3068\u57fa\u65704\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u65b9\u6cd5<\/li>\n\n\n\n<li><strong>\u30d7\u30e9\u30a4\u30e0\u30d5\u30a1\u30af\u30bf\u30fcFFT<\/strong>: \u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c\u7d20\u56e0\u6570\u5206\u89e3\u3067\u304d\u308b\u5834\u5408\u306b\u52b9\u7387\u7684\u306a\u65b9\u6cd5<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u7279\u5b9a\u306e\u6761\u4ef6\u4e0b\u3067\u3088\u308a\u52b9\u7387\u7684\u306a\u8a08\u7b97\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html\">4<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn1_2.html\">8<\/a>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-fftin-place2\">5. FFT\u306e\u8a08\u7b97\u539f\u7406\u30fb\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u57fa\u672c\uff08\u5206\u5272\u7d71\u6cbb\u6cd5\u3001\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u3001In-Place\u6f14\u7b97\u30012\u306e\u3079\u304d\u4e57\uff09<\/h2>\n\n\n\n<p>FFT\u306e\u8a08\u7b97\u539f\u7406\u306f\u3001\u4e00\u898b\u8907\u96d1\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u3044\u304f\u3064\u304b\u306e\u57fa\u672c\u7684\u306a\u6982\u5ff5\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.1 \u5206\u5272\u7d71\u6cbb\u6cd5\u306e\u9069\u7528<\/h3>\n\n\n\n<p>FFT\u306e\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u306f\u300c\u5206\u5272\u7d71\u6cbb\u6cd5\uff08Divide and Conquer\uff09\u300d\u3068\u547c\u3070\u308c\u308b\u554f\u984c\u89e3\u6c7a\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3059\u3002\u5927\u304d\u306a\u554f\u984c\u3092\u5c0f\u3055\u306a\u554f\u984c\u306b\u5206\u5272\u3057\u3001\u305d\u308c\u3089\u3092\u89e3\u3044\u3066\u304b\u3089\u7d50\u679c\u3092\u7d71\u5408\u3059\u308b\u3053\u3068\u3067\u3001\u5168\u4f53\u306e\u554f\u984c\u3092\u52b9\u7387\u7684\u306b\u89e3\u6c7a\u3057\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html\">4<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn1_2.html\">8<\/a>\u3002<\/p>\n\n\n\n<p>FFT\u306e\u5834\u5408\u3001N\u70b9\u306eDFT\u8a08\u7b97\u3092\u3001\u534a\u5206\u306e\u30b5\u30a4\u30ba\u306e2\u3064\u306eDFT\u8a08\u7b97\u306b\u5206\u5272\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u305d\u308c\u3089\u3082\u534a\u5206\u306e\u30b5\u30a4\u30ba\u306b\u5206\u5272\u3057\u3066\u3044\u304d\u3001\u6700\u7d42\u7684\u306b\u8a08\u7b97\u304c\u975e\u5e38\u306b\u5358\u7d14\u306b\u306a\u308b\u307e\u3067\u5206\u5272\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u305d\u306e\u7d50\u679c\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u5143\u306e\u554f\u984c\u306e\u89e3\u3092\u5f97\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html\">4<\/a>\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u30018\u70b9\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308bDFT\u3092\u8a08\u7b97\u3059\u308b\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u5206\u5272\u3067\u304d\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>8\u70b9\u306eDFT \u2192 \u5076\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e4\u70b9\u306eDFT\u3068\u5947\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e4\u70b9\u306eDFT<\/li>\n\n\n\n<li>4\u70b9\u306eDFT \u2192 \u5076\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e2\u70b9\u306eDFT\u3068\u5947\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e2\u70b9\u306eDFT<\/li>\n\n\n\n<li>2\u70b9\u306eDFT \u2192 \u3053\u308c\u306f\u5358\u7d14\u306a\u52a0\u7b97\u3068\u6e1b\u7b97\u3067\u8a08\u7b97\u53ef\u80fd<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">5.2 \u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97<\/h3>\n\n\n\n<p>FFT\u306e\u8a08\u7b97\u904e\u7a0b\u3067\u884c\u308f\u308c\u308b\u57fa\u672c\u7684\u306a\u6f14\u7b97\u306f\u300c\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u300d\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u306e\u540d\u524d\u306f\u3001\u8a08\u7b97\u306e\u6d41\u308c\u56f3\u304c\u8776\u306e\u7fbd\u306e\u3088\u3046\u306a\u5f62\u306b\u306a\u308b\u3053\u3068\u306b\u7531\u6765\u3057\u3066\u3044\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a>\u3002<\/p>\n\n\n\n<p>\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u306f\u30012\u3064\u306e\u5165\u529b\u5024\u304b\u30892\u3064\u306e\u51fa\u529b\u5024\u3092\u8a08\u7b97\u3059\u308b\u6f14\u7b97\u3067\u3001\u57fa\u672c\u5f62\u306f\u6b21\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5165\u529b\u5024\uff1aa, b<\/li>\n\n\n\n<li>\u51fa\u529b\u5024\uff1aa+b, (a-b)\u00d7W<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u3053\u3067\u3001W\u306f\u300c\u56de\u8ee2\u56e0\u5b50\uff08twiddle factor\uff09\u300d\u3068\u547c\u3070\u308c\u308b\u8907\u7d20\u6570\u3067\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a>\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u304c\u3001FFT\u8a08\u7b97\u306e\u57fa\u790e\u3068\u306a\u308a\u307e\u3059\u3002FFT\u5168\u4f53\u306f\u3001\u591a\u6570\u306e\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u3092\u9069\u5207\u306a\u9806\u5e8f\u3067\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.3 In-Place\u6f14\u7b97<\/h3>\n\n\n\n<p>FFT\u306e\u3082\u3046\u4e00\u3064\u306e\u91cd\u8981\u306a\u7279\u5fb4\u306f\u300cIn-Place\u6f14\u7b97\u300d\u304c\u53ef\u80fd\u306a\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u8a08\u7b97\u306e\u904e\u7a0b\u3067\u8ffd\u52a0\u306e\u30e1\u30e2\u30ea\u9818\u57df\u3092\u307b\u3068\u3093\u3069\u5fc5\u8981\u3068\u305b\u305a\u3001\u5165\u529b\u30c7\u30fc\u30bf\u304c\u683c\u7d0d\u3055\u308c\u3066\u3044\u308b\u540c\u3058\u30e1\u30e2\u30ea\u9818\u57df\u306b\u7d50\u679c\u3092\u4e0a\u66f8\u304d\u3067\u304d\u308b\u3068\u3044\u3046\u6027\u8cea\u3067\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a>\u3002<\/p>\n\n\n\n<p>\u3053\u306eIn-Place\u6f14\u7b97\u306e\u6027\u8cea\u306b\u3088\u308a\u3001FFT\u306f\u30e1\u30e2\u30ea\u306e\u4f7f\u7528\u52b9\u7387\u304c\u826f\u304f\u3001\u9650\u3089\u308c\u305f\u30e1\u30e2\u30ea\u30ea\u30bd\u30fc\u30b9\u3067\u3082\u5927\u898f\u6a21\u306a\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306a\u8a08\u7b97\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30e1\u30e2\u30ea\u304b\u3089\u5024a, b\u3092\u8aad\u307f\u8fbc\u3080<\/li>\n\n\n\n<li>a' = a+b, b' = (a-b)\u00d7W\u3092\u8a08\u7b97<\/li>\n\n\n\n<li>\u7d50\u679ca', b'\u3092\u540c\u3058\u30e1\u30e2\u30ea\u4f4d\u7f6e\u306b\u683c\u7d0d<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u5143\u306e\u30c7\u30fc\u30bf\u3092\u4e0a\u66f8\u304d\u3057\u306a\u304c\u3089\u8a08\u7b97\u3092\u9032\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.4 2\u306e\u3079\u304d\u4e57\u306e\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba<\/h3>\n\n\n\n<p>\u57fa\u672c\u7684\u306aFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08\u7279\u306bCooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff09\u306f\u3001\u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c2\u306e\u3079\u304d\u4e57\uff082, 4, 8, 16, 32, 64, 128, 256, 512, 1024\u306a\u3069\uff09\u3067\u3042\u308b\u5834\u5408\u306b\u6700\u3082\u52b9\u7387\u7684\u306b\u52d5\u4f5c\u3057\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/ice-tohtech.jp\/nakagawa\/fourier\/dft1_c1.htm\">3<\/a>\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u306f\u3001FFT\u306e\u5206\u5272\u7d71\u6cbb\u30a2\u30d7\u30ed\u30fc\u30c1\u304c\u3001\u30c7\u30fc\u30bf\u3092\u5747\u7b49\u306b\u534a\u5206\u305a\u3064\u306b\u5206\u5272\u3059\u308b\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002\u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c2\u306e\u3079\u304d\u4e57\u3067\u306a\u3044\u5834\u5408\u3001\u5747\u7b49\u306a\u5206\u5272\u304c\u3067\u304d\u306a\u304f\u306a\u308a\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5909\u66f4\u3084\u8ffd\u52a0\u306e\u51e6\u7406\uff08\u4f8b\u3048\u3070\u30bc\u30ed\u30d1\u30c7\u30a3\u30f3\u30b0\uff09\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001100\u70b9\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066FFT\u3092\u9069\u7528\u3057\u305f\u3044\u5834\u5408\u3001128\u70b9\u306b\u306a\u308b\u3088\u3046\u306b\u30bc\u30ed\u3092\u8ffd\u52a0\uff08\u30bc\u30ed\u30d1\u30c7\u30a3\u30f3\u30b0\uff09\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-on2on-log-n\">6. \u8a08\u7b97\u91cf\u30fb\u8a08\u7b97\u52b9\u7387\uff08O(N^2)\u304b\u3089O(N log N)\u3078\u306e\u524a\u6e1b\uff09<\/h2>\n\n\n\n<p>FFT\u306e\u6700\u5927\u306e\u5229\u70b9\u306f\u3001\u8a08\u7b97\u52b9\u7387\u306e\u5927\u5e45\u306a\u5411\u4e0a\u3067\u3059\u3002\u3053\u3053\u3067\u306f\u3001FFT\u304c\u3069\u308c\u3060\u3051\u8a08\u7b97\u91cf\u3092\u524a\u6e1b\u3067\u304d\u308b\u304b\u3092\u5177\u4f53\u7684\u306b\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.1 DFT\u306e\u8a08\u7b97\u91cf<\/h3>\n\n\n\n<p>\u307e\u305a\u3001DFT\u3092\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u5834\u5408\u306e\u8a08\u7b97\u91cf\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002N\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u306b\u5bfe\u3059\u308bDFT\u306e\u5b9a\u7fa9\u306b\u5f93\u3063\u3066\u7d20\u76f4\u306b\u8a08\u7b97\u3059\u308b\u3068\u3001\u5404\u51fa\u529b\u30dd\u30a4\u30f3\u30c8\uff08N\u500b\uff09\u306b\u5bfe\u3057\u3066N\u56de\u306e\u8907\u7d20\u6570\u4e57\u7b97\u3068\u52a0\u7b97\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5168\u4f53\u306e\u8a08\u7b97\u91cf\u306fO(N\u00b2)\u3068\u306a\u308a\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\">7<\/a>\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u7684\u306a\u4f8b\u3068\u3057\u3066\u30011,024\u70b9\u306eDFT\u3092\u8a08\u7b97\u3059\u308b\u5834\u5408\u3001\u7d04100\u4e07\u56de\uff081,024\u00b2\uff09\u306e\u8907\u7d20\u6570\u6f14\u7b97\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c\u5897\u3048\u308b\u3068\u3001\u8a08\u7b97\u91cf\u306f\u4e8c\u6b21\u95a2\u6570\u7684\u306b\u5897\u5927\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.2 FFT\u306b\u3088\u308b\u8a08\u7b97\u91cf\u306e\u524a\u6e1b<\/h3>\n\n\n\n<p>FFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u3046\u3068\u3001\u8a08\u7b97\u91cf\u3092O(N log\u2082 N)\u306b\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5206\u5272\u7d71\u6cbb\u6cd5\u306b\u3088\u308a\u3001\u8a08\u7b97\u306e\u91cd\u8907\u3092\u907f\u3051\u3066\u3044\u308b\u305f\u3081\u3067\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html\">4<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a>\u3002<\/p>\n\n\n\n<p>\u540c\u30581,024\u70b9\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001FFT\u3067\u306f\u7d0410,000\u56de\uff081,024\u00d7log\u2082 1,024 = 1,024\u00d710\uff09\u306e\u8907\u7d20\u6570\u6f14\u7b97\u3067\u6e08\u307f\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u76f4\u63a5\u8a08\u7b97\u306e\u7d041\/100\u306e\u8a08\u7b97\u91cf\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c\u5897\u3048\u308b\u307b\u3069\u3001FFT\u306e\u52b9\u7387\u306e\u826f\u3055\u306f\u969b\u7acb\u3061\u307e\u3059\u3002\u4f8b\u3048\u3070\u300116,384\u70b9\uff082\u00b9\u2074\uff09\u306e\u5834\u5408\u3001\u76f4\u63a5\u8a08\u7b97\u3067\u306f\u7d042.7\u5104\u56de\u306e\u6f14\u7b97\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001FFT\u3067\u306f\u7d0423\u4e07\u56de\u3067\u6e08\u307f\u3001\u7d041\/2,300\u306b\u524a\u6e1b\u3055\u308c\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.3 \u5b9f\u969b\u306e\u8a08\u7b97\u6642\u9593\u306e\u6bd4\u8f03<\/h3>\n\n\n\n<p>\u8a08\u7b97\u91cf\u306e\u9055\u3044\u306f\u3001\u5b9f\u969b\u306e\u8a08\u7b97\u6642\u9593\u306b\u3082\u5927\u304d\u304f\u53cd\u6620\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u73fe\u4ee3\u306e\u30d1\u30fc\u30bd\u30ca\u30eb\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30671,024\u70b9\u306eDFT\u3092\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u3068\u6570\u79d2\u304b\u304b\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u304c\u3001FFT\u3092\u4f7f\u3046\u3068\u6570\u30df\u30ea\u79d2\u3067\u5b8c\u4e86\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u8a08\u7b97\u52b9\u7387\u306e\u5411\u4e0a\u306b\u3088\u308a\u3001\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u4fe1\u53f7\u51e6\u7406\u3001\u5927\u898f\u6a21\u30c7\u30fc\u30bf\u5206\u6790\u3001\u9ad8\u901f\u753b\u50cf\u51e6\u7406\u306a\u3069\u3001\u591a\u304f\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u304c\u5b9f\u7528\u5316\u3055\u308c\u307e\u3057\u305f\u3002\u30b9\u30de\u30fc\u30c8\u30d5\u30a9\u30f3\u306e\u97f3\u58f0\u8a8d\u8b58\u3084\u3001\u30c7\u30b8\u30bf\u30eb\u30ab\u30e1\u30e9\u306e\u753b\u50cf\u51e6\u7406\u306a\u3069\u3082\u3001FFT\u306e\u9ad8\u901f\u6027\u306e\u6069\u6075\u3092\u53d7\u3051\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.4 \u8a08\u7b97\u52b9\u7387\u5411\u4e0a\u306e\u30e1\u30ab\u30cb\u30ba\u30e0<\/h3>\n\n\n\n<p>FFT\u304c\u8a08\u7b97\u91cf\u3092\u524a\u6e1b\u3067\u304d\u308b\u7406\u7531\u306f\u3001\u300c\u5bfe\u79f0\u6027\u306e\u5229\u7528\u300d\u3068\u300c\u4e2d\u9593\u7d50\u679c\u306e\u518d\u5229\u7528\u300d\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u30018\u70b9\u306eDFT\u3092\u8003\u3048\u305f\u5834\u5408\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u76f4\u63a5\u8a08\u7b97\u3067\u306f8\u00d78=64\u56de\u306e\u8907\u7d20\u6570\u6f14\u7b97\u304c\u5fc5\u8981<\/li>\n\n\n\n<li>FFT\u3067\u306f3\u6bb5\u968e\uff08log\u2082 8=3\uff09\u306e\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u3092\u884c\u3044\u3001\u5404\u6bb5\u968e\u30678\/2=4\u500b\u306e\u30d0\u30bf\u30d5\u30e9\u30a4\uff08\u5404\u30d0\u30bf\u30d5\u30e9\u30a4\u30671\u56de\u306e\u8907\u7d20\u6570\u4e57\u7b97\uff09\u3001\u5408\u8a0812\u56de\u306e\u8907\u7d20\u6570\u6f14\u7b97\u3067\u6e08\u3080<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u3001FFT\u3067\u306f\u4e2d\u9593\u7d50\u679c\u3092\u52b9\u7387\u7684\u306b\u518d\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u91cd\u8907\u3057\u305f\u8a08\u7b97\u3092\u907f\u3051\u3001\u5168\u4f53\u306e\u8a08\u7b97\u91cf\u3092\u5927\u5e45\u306b\u524a\u6e1b\u3057\u3066\u3044\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html\">4<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-fftiot\">7. FFT\u306e\u4e3b\u306a\u7528\u9014\u30fb\u5fdc\u7528\u4f8b\uff08\u97f3\u58f0\u51e6\u7406\u3001\u753b\u50cf\u51e6\u7406\u3001\u632f\u52d5\u89e3\u6790\u3001\u7570\u5e38\u691c\u77e5\u3001IoT\u306a\u3069\uff09<\/h2>\n\n\n\n<p>FFT\u306f\u975e\u5e38\u306b\u5e83\u3044\u5206\u91ce\u3067\u5fdc\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001FFT\u306e\u4e3b\u8981\u306a\u5fdc\u7528\u5206\u91ce\u3068\u5177\u4f53\u7684\u306a\u4f7f\u7528\u4f8b\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">7.1 \u97f3\u97ff\u30fb\u97f3\u58f0\u51e6\u7406<\/h3>\n\n\n\n<p>\u97f3\u58f0\u51e6\u7406\u306fFFT\u306e\u6700\u3082\u4e00\u822c\u7684\u306a\u5fdc\u7528\u5206\u91ce\u306e\u4e00\u3064\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u97f3\u58f0\u8a8d\u8b58<\/strong>: \u30b9\u30de\u30fc\u30c8\u30d5\u30a9\u30f3\u306e\u97f3\u58f0\u30a2\u30b7\u30b9\u30bf\u30f3\u30c8\uff08Siri\u3084Google Assistant\uff09\u306f\u3001\u5165\u529b\u3055\u308c\u305f\u97f3\u58f0\u3092FFT\u3067\u5468\u6ce2\u6570\u5206\u6790\u3057\u3001\u7279\u5fb4\u3092\u62bd\u51fa\u3059\u308b\u3053\u3068\u3067\u8a8d\u8b58\u3092\u884c\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u97f3\u697d\u5206\u6790<\/strong>: \u97f3\u697d\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u3067\u306f\u3001FFT\u3092\u4f7f\u3063\u3066\u97f3\u697d\u306e\u5468\u6ce2\u6570\u30b9\u30da\u30af\u30c8\u30eb\u3092\u5206\u6790\u3057\u3001\u30d3\u30fc\u30c8\u691c\u51fa\u3001\u81ea\u52d5\u8abf\u5f8b\u3001\u697d\u5668\u306e\u8b58\u5225\u306a\u3069\u3092\u884c\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30aa\u30fc\u30c7\u30a3\u30aa\u30a4\u30b3\u30e9\u30a4\u30b6\u30fc<\/strong>: \u30a4\u30e4\u30db\u30f3\u3084\u30b9\u30d4\u30fc\u30ab\u30fc\u306e\u30a4\u30b3\u30e9\u30a4\u30b6\u30fc\u8a2d\u5b9a\u306f\u3001FFT\u3067\u97f3\u58f0\u3092\u5468\u6ce2\u6570\u5e2f\u57df\u306b\u5206\u89e3\u3057\u3001\u5404\u5e2f\u57df\u306e\u97f3\u91cf\u3092\u8abf\u6574\u3057\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\" target=\"_blank\" rel=\"noreferrer noopener\">2<\/a><a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a><a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">7.2 \u753b\u50cf\u51e6\u7406\u30fb\u5727\u7e2e<\/h3>\n\n\n\n<p>FFT\u306f\u4e8c\u6b21\u5143\u306b\u62e1\u5f35\u3057\u3066\u3001\u753b\u50cf\u51e6\u7406\u306b\u3082\u5e83\u304f\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u753b\u50cf\u5727\u7e2e<\/strong>: JPEG\u306a\u3069\u306e\u753b\u50cf\u5727\u7e2e\u5f62\u5f0f\u3067\u306f\u3001\u753b\u50cf\u3092\u30d6\u30ed\u30c3\u30af\u306b\u5206\u5272\u3057\u3001\u5404\u30d6\u30ed\u30c3\u30af\u306b\u5bfe\u3057\u3066FFT\u306b\u4f3c\u305f\u96e2\u6563\u30b3\u30b5\u30a4\u30f3\u5909\u63db\uff08DCT\uff09\u3092\u9069\u7528\u3057\u3001\u91cd\u8981\u3067\u306a\u3044\u5468\u6ce2\u6570\u6210\u5206\u3092\u524a\u9664\u3059\u308b\u3053\u3068\u3067\u5727\u7e2e\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0<\/strong>: \u30ce\u30a4\u30ba\u9664\u53bb\u3084\u753b\u50cf\u5f37\u8abf\u306e\u305f\u3081\u306b\u3001FFT\u3092\u4f7f\u3063\u3066\u753b\u50cf\u3092\u5468\u6ce2\u6570\u9818\u57df\u306b\u5909\u63db\u3057\u3001\u7279\u5b9a\u306e\u5468\u6ce2\u6570\u6210\u5206\u3092\u64cd\u4f5c\u3057\u305f\u5f8c\u3001\u9006\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u753b\u50cf\u8a8d\u8b58<\/strong>: \u4e00\u90e8\u306e\u753b\u50cf\u8a8d\u8b58\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306f\u3001FFT\u3092\u4f7f\u3063\u3066\u753b\u50cf\u306e\u7279\u5fb4\u62bd\u51fa\u3092\u884c\u3044\u307e\u3059<a href=\"https:\/\/arxiv.org\/abs\/1708.08917\" target=\"_blank\" rel=\"noreferrer noopener\">1<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">7.3 \u632f\u52d5\u89e3\u6790\u30fb\u7570\u5e38\u691c\u77e5<\/h3>\n\n\n\n<p>\u5de5\u5b66\u5206\u91ce\u3067\u306f\u3001FFT\u3092\u4f7f\u3063\u305f\u632f\u52d5\u89e3\u6790\u304c\u4e0d\u53ef\u6b20\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6a5f\u68b0\u306e\u72b6\u614b\u76e3\u8996<\/strong>: \u5de5\u5834\u306e\u6a5f\u68b0\u304b\u3089\u53ce\u96c6\u3057\u305f\u632f\u52d5\u30c7\u30fc\u30bf\u306bFFT\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u6a5f\u68b0\u306e\u7570\u5e38\u3092\u65e9\u671f\u306b\u691c\u51fa\u3067\u304d\u307e\u3059\u3002\u7279\u5b9a\u306e\u5468\u6ce2\u6570\u306b\u7570\u5e38\u306a\u30d4\u30fc\u30af\u304c\u73fe\u308c\u308b\u3068\u3001\u8ef8\u53d7\u306e\u6469\u8017\u3084\u90e8\u54c1\u306e\u7834\u640d\u306e\u4e88\u5146\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/li>\n\n\n\n<li><strong>\u69cb\u9020\u7269\u306e\u632f\u52d5\u8a66\u9a13<\/strong>: \u5efa\u7269\u3084\u6a4b\u306a\u3069\u306e\u69cb\u9020\u7269\u306e\u632f\u52d5\u7279\u6027\u3092\u5206\u6790\u3059\u308b\u305f\u3081\u306b\u3001FFT\u304c\u4f7f\u308f\u308c\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5730\u9707\u3084\u98a8\u306b\u5bfe\u3059\u308b\u5b89\u5168\u6027\u3092\u8a55\u4fa1\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u81ea\u52d5\u8eca\u306e\u54c1\u8cea\u7ba1\u7406<\/strong>: \u81ea\u52d5\u8eca\u30e1\u30fc\u30ab\u30fc\u3067\u306f\u3001\u30a8\u30f3\u30b8\u30f3\u3084\u30c9\u30e9\u30a4\u30d6\u30c8\u30ec\u30a4\u30f3\u306e\u632f\u52d5\u3092FFT\u3067\u5206\u6790\u3057\u3001\u88fd\u9020\u54c1\u8cea\u3092\u78ba\u8a8d\u3057\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\" target=\"_blank\" rel=\"noreferrer noopener\">2<\/a><a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">7.4 \u901a\u4fe1\u6280\u8853<\/h3>\n\n\n\n<p>\u901a\u4fe1\u5206\u91ce\u3067\u306f\u3001FFT\u304c\u57fa\u76e4\u6280\u8853\u3068\u306a\u3063\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u7121\u7dda\u901a\u4fe1\uff08OFDM\uff09<\/strong>: \u73fe\u4ee3\u306e\u7121\u7dda\u901a\u4fe1\u898f\u683c\uff08WiFi\u30014G\u30015G\u306a\u3069\uff09\u3067\u4f7f\u308f\u308c\u308bOFDM\uff08\u76f4\u4ea4\u5468\u6ce2\u6570\u5206\u5272\u591a\u91cd\uff09\u6280\u8853\u306f\u3001FFT\u3092\u30d9\u30fc\u30b9\u306b\u3057\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30e2\u30c7\u30e0<\/strong>: \u30c7\u30b8\u30bf\u30eb\u30e2\u30c7\u30e0\u3067\u306f\u3001FFT\u3092\u4f7f\u3063\u3066\u9001\u53d7\u4fe1\u4fe1\u53f7\u306e\u51e6\u7406\u3092\u884c\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30b9\u30da\u30af\u30c8\u30e9\u30e0\u30a2\u30ca\u30e9\u30a4\u30b6\u30fc<\/strong>: \u7121\u7dda\u5468\u6ce2\u6570\u306e\u5206\u6790\u88c5\u7f6e\u3067\u306f\u3001FFT\u3092\u4f7f\u3063\u3066\u5468\u6ce2\u6570\u30b9\u30da\u30af\u30c8\u30eb\u3092\u8868\u793a\u3057\u307e\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">7.5 \u533b\u7642\u8a3a\u65ad<\/h3>\n\n\n\n<p>\u533b\u7642\u5206\u91ce\u3067\u3082FFT\u306e\u5fdc\u7528\u304c\u9032\u3093\u3067\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>MRI\u753b\u50cf\u51e6\u7406<\/strong>: MRI\u88c5\u7f6e\u3067\u306f\u3001\u6e2c\u5b9a\u30c7\u30fc\u30bf\u3092FFT\u3067\u51e6\u7406\u3057\u3066\u753b\u50cf\u3092\u518d\u69cb\u6210\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u8133\u6ce2\u5206\u6790\uff08EEG\uff09<\/strong>: \u8133\u6ce2\u30c7\u30fc\u30bf\u3092FFT\u3067\u89e3\u6790\u3057\u3001\u8133\u306e\u6d3b\u52d5\u72b6\u614b\u3084\u7761\u7720\u6bb5\u968e\u3092\u8a55\u4fa1\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5fc3\u96fb\u56f3\u89e3\u6790<\/strong>: \u5fc3\u96fb\u56f3\u6ce2\u5f62\u3092FFT\u3067\u5206\u6790\u3057\u3001\u4e0d\u6574\u8108\u306a\u3069\u306e\u7570\u5e38\u3092\u691c\u51fa\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">7.6 IoT\u3068\u30b9\u30de\u30fc\u30c8\u30bb\u30f3\u30b7\u30f3\u30b0<\/h3>\n\n\n\n<p>IoT\uff08Internet of Things\uff09\u30c7\u30d0\u30a4\u30b9\u3067\u3082\u3001FFT\u304c\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30b9\u30de\u30fc\u30c8\u632f\u52d5\u30bb\u30f3\u30b5\u30fc<\/strong>: \u5de5\u5834\u306eIoT\u30bb\u30f3\u30b5\u30fc\u306b\u306f\u3001FFT\u3092\u5185\u8535\u3057\u3001\u305d\u306e\u5834\u3067\u632f\u52d5\u30c7\u30fc\u30bf\u3092\u5206\u6790\u3057\u3066\u7570\u5e38\u3092\u691c\u51fa\u3059\u308b\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30b9\u30de\u30fc\u30c8\u30e1\u30fc\u30bf\u30fc<\/strong>: \u96fb\u529b\u306e\u30b9\u30de\u30fc\u30c8\u30e1\u30fc\u30bf\u30fc\u3067\u306f\u3001FFT\u3092\u4f7f\u3063\u3066\u96fb\u529b\u54c1\u8cea\u306e\u5206\u6790\u3092\u884c\u3046\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30a6\u30a7\u30a2\u30e9\u30d6\u30eb\u30c7\u30d0\u30a4\u30b9<\/strong>: \u5065\u5eb7\u30e2\u30cb\u30bf\u30ea\u30f3\u30b0\u7528\u306e\u30a6\u30a7\u30a2\u30e9\u30d6\u30eb\u30c7\u30d0\u30a4\u30b9\u3067\u306f\u3001FFT\u3092\u4f7f\u3063\u3066\u52d5\u304d\u3084\u5fc3\u62cd\u306e\u30d1\u30bf\u30fc\u30f3\u3092\u5206\u6790\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/www.keyence.co.jp\/ss\/general\/iot-glossary\/fft.jsp\" target=\"_blank\" rel=\"noreferrer noopener\">16<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-fft\">8. FFT\u306e\u30e1\u30ea\u30c3\u30c8\u30fb\u5229\u70b9\uff08\u9ad8\u901f\u5316\u3001\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u51e6\u7406\u3001\u5927\u898f\u6a21\u30c7\u30fc\u30bf\u5bfe\u5fdc\u3001\u8aa4\u5dee\u4f4e\u6e1b\uff09<\/h2>\n\n\n\n<p>FFT\u304c\u3053\u308c\u3060\u3051\u5e83\u304f\u4f7f\u308f\u308c\u308b\u7406\u7531\u306f\u3001\u591a\u304f\u306e\u512a\u308c\u305f\u7279\u6027\u3092\u6301\u3063\u3066\u3044\u308b\u304b\u3089\u3067\u3059\u3002\u3053\u3053\u3067\u306f\u3001FFT\u306e\u4e3b\u8981\u306a\u30e1\u30ea\u30c3\u30c8\u3068\u5229\u70b9\u3092\u8a73\u3057\u304f\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">8.1 \u8a08\u7b97\u306e\u9ad8\u901f\u5316<\/h3>\n\n\n\n<p>\u6700\u3082\u660e\u767d\u306a\u5229\u70b9\u306f\u3001\u3082\u3061\u308d\u3093\u8a08\u7b97\u306e\u9ad8\u901f\u5316\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6307\u6570\u95a2\u6570\u7684\u306a\u52b9\u7387\u5411\u4e0a<\/strong>: \u8a08\u7b97\u91cf\u304cO(N\u00b2)\u304b\u3089O(N log N)\u306b\u524a\u6e1b\u3055\u308c\u308b\u3053\u3068\u3067\u3001\u7279\u306b\u5927\u898f\u6a21\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u5287\u7684\u306a\u901f\u5ea6\u5411\u4e0a\u304c\u5b9f\u73fe\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u51e6\u7406\u306e\u5b9f\u73fe<\/strong>: \u3053\u306e\u9ad8\u901f\u6027\u306b\u3088\u308a\u3001\u97f3\u58f0\u3084\u753b\u50cf\u306e\u51e6\u7406\u304c\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u3067\u53ef\u80fd\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u30b9\u30de\u30fc\u30c8\u30d5\u30a9\u30f3\u306e\u97f3\u58f0\u8a8d\u8b58\u3084\u52d5\u753b\u306e\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u51e6\u7406\u306f\u3001FFT\u306a\u3057\u3067\u306f\u5b9f\u73fe\u56f0\u96e3\u3067\u3057\u305f<a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">5<\/a><a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u300116,384\u70b9\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u8003\u3048\u308b\u3068\u3001\u76f4\u63a5\u8a08\u7b97\u3067\u306f\u7d042.7\u5104\u56de\u306e\u6f14\u7b97\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001FFT\u3067\u306f\u7d0423\u4e07\u56de\u3067\u6e08\u307f\u3001\u7d041\/2,300\u306e\u8a08\u7b97\u91cf\u3068\u306a\u308a\u307e\u3059<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">5<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">8.2 \u30e1\u30e2\u30ea\u52b9\u7387\u306e\u5411\u4e0a<\/h3>\n\n\n\n<p>FFT\u306f\u8a08\u7b97\u901f\u5ea6\u3060\u3051\u3067\u306a\u304f\u3001\u30e1\u30e2\u30ea\u4f7f\u7528\u306e\u52b9\u7387\u3082\u512a\u308c\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>In-Place\u6f14\u7b97<\/strong>: FFT\u306f\u540c\u3058\u30e1\u30e2\u30ea\u9818\u57df\u4e0a\u3067\u8a08\u7b97\u3092\u9032\u3081\u3089\u308c\u308b\u305f\u3081\u3001\u5927\u91cf\u306e\u8ffd\u52a0\u30e1\u30e2\u30ea\u3092\u5fc5\u8981\u3068\u3057\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u30e1\u30e2\u30ea\u304c\u9650\u3089\u308c\u3066\u3044\u308b\u30b7\u30b9\u30c6\u30e0\uff08\u7d44\u307f\u8fbc\u307f\u30b7\u30b9\u30c6\u30e0\u306a\u3069\uff09\u3067\u7279\u306b\u91cd\u8981\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf\u5c40\u6240\u6027<\/strong>: FFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u306e\u30d1\u30bf\u30fc\u30f3\u304c\u898f\u5247\u7684\u3067\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u7387\u304c\u9ad8\u304f\u306a\u308a\u3084\u3059\u3044\u8a2d\u8a08\u306b\u306a\u3063\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">5<\/a><a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">8.3 \u8a08\u7b97\u7cbe\u5ea6\u306e\u5411\u4e0a<\/h3>\n\n\n\n<p>FFT\u306f\u8a08\u7b97\u7cbe\u5ea6\u306e\u9762\u3067\u3082\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4e38\u3081\u8aa4\u5dee\u306e\u4f4e\u6e1b<\/strong>: \u76f4\u63a5\u8a08\u7b97\u306b\u6bd4\u3079\u3066\u4e57\u7b97\u56de\u6570\u304c\u5c11\u306a\u3044\u305f\u3081\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u306e\u4e38\u3081\u8aa4\u5dee\u304c\u7a4d\u307f\u91cd\u306a\u308b\u5f71\u97ff\u304c\u5c0f\u3055\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u6570\u5024\u5b89\u5b9a\u6027<\/strong>: \u591a\u304f\u306eFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u6570\u5024\u7684\u306b\u5b89\u5b9a\u3057\u305f\u65b9\u6cd5\u3067\u8a2d\u8a08\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5927\u304d\u306a\u5024\u3068\u5c0f\u3055\u306a\u5024\u304c\u6df7\u5728\u3059\u308b\u30c7\u30fc\u30bf\u3067\u3082\u7cbe\u5ea6\u826f\u304f\u8a08\u7b97\u3067\u304d\u307e\u3059<a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">5<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">8.4 \u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u5b9f\u88c5\u306e\u5bb9\u6613\u3055<\/h3>\n\n\n\n<p>FFT\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u5b9f\u88c5\u306b\u9069\u3057\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4e26\u5217\u51e6\u7406\u306e\u53ef\u80fd\u6027<\/strong>: FFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u672c\u8cea\u7684\u306b\u4e26\u5217\u5316\u53ef\u80fd\u306a\u69cb\u9020\u3092\u6301\u3063\u3066\u3044\u308b\u305f\u3081\u3001GPU\u3084\u5c02\u7528\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u3067\u52b9\u7387\u3088\u304f\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u6a19\u6e96\u5316\u3055\u308c\u305f\u5b9f\u88c5<\/strong>: \u591a\u304f\u306e\u30c7\u30b8\u30bf\u30eb\u4fe1\u53f7\u30d7\u30ed\u30bb\u30c3\u30b5\uff08DSP\uff09\u3084\u30de\u30a4\u30af\u30ed\u30b3\u30f3\u30c8\u30ed\u30fc\u30e9\u306b\u306f\u3001FFT\u3092\u9ad8\u901f\u306b\u5b9f\u884c\u3059\u308b\u305f\u3081\u306e\u5c02\u7528\u547d\u4ee4\u3084\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.semanticscholar.org\/paper\/9accea3fc84a74bfd19088f5641630f64c143ed4\" target=\"_blank\" rel=\"noreferrer noopener\">13<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u30b9\u30de\u30fc\u30c8\u30d5\u30a9\u30f3\u306e\u30c1\u30c3\u30d7\u306b\u306f\u3001FFT\u3092\u9ad8\u901f\u306b\u5b9f\u884c\u3059\u308b\u305f\u3081\u306e\u5c02\u7528\u56de\u8def\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u591a\u304f\u3001\u3053\u308c\u306b\u3088\u308a\u96fb\u529b\u52b9\u7387\u306e\u826f\u3044\u4fe1\u53f7\u51e6\u7406\u304c\u53ef\u80fd\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">8.5 \u69d8\u3005\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3078\u306e\u9069\u5fdc\u6027<\/h3>\n\n\n\n<p>FFT\u306f\u975e\u5e38\u306b\u67d4\u8edf\u3067\u3001\u69d8\u3005\u306a\u5fdc\u7528\u306b\u9069\u5fdc\u3067\u304d\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6b21\u5143\u306e\u62e1\u5f35<\/strong>: \u4e00\u6b21\u5143\u306eFFT\u3092\u62e1\u5f35\u3057\u3066\u3001\u4e8c\u6b21\u5143\uff08\u753b\u50cf\u51e6\u7406\uff09\u3084\u4e09\u6b21\u5143\uff08\u30dc\u30ea\u30e5\u30fc\u30e0\u30c7\u30fc\u30bf\u51e6\u7406\uff09\u306b\u3082\u9069\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5b9f\u6570\u30fb\u8907\u7d20\u6570\u30c7\u30fc\u30bf\u3078\u306e\u5bfe\u5fdc<\/strong>: \u5165\u529b\u304c\u5b9f\u6570\u306e\u307f\u306e\u5834\u5408\u3067\u3082\u3001\u8907\u7d20\u6570\u306e\u5834\u5408\u3067\u3082\u9069\u7528\u53ef\u80fd\u3067\u3059\u3002\u5b9f\u6570\u5165\u529b\u306b\u7279\u5316\u3057\u305f\u9ad8\u901f\u5b9f\u88c5\u3082\u5b58\u5728\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u69d8\u3005\u306a\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u3078\u306e\u5bfe\u5fdc<\/strong>: \u57fa\u672c\u7684\u306b\u306f2\u306e\u3079\u304d\u4e57\u30b5\u30a4\u30ba\u304c\u6700\u9069\u3067\u3059\u304c\u3001\u4ed6\u306e\u30b5\u30a4\u30ba\u306e\u30c7\u30fc\u30bf\u306b\u3082\u9069\u7528\u53ef\u80fd\u306a\u62e1\u5f35\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3082\u958b\u767a\u3055\u308c\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a><a href=\"https:\/\/www.semanticscholar.org\/paper\/2dd38cb1fc7efa9ddaa5e08277aa48229d836a72\" target=\"_blank\" rel=\"noreferrer noopener\">11<\/a><a href=\"https:\/\/www.semanticscholar.org\/paper\/9accea3fc84a74bfd19088f5641630f64c143ed4\" target=\"_blank\" rel=\"noreferrer noopener\">13<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-fft2\">9. FFT\u306e\u5b9f\u88c5\u4e0a\u306e\u6ce8\u610f\u70b9\uff08\u30b5\u30f3\u30d7\u30eb\u6570\u30012\u306e\u3079\u304d\u4e57\u3001\u524d\u51e6\u7406\u30fb\u5f8c\u51e6\u7406\u3001\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306a\u3069\uff09<\/h2>\n\n\n\n<p>FFT\u3092\u5b9f\u7528\u7684\u306b\u5fdc\u7528\u3059\u308b\u969b\u306b\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u91cd\u8981\u306a\u6ce8\u610f\u70b9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u3092\u9069\u5207\u306b\u7406\u89e3\u3057\u5bfe\u5fdc\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u6b63\u78ba\u3067\u52b9\u679c\u7684\u306a\u7d50\u679c\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">9.1 \u30b5\u30f3\u30d7\u30eb\u6570\u30682\u306e\u3079\u304d\u4e57<\/h3>\n\n\n\n<p>FFT\u3092\u52b9\u7387\u7684\u306b\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u6570\u306b\u95a2\u3059\u308b\u8003\u616e\u304c\u91cd\u8981\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>2\u306e\u3079\u304d\u4e57\u306e\u30b5\u30a4\u30ba<\/strong>: \u57fa\u672c\u7684\u306aCooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306eFFT\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u6570\u304c2\u306e\u3079\u304d\u4e57\uff08256, 512, 1024\u306a\u3069\uff09\u306e\u5834\u5408\u306b\u6700\u3082\u52b9\u7387\u7684\u306b\u52d5\u4f5c\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30bc\u30ed\u30d1\u30c7\u30a3\u30f3\u30b0<\/strong>: \u30b5\u30f3\u30d7\u30eb\u6570\u304c2\u306e\u3079\u304d\u4e57\u3067\u306a\u3044\u5834\u5408\u3001\u6b21\u306e2\u306e\u3079\u304d\u4e57\u307e\u3067\u30bc\u30ed\u3092\u8ffd\u52a0\uff08\u30bc\u30ed\u30d1\u30c7\u30a3\u30f3\u30b0\uff09\u3059\u308b\u65b9\u6cd5\u304c\u3088\u304f\u4f7f\u308f\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001600\u70b9\u306e\u30c7\u30fc\u30bf\u304c\u3042\u308b\u5834\u5408\u30011024\u70b9\u306b\u306a\u308b\u307e\u3067\u30bc\u30ed\u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u305d\u306e\u4ed6\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/strong>: \u30b5\u30f3\u30d7\u30eb\u6570\u304c2\u306e\u3079\u304d\u4e57\u3067\u306a\u3044\u5834\u5408\u306e\u305f\u3081\u306b\u3001\u69d8\u3005\u306a\u62e1\u5f35FFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3082\u958b\u767a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u5b9f\u88c5\u304c\u8907\u96d1\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/ice-tohtech.jp\/nakagawa\/fourier\/dft1_c1.htm\" target=\"_blank\" rel=\"noreferrer noopener\">3<\/a><a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">9.2 \u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306e\u9069\u7528<\/h3>\n\n\n\n<p>FFT\u3092\u9069\u7528\u3059\u308b\u524d\u306b\u3001\u4fe1\u53f7\u306b\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u3092\u639b\u3051\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30ea\u30fc\u30b1\u30fc\u30b8\u554f\u984c<\/strong>: FFT\u306f\u4fe1\u53f7\u304c\u5468\u671f\u7684\u306b\u7e70\u308a\u8fd4\u3059\u3053\u3068\u3092\u4eee\u5b9a\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u5b9f\u969b\u306e\u4fe1\u53f7\u306f\u5fc5\u305a\u3057\u3082\u305d\u3046\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u4e0d\u4e00\u81f4\u306b\u3088\u308a\u3001\u30b9\u30da\u30af\u30c8\u30eb\u6f0f\u308c\uff08\u30ea\u30fc\u30b1\u30fc\u30b8\uff09\u304c\u767a\u751f\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306e\u76ee\u7684<\/strong>: \u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u4fe1\u53f7\u306e\u59cb\u70b9\u3068\u7d42\u70b9\u3092\u6ed1\u3089\u304b\u306b\u30bc\u30ed\u306b\u8fd1\u3065\u3051\u3001\u30ea\u30fc\u30b1\u30fc\u30b8\u3092\u8efd\u6e1b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u4ee3\u8868\u7684\u306a\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570<\/strong>: \u30cf\u30cb\u30f3\u30b0\u7a93\u3001\u30cf\u30df\u30f3\u30b0\u7a93\u3001\u30d6\u30e9\u30c3\u30af\u30de\u30f3\u7a93\u3001\u30d5\u30e9\u30c3\u30c8\u30c8\u30c3\u30d7\u7a93\u306a\u3069\u3001\u69d8\u3005\u306a\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u304c\u3042\u308a\u3001\u7528\u9014\u306b\u3088\u3063\u3066\u4f7f\u3044\u5206\u3051\u307e\u3059<a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u5358\u4e00\u5468\u6ce2\u6570\u306e\u30b5\u30a4\u30f3\u6ce2\u3092FFT\u51e6\u7406\u3059\u308b\u5834\u5408\u3067\u3082\u3001\u6ce2\u5f62\u304c\u5207\u308c\u76ee\u306a\u304f\u5468\u671f\u7684\u306b\u7e70\u308a\u8fd4\u3055\u306a\u3044\u5834\u5408\uff08\u30b5\u30f3\u30d7\u30eb\u6570\u304c\u6ce2\u306e\u5468\u671f\u306e\u6574\u6570\u500d\u3067\u306a\u3044\u5834\u5408\uff09\u306b\u306f\u3001\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u3092\u9069\u7528\u3057\u306a\u3044\u3068\u30b9\u30da\u30af\u30c8\u30eb\u304c\u5e83\u304c\u3063\u3066\u6b63\u78ba\u306a\u5468\u6ce2\u6570\u3092\u7279\u5b9a\u3057\u306b\u304f\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">9.3 \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5468\u6ce2\u6570\u3068\u5468\u6ce2\u6570\u5206\u89e3\u80fd<\/h3>\n\n\n\n<p>FFT\u306e\u7d50\u679c\u3092\u6b63\u3057\u304f\u89e3\u91c8\u3059\u308b\u306b\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u95a2\u4fc2\u3092\u7406\u89e3\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30ca\u30a4\u30ad\u30b9\u30c8\u5468\u6ce2\u6570<\/strong>: \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5468\u6ce2\u6570(fs)\u306e\u534a\u5206\u307e\u3067\u306e\u5468\u6ce2\u6570\u3057\u304b\u6b63\u78ba\u306b\u691c\u51fa\u3067\u304d\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\u300144.1kHz\u3067\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u305f\u5834\u5408\u300122.05kHz\u307e\u3067\u306e\u5468\u6ce2\u6570\u6210\u5206\u3057\u304b\u5206\u6790\u3067\u304d\u307e\u305b\u3093\u3002<\/li>\n\n\n\n<li><strong>\u5468\u6ce2\u6570\u5206\u89e3\u80fd<\/strong>: \u5468\u6ce2\u6570\u5206\u89e3\u80fd(df)\u306f\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5468\u6ce2\u6570\u3092\u30d6\u30ed\u30c3\u30af\u30b5\u30a4\u30ba\u3067\u5272\u3063\u305f\u5024\uff08df = fs \/ BL\uff09\u3067\u3059\u3002\u4f8b\u3048\u3070\u300148kHz\u30671024\u70b9\u306eFFT\u3092\u884c\u3046\u3068\u3001\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u306f\u7d0446.9Hz\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u6642\u9593\u7a93\u9577<\/strong>: \u6642\u9593\u7a93\u9577\u306f\u30d6\u30ed\u30c3\u30af\u30b5\u30a4\u30ba\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5468\u6ce2\u6570\u3067\u5272\u3063\u305f\u5024\uff08D = BL \/ fs\uff09\u3067\u3059\u3002\u3053\u308c\u306f\u5206\u6790\u306b\u4f7f\u7528\u3059\u308b\u30c7\u30fc\u30bf\u306e\u6642\u9593\u9577\u306b\u76f8\u5f53\u3057\u307e\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a><a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u97f3\u58f0\u5206\u6790\u306748kHz\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u30ec\u30fc\u30c8\u30671024\u70b9\u306eFFT\u3092\u4f7f\u3046\u3068\u300146.9Hz\u9593\u9694\u3067\u6700\u592724kHz\u307e\u3067\u306e\u5468\u6ce2\u6570\u6210\u5206\u3092\u5206\u6790\u3067\u304d\u3001\u305d\u306e\u6642\u9593\u5206\u89e3\u80fd\u306f\u7d0421.3\u30df\u30ea\u79d2\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">9.4 \u30b9\u30da\u30af\u30c8\u30eb\u7d50\u679c\u306e\u89e3\u91c8<\/h3>\n\n\n\n<p>FFT\u306e\u7d50\u679c\u3092\u6b63\u3057\u304f\u89e3\u91c8\u3059\u308b\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u70b9\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8907\u7d20\u6570\u306e\u6271\u3044<\/strong>: FFT\u306e\u7d50\u679c\u306f\u8907\u7d20\u6570\u306b\u306a\u308a\u307e\u3059\u3002\u901a\u5e38\u3001\u632f\u5e45\u30b9\u30da\u30af\u30c8\u30eb\uff08\u5927\u304d\u3055\uff09\u3068\u4f4d\u76f8\u30b9\u30da\u30af\u30c8\u30eb\uff08\u89d2\u5ea6\uff09\u306b\u5206\u3051\u3066\u8003\u3048\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u4e21\u5074\u30b9\u30da\u30af\u30c8\u30eb vs \u7247\u5074\u30b9\u30da\u30af\u30c8\u30eb<\/strong>: FFT\u306e\u7d50\u679c\u306f\u300c\u4e21\u5074\u30b9\u30da\u30af\u30c8\u30eb\u300d\u3067\u3001\u6b63\u3068\u8ca0\u306e\u5468\u6ce2\u6570\u3092\u542b\u307f\u307e\u3059\u3002\u5b9f\u6570\u4fe1\u53f7\u306e\u5834\u5408\u3001\u901a\u5e38\u306f\u6b63\u306e\u5468\u6ce2\u6570\u90e8\u5206\u306e\u307f\u3092\u4f7f\u3046\u300c\u7247\u5074\u30b9\u30da\u30af\u30c8\u30eb\u300d\u306b\u5909\u63db\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5bfe\u6570\u30b9\u30b1\u30fc\u30eb<\/strong>: \u632f\u5e45\u30b9\u30da\u30af\u30c8\u30eb\u306f\u3001\u3057\u3070\u3057\u3070\u30c7\u30b7\u30d9\u30eb\uff08dB\uff09\u306a\u3069\u306e\u5bfe\u6570\u30b9\u30b1\u30fc\u30eb\u3067\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5927\u304d\u306a\u5024\u3068\u5c0f\u3055\u306a\u5024\u306e\u4e21\u65b9\u3092\u540c\u6642\u306b\u8996\u899a\u5316\u3067\u304d\u307e\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">9.5 \u5b9f\u88c5\u306b\u304a\u3051\u308b\u6ce8\u610f\u70b9<\/h3>\n\n\n\n<p>\u5b9f\u969b\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067FFT\u3092\u5b9f\u88c5\u3059\u308b\u969b\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u70b9\u306b\u6ce8\u610f\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u65e2\u5b58\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6d3b\u7528<\/strong>: \u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u306f\u3001\u6700\u9069\u5316\u3055\u308c\u305fFFT\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u4f8b\uff1aPython\u306eNumPy\u3001C\u8a00\u8a9e\u306eFFTW\uff09\u3002\u901a\u5e38\u306f\u81ea\u524d\u3067\u5b9f\u88c5\u3059\u308b\u3088\u308a\u3053\u308c\u3089\u3092\u4f7f\u3046\u65b9\u304c\u52b9\u7387\u7684\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u7cbe\u5ea6\u3068\u901f\u5ea6\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5<\/strong>: \u7cbe\u5ea6\u304c\u91cd\u8981\u306a\u5834\u5408\u306f\u500d\u7cbe\u5ea6\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3092\u3001\u901f\u5ea6\u304c\u91cd\u8981\u306a\u5834\u5408\u306f\u5358\u7cbe\u5ea6\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3084\u56fa\u5b9a\u5c0f\u6570\u70b9\u6570\u3092\u4f7f\u3046\u306a\u3069\u3001\u7528\u9014\u306b\u5fdc\u3058\u305f\u9078\u629e\u304c\u5fc5\u8981\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30e1\u30e2\u30ea\u30a2\u30e9\u30a4\u30e1\u30f3\u30c8<\/strong>: \u4e00\u90e8\u306eFFT\u5b9f\u88c5\u3067\u306f\u3001\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u304c\u7279\u5b9a\u306e\u5883\u754c\uff08\u4f8b\uff1a16\u30d0\u30a4\u30c8\u5883\u754c\uff09\u306b\u6574\u5217\u3057\u3066\u3044\u308b\u3068\u6027\u80fd\u304c\u5411\u4e0a\u3057\u307e\u3059<a href=\"https:\/\/arxiv.org\/abs\/1712.04910\" target=\"_blank\" rel=\"noreferrer noopener\">6<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-fft\">10. FFT\u306e\u9650\u754c\u30fb\u6ce8\u610f\u4e8b\u9805\uff08\u6b63\u3057\u3044\u5468\u6ce2\u6570\u7279\u6027\u3092\u5f97\u308b\u305f\u3081\u306e\u6761\u4ef6\u3001\u7e70\u308a\u8fd4\u3057\u4fe1\u53f7\u306e\u4eee\u5b9a\u3001\u30a8\u30a4\u30ea\u30a2\u30b7\u30f3\u30b0\u306a\u3069\uff09<\/h2>\n\n\n\n<p>FFT\u306f\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3067\u3059\u304c\u3001\u9069\u5207\u306b\u4f7f\u7528\u3057\u306a\u3044\u3068\u8aa4\u3063\u305f\u7d50\u679c\u3092\u5c0e\u304f\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001FFT\u306e\u9650\u754c\u3068\u4f7f\u7528\u4e0a\u306e\u6ce8\u610f\u70b9\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">10.1 \u5468\u671f\u7684\u5ef6\u9577\u306e\u4eee\u5b9a<\/h3>\n\n\n\n<p>FFT\u306e\u57fa\u672c\u7684\u306a\u524d\u63d0\u6761\u4ef6\u306e\u4e00\u3064\u306f\u3001\u4fe1\u53f7\u304c\u5468\u671f\u7684\u306b\u7e70\u308a\u8fd4\u3055\u308c\u308b\u3068\u3044\u3046\u4eee\u5b9a\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4eee\u5b9a\u3068\u73fe\u5b9f\u306e\u30ae\u30e3\u30c3\u30d7<\/strong>: FFT\u306f\u3001\u89e3\u6790\u5bfe\u8c61\u306e\u6642\u9593\u7a93\u306e\u5916\u5074\u3067\u3082\u4fe1\u53f7\u304c\u540c\u3058\u30d1\u30bf\u30fc\u30f3\u3067\u5468\u671f\u7684\u306b\u7e70\u308a\u8fd4\u3059\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5b9f\u969b\u306e\u4fe1\u53f7\u306f\u305d\u3046\u3067\u306a\u3044\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u4e0d\u9023\u7d9a\u70b9\u306e\u554f\u984c<\/strong>: \u6642\u9593\u7a93\u306e\u7d42\u7aef\u3068\u6b21\u306e\u5468\u671f\u306e\u958b\u59cb\u70b9\u3067\u4fe1\u53f7\u304c\u4e0d\u9023\u7d9a\u306b\u306a\u308b\u3068\u3001\u30b9\u30da\u30af\u30c8\u30eb\u306b\u507d\u306e\u9ad8\u5468\u6ce2\u6210\u5206\uff08\u30ea\u30fc\u30b1\u30fc\u30b8\uff09\u304c\u73fe\u308c\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5bfe\u7b56<\/strong>: \u3053\u306e\u554f\u984c\u306f\u3001\u524d\u8ff0\u306e\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306e\u9069\u7528\u306b\u3088\u3063\u3066\u8efd\u6e1b\u3067\u304d\u307e\u3059<a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u5358\u4e00\u5468\u6ce2\u6570\u306e\u30b5\u30a4\u30f3\u6ce2\u3067\u3082\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u671f\u9593\u304c\u305d\u306e\u6ce2\u306e\u5468\u671f\u306e\u6574\u6570\u500d\u3067\u306a\u3044\u5834\u5408\u3001FFT\u30b9\u30da\u30af\u30c8\u30eb\u3067\u306f\u5358\u4e00\u306e\u30d4\u30fc\u30af\u3067\u306f\u306a\u304f\u3001\u5468\u8fba\u306e\u5468\u6ce2\u6570\u306b\u3082\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u6f0f\u308c\u3066\u5e83\u304c\u3063\u305f\u30d4\u30fc\u30af\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">10.2 \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5b9a\u7406\u3068\u30a8\u30a4\u30ea\u30a2\u30b7\u30f3\u30b0<\/h3>\n\n\n\n<p>\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306b\u95a2\u9023\u3059\u308b\u57fa\u672c\u7684\u306a\u5236\u9650\u4e8b\u9805\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30ca\u30a4\u30ad\u30b9\u30c8\u306e\u5b9a\u7406<\/strong>: \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5468\u6ce2\u6570\u306e\u534a\u5206\uff08\u30ca\u30a4\u30ad\u30b9\u30c8\u5468\u6ce2\u6570\uff09\u3088\u308a\u9ad8\u3044\u5468\u6ce2\u6570\u6210\u5206\u306f\u3001\u6b63\u78ba\u306b\u518d\u73fe\u3067\u304d\u307e\u305b\u3093\u3002<\/li>\n\n\n\n<li><strong>\u30a8\u30a4\u30ea\u30a2\u30b7\u30f3\u30b0<\/strong>: \u30ca\u30a4\u30ad\u30b9\u30c8\u5468\u6ce2\u6570\u3092\u8d85\u3048\u308b\u5468\u6ce2\u6570\u6210\u5206\u304c\u4fe1\u53f7\u306b\u542b\u307e\u308c\u308b\u3068\u3001\u305d\u308c\u3089\u306f\u4f4e\u3044\u5468\u6ce2\u6570\u306b\u300c\u6298\u308a\u8fd4\u3057\u300d\u3066\u73fe\u308c\u307e\u3059\u3002\u3053\u308c\u3092\u30a8\u30a4\u30ea\u30a2\u30b7\u30f3\u30b0\uff08\u30a8\u30a4\u30ea\u30a2\u30b7\u30f3\u30b0\uff09\u3068\u3044\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5bfe\u7b56<\/strong>: \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u524d\u306b\u3001\u30a2\u30ca\u30ed\u30b0\u306e\u4f4e\u57df\u901a\u904e\u30d5\u30a3\u30eb\u30bf\uff08\u30a2\u30f3\u30c1\u30a8\u30a4\u30ea\u30a2\u30b7\u30f3\u30b0\u30d5\u30a3\u30eb\u30bf\uff09\u3092\u4f7f\u7528\u3057\u3066\u3001\u30ca\u30a4\u30ad\u30b9\u30c8\u5468\u6ce2\u6570\u3092\u8d85\u3048\u308b\u6210\u5206\u3092\u30ab\u30c3\u30c8\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u300120kHz\u306e\u97f3\u309216kHz\u3067\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b\u3068\u3001\u305d\u306e\u4fe1\u53f7\u306f4kHz\u306e\u6210\u5206\u3068\u3057\u3066\u8aa4\u3063\u3066\u73fe\u308c\u307e\u3059\uff0820kHz - 16kHz = 4kHz\uff09\u3002\u3053\u308c\u306f\u97f3\u8cea\u52a3\u5316\u3084\u89e3\u6790\u8aa4\u5dee\u306e\u539f\u56e0\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">10.3 \u5468\u6ce2\u6570\u5206\u89e3\u80fd\u3068\u6642\u9593\u5206\u89e3\u80fd\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5<\/h3>\n\n\n\n<p>FFT\u5206\u6790\u306b\u306f\u3001\u57fa\u672c\u7684\u306a\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u304c\u5b58\u5728\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6642\u9593-\u5468\u6ce2\u6570\u306e\u4e0d\u78ba\u5b9a\u6027\u539f\u7406<\/strong>: \u5468\u6ce2\u6570\u5206\u89e3\u80fd\u3092\u9ad8\u3081\u308b\u3068\u6642\u9593\u5206\u89e3\u80fd\u304c\u4e0b\u304c\u308a\u3001\u9006\u306b\u6642\u9593\u5206\u89e3\u80fd\u3092\u9ad8\u3081\u308b\u3068\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u304c\u4e0b\u304c\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>FFT\u30b5\u30a4\u30ba\u306e\u5f71\u97ff<\/strong>: \u3088\u308a\u591a\u304f\u306e\u30b5\u30f3\u30d7\u30eb\u70b9\uff08\u9577\u3044\u6642\u9593\u7a93\uff09\u3092\u4f7f\u7528\u3059\u308c\u3070\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u306f\u5411\u4e0a\u3057\u307e\u3059\u304c\u3001\u6642\u9593\u7684\u306a\u5909\u5316\u3092\u6349\u3048\u308b\u80fd\u529b\u304c\u4f4e\u4e0b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5bfe\u7b56<\/strong>: \u77ed\u6642\u9593\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff08STFT\uff09\u3067\u306f\u3001\u4fe1\u53f7\u3092\u5c0f\u3055\u306a\u6642\u9593\u7a93\u306b\u5206\u5272\u3057\u3001\u5404\u7a93\u3054\u3068\u306bFFT\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u3042\u308b\u7a0b\u5ea6\u306e\u6642\u9593\u5909\u5316\u3092\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a><a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u97f3\u697d\u4fe1\u53f7\u306e\u5206\u6790\u3067\u306f\u3001\u4f4e\u3044\u5468\u6ce2\u6570\uff08\u30d9\u30fc\u30b9\u97f3\uff09\u3092\u6b63\u78ba\u306b\u6349\u3048\u308b\u306b\u306f\u9577\u3044\u6642\u9593\u7a93\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u7d20\u65e9\u3044\u6253\u697d\u5668\u306e\u97f3\u306a\u3069\u3092\u6642\u9593\u7684\u306b\u6b63\u78ba\u306b\u6349\u3048\u308b\u306b\u306f\u77ed\u3044\u6642\u9593\u7a93\u304c\u5fc5\u8981\u3068\u3044\u3046\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u304c\u751f\u3058\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">10.4 \u4e38\u3081\u8aa4\u5dee\u3068\u6570\u5024\u5b89\u5b9a\u6027<\/h3>\n\n\n\n<p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u8a08\u7b97\u306b\u95a2\u9023\u3059\u308b\u5236\u9650\u3082\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6d6e\u52d5\u5c0f\u6570\u70b9\u7cbe\u5ea6<\/strong>: \u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u306e\u7cbe\u5ea6\u9650\u754c\u306b\u3088\u308a\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u5024\u3068\u5c0f\u3055\u306a\u5024\u304c\u6df7\u5728\u3059\u308b\u4fe1\u53f7\u3067\u306f\u3001\u5c0f\u3055\u306a\u6210\u5206\u304c\u4e38\u3081\u8aa4\u5dee\u3067\u5931\u308f\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u7d2f\u7a4d\u8aa4\u5dee<\/strong>: \u7279\u306b\u5927\u898f\u6a21\u306aFFT\uff08\u4f8b\uff1a\u6570\u767e\u4e07\u70b9\uff09\u3067\u306f\u3001\u8a08\u7b97\u306e\u5404\u6bb5\u968e\u3067\u306e\u5fae\u5c0f\u306a\u4e38\u3081\u8aa4\u5dee\u304c\u7d2f\u7a4d\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5bfe\u7b56<\/strong>: \u9069\u5207\u306a\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u3001\u500d\u7cbe\u5ea6\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306e\u4f7f\u7528\u3001\u6570\u5024\u7684\u306b\u5b89\u5b9a\u3057\u305fFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u9078\u629e\u306a\u3069\u304c\u91cd\u8981\u3067\u3059<a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">5<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">10.5 \u30d4\u30fc\u30af\u691c\u51fa\u3068\u88dc\u9593<\/h3>\n\n\n\n<p>FFT\u306e\u7d50\u679c\u304b\u3089\u6b63\u78ba\u306a\u5468\u6ce2\u6570\u3092\u6c7a\u5b9a\u3059\u308b\u969b\u306e\u5236\u9650\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u96e2\u6563\u7684\u306a\u5468\u6ce2\u6570\u30d3\u30f3<\/strong>: FFT\u306f\u96e2\u6563\u7684\u306a\u5468\u6ce2\u6570\u30dd\u30a4\u30f3\u30c8\uff08\u30d3\u30f3\uff09\u3067\u306e\u307f\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u5b9f\u969b\u306e\u4fe1\u53f7\u306e\u5468\u6ce2\u6570\u304c\u30d3\u30f3\u9593\u306b\u3042\u308b\u5834\u5408\u3001\u6b63\u78ba\u306a\u5468\u6ce2\u6570\u3092\u76f4\u63a5\u8aad\u307f\u53d6\u308c\u307e\u305b\u3093\u3002<\/li>\n\n\n\n<li><strong>\u30b9\u30da\u30af\u30c8\u30eb\u6f0f\u308c<\/strong>: \u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3082\u5b8c\u5168\u306b\u306f\u89e3\u6c7a\u3067\u304d\u306a\u3044\u30b9\u30da\u30af\u30c8\u30eb\u6f0f\u308c\u306b\u3088\u308a\u3001\u5468\u6ce2\u6570\u306e\u30d4\u30fc\u30af\u4f4d\u7f6e\u304c\u305a\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5bfe\u7b56<\/strong>: \u30d4\u30fc\u30af\u5468\u6ce2\u6570\u3092\u3088\u308a\u6b63\u78ba\u306b\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u5468\u6ce2\u6570\u30d3\u30f3\u9593\u306e\u88dc\u9593\u6280\u8853\uff08\u653e\u7269\u7dda\u88dc\u9593\u3001\u91cd\u5fc3\u8a08\u7b97\u306a\u3069\uff09\u304c\u4f7f\u308f\u308c\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001440Hz\u306e\u7d14\u97f3\u3092\u5206\u6790\u3059\u308b\u5834\u5408\u3001FFT\u306e\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u304c10Hz\u3060\u3068\u3059\u308b\u3068\u3001435Hz\u3068445Hz\u306e\u30d3\u30f3\u306b\u5206\u304b\u308c\u3066\u8868\u793a\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u88dc\u9593\u6280\u8853\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u969b\u306e\u5468\u6ce2\u6570\u3092\u3088\u308a\u6b63\u78ba\u306b\u63a8\u5b9a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-fft\">11. \u4ee3\u8868\u7684\u306aFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7a2e\u985e\uff08\u6642\u9593\u9593\u5f15\u304d\u6cd5\u3001\u5468\u6ce2\u6570\u9593\u5f15\u304d\u6cd5\u306a\u3069\uff09<\/h2>\n\n\n\n<p>FFT\u306b\u306f\u69d8\u3005\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u7279\u5fb4\u3068\u9069\u3057\u305f\u7528\u9014\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u4ee3\u8868\u7684\u306aFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u305d\u306e\u7279\u5fb4\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">11.1 \u6642\u9593\u9593\u5f15\u304d\u6cd5\uff08Decimation in Time: DIT\uff09<\/h3>\n\n\n\n<p>\u6642\u9593\u9593\u5f15\u304d\u6cd5\u306f\u3001\u6700\u3082\u57fa\u672c\u7684\u306aFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u3064\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u57fa\u672c\u539f\u7406<\/strong>: \u5165\u529b\u30c7\u30fc\u30bf\u3092\u5076\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u5947\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u4e8c\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u5272\u3057\u3001\u305d\u308c\u305e\u308c\u306b\u5bfe\u3057\u3066\u5c0f\u3055\u3044\u30b5\u30a4\u30ba\u306eDFT\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf\u306e\u4e26\u3073\u66ff\u3048<\/strong>: \u5165\u529b\u30c7\u30fc\u30bf\u3092\u30d3\u30c3\u30c8\u53cd\u8ee2\u9806\u5e8f\u3067\u4e26\u3073\u66ff\u3048\u3066\u304b\u3089\u8a08\u7b97\u3092\u884c\u3044\u3001\u51fa\u529b\u306f\u81ea\u7136\u306a\u9806\u5e8f\u3067\u5f97\u3089\u308c\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97<\/strong>: \u6642\u9593\u9593\u5f15\u304d\u6cd5\u3067\u306f\u3001\u7279\u5b9a\u306e\u5f62\u5f0f\u306e\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u5165\u529ba\u3068b\u306b\u5bfe\u3057\u3066\u3001\u51fa\u529b\u306fa+b\u3068(a-b)\u00d7W\u306b\u306a\u308a\u307e\u3059<a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">5<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u30018\u70b9\u306eFFT\u3067\u306f\u3001\u6700\u521d\u306b\u5165\u529b\u30c7\u30fc\u30bf\u3092[x0, x4, x2, x6, x1, x5, x3, x7]\u306e\u3088\u3046\u306b\u4e26\u3073\u66ff\u3048\u3001\u305d\u306e\u5f8c\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u3092\u9069\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">11.2 \u5468\u6ce2\u6570\u9593\u5f15\u304d\u6cd5\uff08Decimation in Frequency: DIF\uff09<\/h3>\n\n\n\n<p>\u5468\u6ce2\u6570\u9593\u5f15\u304d\u6cd5\u306f\u3001\u6642\u9593\u9593\u5f15\u304d\u6cd5\u3068\u53cc\u5bfe\u7684\u306a\u95a2\u4fc2\u306b\u3042\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u57fa\u672c\u539f\u7406<\/strong>: DFT\u306e\u51fa\u529b\u3092\u5076\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u5947\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u4e8c\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u5272\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf\u306e\u4e26\u3073\u66ff\u3048<\/strong>: \u5165\u529b\u30c7\u30fc\u30bf\u306f\u81ea\u7136\u306a\u9806\u5e8f\u3067\u51e6\u7406\u3057\u3001\u51fa\u529b\u3092\u30d3\u30c3\u30c8\u53cd\u8ee2\u9806\u5e8f\u3067\u5f97\u307e\u3059\u3002\u3042\u308b\u3044\u306f\u6700\u7d42\u6bb5\u968e\u3067\u30c7\u30fc\u30bf\u306e\u4e26\u3073\u66ff\u3048\u3092\u884c\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97<\/strong>: \u5468\u6ce2\u6570\u9593\u5f15\u304d\u6cd5\u306e\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u306f\u3001\u6642\u9593\u9593\u5f15\u304d\u6cd5\u3068\u306f\u5c11\u3057\u7570\u306a\u308a\u307e\u3059\u3002\u5165\u529ba\u3068b\u306b\u5bfe\u3057\u3066\u3001\u51fa\u529b\u306fa+b\u3068a-b\u306b\u306a\u308a\u3001\u5f8c\u8005\u306b\u56de\u8ee2\u56e0\u5b50W\u3092\u639b\u3051\u308b\u306e\u306f\u6b21\u306e\u6bb5\u968e\u3067\u3059<a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">5<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5468\u6ce2\u6570\u9593\u5f15\u304d\u6cd5\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u5fdc\u7528\u3067\u306f\u5b9f\u88c5\u304c\u3088\u308a\u5358\u7d14\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">11.3 \u57fa\u65704FFT\uff08Radix-4 FFT\uff09<\/h3>\n\n\n\n<p>\u57fa\u65704FFT\u306f\u3001\u30c7\u30fc\u30bf\u30924\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u5272\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u57fa\u672c\u539f\u7406<\/strong>: 1\u56de\u306e\u5206\u5272\u30674\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b\u305f\u3081\u3001\u30d0\u30bf\u30d5\u30e9\u30a4\u6f14\u7b97\u306e\u30b9\u30c6\u30fc\u30b8\u6570\u304c\u6e1b\u5c11\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u52b9\u7387\u6027<\/strong>: \u57fa\u65702\uff08\u901a\u5e38\u306eCooley-Tukey\uff09\u3068\u6bd4\u8f03\u3057\u3066\u3001\u4e57\u7b97\u56de\u6570\u3092\u7d0425%\u524a\u6e1b\u3067\u304d\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5236\u7d04<\/strong>: \u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c4\u306e\u3079\u304d\u4e57\uff084, 16, 64, 256, 1024\uff08=4\u2075\uff09\u306a\u3069\uff09\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/www.semanticscholar.org\/paper\/2dd38cb1fc7efa9ddaa5e08277aa48229d836a72\" target=\"_blank\" rel=\"noreferrer noopener\">11<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u57fa\u65704FFT\u306f\u3001\u4e00\u90e8\u306e\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u5b9f\u88c5\u3067\u52b9\u7387\u7684\u306b\u52d5\u4f5c\u3057\u307e\u3059\u30024\u70b9\u306eDFT\u306f\u76f4\u63a5\u8a08\u7b97\u3067\u304d\u308b\u305f\u3081\u3001\u57fa\u5e95\u30b1\u30fc\u30b9\u3068\u3057\u3066\u3082\u4fbf\u5229\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">11.4 \u5206\u5272\u57fa\u6570FFT\uff08Split-Radix FFT\uff09<\/h3>\n\n\n\n<p>\u5206\u5272\u57fa\u6570FFT\u306f\u3001\u57fa\u65702\u3068\u57fa\u65704\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u3082\u306e\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u57fa\u672c\u539f\u7406<\/strong>: \u5076\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u3057\u3066\u306f\u57fa\u65702\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f7f\u3044\u3001\u5947\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u3057\u3066\u306f\u57fa\u65704\u306e\u3088\u3046\u306a\u51e6\u7406\u3092\u884c\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u52b9\u7387\u6027<\/strong>: \u7d14\u7c8b\u306a\u57fa\u65702\u3084\u57fa\u65704\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3088\u308a\u4e57\u7b97\u56de\u6570\u304c\u5c11\u306a\u304f\u3001\u7406\u8ad6\u7684\u306b\u306f\u6700\u3082\u52b9\u7387\u7684\u306a\u5b9f\u6570\u5024FFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u3064\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u8907\u96d1\u6027<\/strong>: \u5b9f\u88c5\u304c\u3084\u3084\u8907\u96d1\u306b\u306a\u308b\u3068\u3044\u3046\u6b20\u70b9\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">11.5 \u30d7\u30e9\u30a4\u30e0\u30d5\u30a1\u30af\u30bf\u30fc\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08PFA: Prime Factor Algorithm\uff09<\/h3>\n\n\n\n<p>\u30d7\u30e9\u30a4\u30e0\u30d5\u30a1\u30af\u30bf\u30fc\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u304c\u4e92\u3044\u306b\u7d20\u306a\u56e0\u6570\u306b\u5206\u89e3\u3067\u304d\u308b\u5834\u5408\u306b\u6709\u52b9\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u57fa\u672c\u539f\u7406<\/strong>: \u30c7\u30fc\u30bf\u30b5\u30a4\u30baN\u304cN=N1\u00d7N2\u00d7...\u00d7Nk\u3068\u7d20\u56e0\u6570\u5206\u89e3\u3067\u304d\u3001\u5404\u56e0\u6570\u304c\u4e92\u3044\u306b\u7d20\uff08\u6700\u5927\u516c\u7d04\u6570\u304c1\uff09\u3067\u3042\u308b\u5834\u5408\u3001\u591a\u6b21\u5143DFT\u306b\u5e30\u7740\u3057\u3066\u8a08\u7b97\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u52b9\u7387\u6027<\/strong>: \u9069\u5207\u306a\u6761\u4ef6\u4e0b\u3067\u306f\u3001Cooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3088\u308a\u52b9\u7387\u7684\u3067\u3042\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5fdc\u7528<\/strong>: \u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u304c2\u306e\u3079\u304d\u4e57\u3067\u306a\u3044\u5834\u5408\uff08\u4f8b\uff1a3\u00d75\u00d77=105\u70b9\u306a\u3069\uff09\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">11.6 \u30d6\u30eb\u30fc\u30b9\u30bf\u30a4\u30f3\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08Bluestein's Algorithm\uff09<\/h3>\n\n\n\n<p>\u30d6\u30eb\u30fc\u30b9\u30bf\u30a4\u30f3\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u4efb\u610f\u306e\u30b5\u30a4\u30ba\u306eDFT\u3092\u8a08\u7b97\u3067\u304d\u308b\u67d4\u8edf\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u57fa\u672c\u539f\u7406<\/strong>: \u7573\u307f\u8fbc\u307f\u64cd\u4f5c\u3092\u5229\u7528\u3057\u3066DFT\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u4efb\u610f\u306e\u30b5\u30a4\u30baN\u306eDFT\u3092\u3088\u308a\u5927\u304d\u30442\u306e\u3079\u304d\u4e57\u30b5\u30a4\u30ba\u306e\u7573\u307f\u8fbc\u307f\u306b\u5909\u63db\u3057\u3001\u305d\u308c\u3092FFT\u3067\u8a08\u7b97\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u67d4\u8edf\u6027<\/strong>: \u30c7\u30fc\u30bf\u70b9\u306e\u6570\u306b\u5236\u7d04\u304c\u306a\u304f\u3001\u7d20\u6570\u306e\u30b5\u30a4\u30ba\u306eDFT\u3082\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u52b9\u7387\u6027<\/strong>: \u4e00\u822c\u7684\u306b\u306fCooley-Tukey\u307b\u3069\u52b9\u7387\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u4efb\u610f\u306e\u30b5\u30a4\u30ba\u306b\u5bfe\u5fdc\u3067\u304d\u308b\u70b9\u304c\u5229\u70b9\u3067\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001101\u70b9\uff08\u7d20\u6570\uff09\u306eDFT\u3092\u8a08\u7b97\u3059\u308b\u5834\u5408\u3001\u901a\u5e38\u306eCooley-Tukey\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u76f4\u63a5\u9069\u7528\u3067\u304d\u307e\u305b\u3093\u304c\u3001\u30d6\u30eb\u30fc\u30b9\u30bf\u30a4\u30f3\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u3048\u3070\u52b9\u7387\u7684\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12\">12. \u307e\u3068\u3081\u30fb\u4eca\u5f8c\u306e\u5c55\u671b<\/h2>\n\n\n\n<p>FFT\uff08\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff09\u306f\u3001\u6570\u5b66\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u304b\u3089\u751f\u307e\u308c\u305f\u52b9\u7387\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3042\u308a\u3001\u73fe\u4ee3\u306e\u30c7\u30b8\u30bf\u30eb\u4fe1\u53f7\u51e6\u7406\u306b\u9769\u547d\u3092\u3082\u305f\u3089\u3057\u307e\u3057\u305f\u3002\u3053\u3053\u3067\u306f\u3001FFT\u306e\u91cd\u8981\u6027\u3068\u4eca\u5f8c\u306e\u5c55\u671b\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">12.1 FFT\u306e\u91cd\u8981\u6027\u306e\u518d\u78ba\u8a8d<\/h3>\n\n\n\n<p>FFT\u306e\u6301\u3064\u91cd\u8981\u6027\u3092\u6539\u3081\u3066\u78ba\u8a8d\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8a08\u7b97\u52b9\u7387\u306e\u5287\u7684\u5411\u4e0a<\/strong>: FFT\u306f\u8a08\u7b97\u91cf\u3092O(N\u00b2)\u304b\u3089O(N log N)\u306b\u524a\u6e1b\u3057\u3001\u5927\u898f\u6a21\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u5b9f\u7528\u7684\u306a\u3082\u306e\u306b\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u4fe1\u53f7\u51e6\u7406\u306a\u3069\u591a\u304f\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3057\u305f<a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">5<\/a>\u3002<\/li>\n\n\n\n<li><strong>\u5e45\u5e83\u3044\u5fdc\u7528\u5206\u91ce<\/strong>: \u97f3\u58f0\u30fb\u97f3\u97ff\u51e6\u7406\u3001\u753b\u50cf\u51e6\u7406\u3001\u901a\u4fe1\u6280\u8853\u3001\u533b\u7642\u8a3a\u65ad\u3001\u632f\u52d5\u89e3\u6790\u306a\u3069\u3001\u591a\u5c90\u306b\u308f\u305f\u308b\u5206\u91ce\u3067FFT\u304c\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u73fe\u4ee3\u306e\u30c7\u30b8\u30bf\u30eb\u6280\u8853\u306e\u591a\u304f\u304cFFT\u306b\u4f9d\u5b58\u3057\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\" target=\"_blank\" rel=\"noreferrer noopener\">2<\/a><a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a><a href=\"https:\/\/www.keyence.co.jp\/ss\/general\/iot-glossary\/fft.jsp\" target=\"_blank\" rel=\"noreferrer noopener\">16<\/a><a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n\n\n\n<li><strong>\u7406\u8ad6\u3068\u5b9f\u8df5\u306e\u6a4b\u6e21\u3057<\/strong>: FFT\u306f\u6570\u5b66\u7684\u306a\u7f8e\u3057\u3055\u3068\u5b9f\u7528\u7684\u306a\u4fa1\u5024\u3092\u517c\u306d\u5099\u3048\u305f\u73cd\u3057\u3044\u4f8b\u3067\u3059\u3002\u5206\u5272\u7d71\u6cbb\u6cd5\u3068\u3044\u3046\u5358\u7d14\u306a\u30a2\u30a4\u30c7\u30a2\u304c\u3001\u5e83\u5927\u306a\u5fdc\u7528\u9818\u57df\u3092\u751f\u307f\u51fa\u3057\u307e\u3057\u305f<a href=\"http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html\" target=\"_blank\" rel=\"noreferrer noopener\">4<\/a><a href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn1_2.html\" target=\"_blank\" rel=\"noreferrer noopener\">8<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">12.2 FFT\u306e\u8ab2\u984c\u3068\u9650\u754c<\/h3>\n\n\n\n<p>\u4e00\u65b9\u3067\u3001FFT\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u8ab2\u984c\u3084\u9650\u754c\u3082\u5b58\u5728\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6642\u9593-\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5<\/strong>: \u5468\u6ce2\u6570\u5206\u89e3\u80fd\u3092\u9ad8\u3081\u308b\u3068\u6642\u9593\u5206\u89e3\u80fd\u304c\u4e0b\u304c\u308a\u3001\u9006\u306b\u6642\u9593\u5206\u89e3\u80fd\u3092\u9ad8\u3081\u308b\u3068\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u304c\u4e0b\u304c\u308b\u3068\u3044\u3046\u57fa\u672c\u7684\u306a\u5236\u7d04\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a><a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\" target=\"_blank\" rel=\"noreferrer noopener\">17<\/a>\u3002<\/li>\n\n\n\n<li><strong>\u975e\u5b9a\u5e38\u4fe1\u53f7\u3078\u306e\u5bfe\u5fdc<\/strong>: FFT\u306f\u672c\u8cea\u7684\u306b\u4fe1\u53f7\u5168\u4f53\u3092\u4e00\u5ea6\u306b\u51e6\u7406\u3059\u308b\u305f\u3081\u3001\u6642\u9593\u3068\u3068\u3082\u306b\u7279\u6027\u304c\u5909\u5316\u3059\u308b\u975e\u5b9a\u5e38\u4fe1\u53f7\u306e\u5206\u6790\u306b\u306f\u8ffd\u52a0\u306e\u5de5\u592b\u304c\u5fc5\u8981\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>2\u306e\u3079\u304d\u4e57\u5236\u7d04<\/strong>: \u6a19\u6e96\u7684\u306aFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30c7\u30fc\u30bf\u70b9\u306e\u6570\u304c2\u306e\u3079\u304d\u4e57\u3067\u3042\u308b\u5834\u5408\u306b\u6700\u3082\u52b9\u7387\u7684\u306b\u52d5\u4f5c\u3059\u308b\u3068\u3044\u3046\u5236\u7d04\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/ice-tohtech.jp\/nakagawa\/fourier\/dft1_c1.htm\" target=\"_blank\" rel=\"noreferrer noopener\">3<\/a><a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\" target=\"_blank\" rel=\"noreferrer noopener\">7<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">12.3 FFT\u306e\u6700\u65b0\u30c8\u30ec\u30f3\u30c9\u3068\u9032\u5316<\/h3>\n\n\n\n<p>FFT\u6280\u8853\u306f\u73fe\u5728\u3082\u9032\u5316\u3092\u7d9a\u3051\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u5b9f\u88c5\u306e\u9032\u6b69<\/strong>: GPU\u3084\u5c02\u7528\u30c1\u30c3\u30d7\u4e0a\u3067\u306eFFT\u5b9f\u88c5\u304c\u9ad8\u5ea6\u5316\u3057\u3001\u3055\u3089\u306a\u308b\u9ad8\u901f\u5316\u3068\u7701\u96fb\u529b\u5316\u304c\u9032\u3093\u3067\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30b9\u30de\u30fc\u30c8\u30d5\u30a9\u30f3\u306eAI\u30c1\u30c3\u30d7\u3084IoT\u30c7\u30d0\u30a4\u30b9\u3067\u3082\u52b9\u7387\u7684\u306bFFT\u3092\u5b9f\u884c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u307e\u3059<a href=\"https:\/\/arxiv.org\/abs\/1712.04910\" target=\"_blank\" rel=\"noreferrer noopener\">6<\/a><a href=\"https:\/\/www.semanticscholar.org\/paper\/9accea3fc84a74bfd19088f5641630f64c143ed4\" target=\"_blank\" rel=\"noreferrer noopener\">13<\/a><a href=\"https:\/\/www.keyence.co.jp\/ss\/general\/iot-glossary\/fft.jsp\" target=\"_blank\" rel=\"noreferrer noopener\">16<\/a>\u3002<\/li>\n\n\n\n<li><strong>\u91cf\u5b50FFT\u306e\u7814\u7a76<\/strong>: \u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u4e0a\u3067\u306eFFT\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08\u91cf\u5b50FFT\uff09\u306e\u7814\u7a76\u3082\u9032\u3093\u3067\u304a\u308a\u3001\u5c06\u6765\u7684\u306b\u306f\u53e4\u5178\u7684\u306aFFT\u3092\u8d85\u3048\u308b\u6027\u80fd\u3092\u767a\u63ee\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30b9\u30d1\u30fc\u30b9FFT\u306e\u958b\u767a<\/strong>: \u591a\u304f\u306e\u30bc\u30ed\u6210\u5206\u3084\u7121\u8996\u3067\u304d\u308b\u6210\u5206\u3092\u542b\u3080\u4fe1\u53f7\uff08\u30b9\u30d1\u30fc\u30b9\u4fe1\u53f7\uff09\u306b\u5bfe\u3057\u3066\u3001\u3055\u3089\u306b\u52b9\u7387\u7684\u306b\u8a08\u7b97\u3067\u304d\u308b\u30b9\u30d1\u30fc\u30b9FFT\u306e\u7814\u7a76\u3082\u9032\u3093\u3067\u3044\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">12.4 FFT\u306e\u65b0\u305f\u306a\u5fdc\u7528\u9818\u57df<\/h3>\n\n\n\n<p>FFT\u306e\u5fdc\u7528\u9818\u57df\u306f\u3055\u3089\u306b\u5e83\u304c\u308a\u3064\u3064\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6df1\u5c64\u5b66\u7fd2\u3068\u306e\u878d\u5408<\/strong>: \u7573\u307f\u8fbc\u307f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08CNN\uff09\u306e\u8a08\u7b97\u3092\u9ad8\u901f\u5316\u3059\u308b\u305f\u3081\u306bFFT\u3092\u6d3b\u7528\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\uff08\u4f8b\uff1aCirCNN\uff09\u304c\u7814\u7a76\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001AI\u306e\u5b66\u7fd2\u3068\u63a8\u8ad6\u304c\u9ad8\u901f\u5316\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059<a href=\"https:\/\/arxiv.org\/abs\/1708.08917\" target=\"_blank\" rel=\"noreferrer noopener\">1<\/a><a href=\"https:\/\/arxiv.org\/abs\/1712.04910\" target=\"_blank\" rel=\"noreferrer noopener\">6<\/a>\u3002<\/li>\n\n\n\n<li><strong>\u30a8\u30c3\u30b8\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0<\/strong>: \u7701\u96fb\u529b\u304b\u3064\u9ad8\u901f\u306aFFT\u5b9f\u88c5\u306b\u3088\u308a\u3001\u5c0f\u578bIoT\u30c7\u30d0\u30a4\u30b9\u3067\u3082\u8907\u96d1\u306a\u4fe1\u53f7\u51e6\u7406\u304c\u53ef\u80fd\u306b\u306a\u308a\u3064\u3064\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u97f3\u58f0\u30ad\u30fc\u30ef\u30fc\u30c9\u3092\u8a8d\u8b58\u3059\u308b\u30a6\u30a7\u30a4\u30af\u30ef\u30fc\u30c9\u691c\u51fa\u30b7\u30b9\u30c6\u30e0\u306bFFT\u30d9\u30fc\u30b9\u306e\u51e6\u7406\u304c\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.semanticscholar.org\/paper\/9accea3fc84a74bfd19088f5641630f64c143ed4\" target=\"_blank\" rel=\"noreferrer noopener\">13<\/a><a href=\"https:\/\/www.keyence.co.jp\/ss\/general\/iot-glossary\/fft.jsp\" target=\"_blank\" rel=\"noreferrer noopener\">16<\/a>\u3002<\/li>\n\n\n\n<li><strong>\u30de\u30c6\u30ea\u30a2\u30eb\u30b5\u30a4\u30a8\u30f3\u30b9<\/strong>: \u6750\u6599\u79d1\u5b66\u306e\u5206\u91ce\u3067\u3082\u3001FFT\u30d9\u30fc\u30b9\u306e\u8a08\u7b97\u624b\u6cd5\u304c\u5fae\u7d30\u69cb\u9020\u89e3\u6790\u3084\u7269\u6027\u4e88\u6e2c\u306b\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059<a href=\"https:\/\/www.semanticscholar.org\/paper\/d2d2f71befa91540e96f78a12f7a4803ce886297\" target=\"_blank\" rel=\"noreferrer noopener\">9<\/a><a href=\"https:\/\/www.semanticscholar.org\/paper\/aa2cd9cf55b1e1d6fb2e0f00761a8d6dfe40a873\" target=\"_blank\" rel=\"noreferrer noopener\">14<\/a>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">12.5 \u7d50\u8ad6<\/h3>\n\n\n\n<p>FFT\u306f\u30011960\u5e74\u4ee3\u306b\u518d\u767a\u898b\u3055\u308c\u3066\u304b\u3089\u534a\u4e16\u7d00\u4ee5\u4e0a\u7d4c\u3063\u305f\u4eca\u3067\u3082\u3001\u30c7\u30b8\u30bf\u30eb\u4fe1\u53f7\u51e6\u7406\u306e\u4e2d\u5fc3\u7684\u306a\u6280\u8853\u3067\u3042\u308a\u7d9a\u3051\u3066\u3044\u307e\u3059\u3002\u8a08\u7b97\u52b9\u7387\u306e\u5287\u7684\u306a\u6539\u5584\u3092\u3082\u305f\u3089\u3057\u305fFFT\u306f\u3001\u73fe\u4ee3\u306e\u30c7\u30b8\u30bf\u30eb\u6280\u8853\u306e\u591a\u304f\u306e\u5206\u91ce\u3067\u6839\u5e79\u3092\u652f\u3048\u308b\u6280\u8853\u3068\u306a\u308a\u3001\u4eca\u5f8c\u3082\u65b0\u305f\u306a\u6280\u8853\u3084\u5fdc\u7528\u5206\u91ce\u3068\u7d50\u3073\u3064\u3044\u3066\u767a\u5c55\u3092\u7d9a\u3051\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>FFT\u306e\u539f\u7406\u3092\u7406\u89e3\u3057\u3001\u305d\u306e\u7279\u6027\u3068\u9650\u754c\u3092\u8a8d\u8b58\u3059\u308b\u3053\u3068\u3067\u3001\u69d8\u3005\u306a\u5206\u91ce\u3067\u3053\u306e\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3092\u9069\u5207\u306b\u6d3b\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002FFT\u306f\u3059\u3067\u306b\u79c1\u305f\u3061\u306e\u751f\u6d3b\u3092\u5927\u304d\u304f\u5909\u3048\u307e\u3057\u305f\u304c\u3001\u4eca\u5f8c\u3082\u65b0\u3057\u3044\u6280\u8853\u9769\u65b0\u3092\u3082\u305f\u3089\u3057\u7d9a\u3051\u308b\u3053\u3068\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u4eba\u9593\u3068\u6a5f\u68b0\u306e\u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u304c\u91cd\u8981\u6027\u3092\u5897\u3059\u73fe\u4ee3\u306b\u304a\u3044\u3066\u3001\u4fe1\u53f7\u51e6\u7406\u306e\u57fa\u76e4\u6280\u8853\u3067\u3042\u308bFFT\u306e\u91cd\u8981\u6027\u306f\u3055\u3089\u306b\u9ad8\u307e\u3063\u3066\u3044\u304f\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u305d\u308c\u3086\u3048\u3001FFT\u306f\u4eca\u5f8c\u3082\u79d1\u5b66\u6280\u8853\u306e\u767a\u5c55\u306b\u304a\u3051\u308b\u91cd\u8981\u306a\u57fa\u76e4\u6280\u8853\u3067\u3042\u308a\u7d9a\u3051\u308b\u3067\u3057\u3087\u3046<a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1708.08917\">1<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1712.04910\">6<\/a><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"http:\/\/arxiv.org\/pdf\/2402.01843.pdf\">15<\/a>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Citations:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/arxiv.org\/abs\/1708.08917\">https:\/\/arxiv.org\/abs\/1708.08917<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.murata-s.co.jp\/research\/fourier\">https:\/\/www.murata-s.co.jp\/research\/fourier<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ice-tohtech.jp\/nakagawa\/fourier\/dft1_c1.htm\">https:\/\/ice-tohtech.jp\/nakagawa\/fourier\/dft1_c1.htm<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html\">http:\/\/wwwa.pikara.ne.jp\/okojisan\/stockham\/cooley-tukey.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf\">https:\/\/www.onosokki.co.jp\/HP-WK\/eMM_back\/emm140.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/abs\/1712.04910\">https:\/\/arxiv.org\/abs\/1712.04910<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm\">https:\/\/www.ni.com\/docs\/ja-JP\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_fouriertransform.htm<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn1_2.html\">https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn1_2.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/d2d2f71befa91540e96f78a12f7a4803ce886297\">https:\/\/www.semanticscholar.org\/paper\/d2d2f71befa91540e96f78a12f7a4803ce886297<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\">https:\/\/ja.wikipedia.org\/wiki\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/2dd38cb1fc7efa9ddaa5e08277aa48229d836a72\">https:\/\/www.semanticscholar.org\/paper\/2dd38cb1fc7efa9ddaa5e08277aa48229d836a72<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Cooley%E2%80%93Tukey_FFT_algorithm\">https:\/\/en.wikipedia.org\/wiki\/Cooley%E2%80%93Tukey_FFT_algorithm<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/9accea3fc84a74bfd19088f5641630f64c143ed4\">https:\/\/www.semanticscholar.org\/paper\/9accea3fc84a74bfd19088f5641630f64c143ed4<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/aa2cd9cf55b1e1d6fb2e0f00761a8d6dfe40a873\">https:\/\/www.semanticscholar.org\/paper\/aa2cd9cf55b1e1d6fb2e0f00761a8d6dfe40a873<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/arxiv.org\/pdf\/2402.01843.pdf\">http:\/\/arxiv.org\/pdf\/2402.01843.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.keyence.co.jp\/ss\/general\/iot-glossary\/fft.jsp\">https:\/\/www.keyence.co.jp\/ss\/general\/iot-glossary\/fft.jsp<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\">https:\/\/www.nti-audio.com\/ja\/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88\/%E6%B8%AC%E5%AE%9A%E3%83%8E%E3%82%A6%E3%83%8F%E3%82%A6\/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/efef419349297913ec4d1f929c26ec7727ae7455\">https:\/\/www.semanticscholar.org\/paper\/efef419349297913ec4d1f929c26ec7727ae7455<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/674db8f0f7005cf27f770130a3e8717fcbb7996e\">https:\/\/www.semanticscholar.org\/paper\/674db8f0f7005cf27f770130a3e8717fcbb7996e<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/ebe41d33b83c2091abe94f08c57fd5bd9cb22519\">https:\/\/www.semanticscholar.org\/paper\/ebe41d33b83c2091abe94f08c57fd5bd9cb22519<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/fc914331b9b413014cba3438c32053b1c0b4768b\">https:\/\/www.semanticscholar.org\/paper\/fc914331b9b413014cba3438c32053b1c0b4768b<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/2003.03011.pdf\">https:\/\/arxiv.org\/pdf\/2003.03011.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/1911.03055.pdf\">https:\/\/arxiv.org\/pdf\/1911.03055.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/html\/2412.12308v1\">https:\/\/arxiv.org\/html\/2412.12308v1<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/2008.12559.pdf\">https:\/\/arxiv.org\/pdf\/2008.12559.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/jp.mathworks.com\/discovery\/fourier-transform.html\">https:\/\/jp.mathworks.com\/discovery\/fourier-transform.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.yacmo.co.jp\/technology\/tips\/fft-analysis\/\">https:\/\/www.yacmo.co.jp\/technology\/tips\/fft-analysis\/<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.netattest.com\/fast-fourier-transform-2024_mkt_tst\">https:\/\/www.netattest.com\/fast-fourier-transform-2024_mkt_tst<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/zenn.dev\/masswork\/articles\/fft-understanding-01\">https:\/\/zenn.dev\/masswork\/articles\/fft-understanding-01<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B\">https:\/\/ja.wikipedia.org\/wiki\/%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.sit.ac.jp\/user\/cao\/documents\/CH2-2.pdf\">https:\/\/www.sit.ac.jp\/user\/cao\/documents\/CH2-2.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.techeyesonline.com\/glossary\/detail\/FFT\/\">https:\/\/www.techeyesonline.com\/glossary\/detail\/FFT\/<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.fukudaco.co.jp\/support\/glossary\/fft.html\">https:\/\/www.fukudaco.co.jp\/support\/glossary\/fft.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.weblio.jp\/content\/Fourier+transform\">https:\/\/www.weblio.jp\/content\/Fourier+transform<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gochikika.ntt.com\/Visualization_and_EDA\/fourier_transform.html\">https:\/\/gochikika.ntt.com\/Visualization_and_EDA\/fourier_transform.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/qiita.com\/ageprocpp\/items\/0d63d4ed80de4a35fe79\">https:\/\/qiita.com\/ageprocpp\/items\/0d63d4ed80de4a35fe79<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/svmeas.rion.co.jp\/support\/p38veq0000000cmg-att\/FFT_07881.pdf\">https:\/\/svmeas.rion.co.jp\/support\/p38veq0000000cmg-att\/FFT_07881.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/skill-hacks.co.jp\/media\/fourier-transform\/\">https:\/\/skill-hacks.co.jp\/media\/fourier-transform\/<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/acserv.st.seikei.ac.jp\/biolab\/lecture\/Bioelecronics\/2.5Fourier.pdf\">http:\/\/acserv.st.seikei.ac.jp\/biolab\/lecture\/Bioelecronics\/2.5Fourier.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ni.com\/ja\/shop\/data-acquisition\/measurement-fundamentals\/analog-fundamentals\/understanding-ffts-and-windowing.html\">https:\/\/www.ni.com\/ja\/shop\/data-acquisition\/measurement-fundamentals\/analog-fundamentals\/understanding-ffts-and-windowing.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.fbs.osaka-u.ac.jp\/labs\/ishijima\/FFT-05.html\">https:\/\/www.fbs.osaka-u.ac.jp\/labs\/ishijima\/FFT-05.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/a9794a8272381e9729dd9e8f6fc150d710e1d0da\">https:\/\/www.semanticscholar.org\/paper\/a9794a8272381e9729dd9e8f6fc150d710e1d0da<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/7faf29864ea7f88145877e9a2960de8b8592b8d5\">https:\/\/www.semanticscholar.org\/paper\/7faf29864ea7f88145877e9a2960de8b8592b8d5<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/ab24993db75218241541ad236879094207c009b0\">https:\/\/www.semanticscholar.org\/paper\/ab24993db75218241541ad236879094207c009b0<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/16f6134623d08992c919ed1f76b60cf7c77a4f93\">https:\/\/www.semanticscholar.org\/paper\/16f6134623d08992c919ed1f76b60cf7c77a4f93<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E6%99%82%E9%96%93%E9%A0%98%E5%9F%9F\">https:\/\/ja.wikipedia.org\/wiki\/%E6%99%82%E9%96%93%E9%A0%98%E5%9F%9F<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/techblog.raccoon.ne.jp\/archives\/1699519432.html\">https:\/\/techblog.raccoon.ne.jp\/archives\/1699519432.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E6%99%82%E9%96%93%E5%91%A8%E6%B3%A2%E6%95%B0%E8%A7%A3%E6%9E%90\">https:\/\/ja.wikipedia.org\/wiki\/%E6%99%82%E9%96%93%E5%91%A8%E6%B3%A2%E6%95%B0%E8%A7%A3%E6%9E%90<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.pgv.co.jp\/nais-entry\/case-study\/-0\">https:\/\/www.pgv.co.jp\/nais-entry\/case-study\/-0<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.te.chiba-u.jp\/lab\/ken\/lecture\/Trans-2.pdf\">https:\/\/www.te.chiba-u.jp\/lab\/ken\/lecture\/Trans-2.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/qiita.com\/TumoiYorozu\/items\/5855d75a47ef2c7e62c8\">https:\/\/qiita.com\/TumoiYorozu\/items\/5855d75a47ef2c7e62c8<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.klv.co.jp\/corner\/fft-in-freq-analysis.html\">https:\/\/www.klv.co.jp\/corner\/fft-in-freq-analysis.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.mech.kumamoto-u.ac.jp\/Info\/lab\/sensor\/lect\/Signal_Ch_3.pdf\">https:\/\/www.mech.kumamoto-u.ac.jp\/Info\/lab\/sensor\/lect\/Signal_Ch_3.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/delta-beta.com\/ja\/fft\/\">https:\/\/delta-beta.com\/ja\/fft\/<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/zenn.dev\/yuto_mo\/articles\/1b2fdde0bf9d79\">https:\/\/zenn.dev\/yuto_mo\/articles\/1b2fdde0bf9d79<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E5%91%A8%E6%B3%A2%E6%95%B0%E9%A0%98%E5%9F%9F\">https:\/\/ja.wikipedia.org\/wiki\/%E5%91%A8%E6%B3%A2%E6%95%B0%E9%A0%98%E5%9F%9F<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.jasco.co.jp\/jpn\/technique\/internet-seminar\/ftir\/ftir3.html\">https:\/\/www.jasco.co.jp\/jpn\/technique\/internet-seminar\/ftir\/ftir3.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/c5b760f0bf96c1b48cceefd5895992a8a45dbfb4\">https:\/\/www.semanticscholar.org\/paper\/c5b760f0bf96c1b48cceefd5895992a8a45dbfb4<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/4dc43a06312508b40f681e7e3d71f72034715c73\">https:\/\/www.semanticscholar.org\/paper\/4dc43a06312508b40f681e7e3d71f72034715c73<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/379713ae114b57e7e259a364beb1ca1bbcf91c41\">https:\/\/www.semanticscholar.org\/paper\/379713ae114b57e7e259a364beb1ca1bbcf91c41<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/4170add1786c863194d24f4560bd3aae43365717\">https:\/\/www.semanticscholar.org\/paper\/4170add1786c863194d24f4560bd3aae43365717<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/2002.03260.pdf\">https:\/\/arxiv.org\/pdf\/2002.03260.pdf<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/arxiv.org\/pdf\/2405.05163.pdf\">http:\/\/arxiv.org\/pdf\/2405.05163.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn2_12.html\">https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn2_12.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/qiita.com\/shushin\/items\/dd8770625853def6d1fc\">https:\/\/qiita.com\/shushin\/items\/dd8770625853def6d1fc<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/qiita.com\/habuyoshiaki\/items\/68d502c7bc0c35c168ef\">https:\/\/qiita.com\/habuyoshiaki\/items\/68d502c7bc0c35c168ef<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.momoyama-usagi.com\/entry\/math-seigyo14\">https:\/\/www.momoyama-usagi.com\/entry\/math-seigyo14<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/www.na.scitec.kobe-u.ac.jp\/~yamamoto\/lectures\/parallelFFT\/parallelFFT1.PDF\">http:\/\/www.na.scitec.kobe-u.ac.jp\/~yamamoto\/lectures\/parallelFFT\/parallelFFT1.PDF<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/mkguytone.github.io\/java-opencl\/ch12s04.html\">https:\/\/mkguytone.github.io\/java-opencl\/ch12s04.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/qiita.com\/pentargon\/items\/927f7f7f88a1532d81eb\">https:\/\/qiita.com\/pentargon\/items\/927f7f7f88a1532d81eb<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/tech.preferred.jp\/ja\/blog\/fft-for-mn-core\/\">https:\/\/tech.preferred.jp\/ja\/blog\/fft-for-mn-core\/<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/detail.chiebukuro.yahoo.co.jp\/qa\/question_detail\/q129532137\">https:\/\/detail.chiebukuro.yahoo.co.jp\/qa\/question_detail\/q129532137<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn1_23.html\">https:\/\/www.kurims.kyoto-u.ac.jp\/~ooura\/fftman\/ftmn1_23.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.tsuyama-ct.ac.jp\/matsuda\/surikogaku\/surib3.pdf\">https:\/\/www.tsuyama-ct.ac.jp\/matsuda\/surikogaku\/surib3.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/qiita.com\/chalharu\/items\/14ee4bd8396792d5175c\">https:\/\/qiita.com\/chalharu\/items\/14ee4bd8396792d5175c<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/oshiete.goo.ne.jp\/qa\/5403159.html\">https:\/\/oshiete.goo.ne.jp\/qa\/5403159.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/1908.02461.pdf\">https:\/\/arxiv.org\/pdf\/1908.02461.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/1507.01832.pdf\">https:\/\/arxiv.org\/pdf\/1507.01832.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/abs\/1301.1248\">https:\/\/arxiv.org\/abs\/1301.1248<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/1006.2811.pdf\">https:\/\/arxiv.org\/pdf\/1006.2811.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/pdf\/0808.2172.pdf\">https:\/\/arxiv.org\/pdf\/0808.2172.pdf<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/hkawabata.github.io\/technical-note\/note\/Algorithm\/fft.html\">https:\/\/hkawabata.github.io\/technical-note\/note\/Algorithm\/fft.html<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.cybernet.co.jp\/ansys\/learning\/glossary\/fftkaiseki\/\">https:\/\/www.cybernet.co.jp\/ansys\/learning\/glossary\/fftkaiseki\/<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/a30a7a051ca7bc99eb33a014297e0467a6d5c7f7\">https:\/\/www.semanticscholar.org\/paper\/a30a7a051ca7bc99eb33a014297e0467a6d5c7f7<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/e8d13e207d0362c5fbae67422befb7a1ee4bf0b4\">https:\/\/www.semanticscholar.org\/paper\/e8d13e207d0362c5fbae67422befb7a1ee4bf0b4<\/a><\/li>\n\n\n\n<li><a 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href=\"https:\/\/www.isc.meiji.ac.jp\/~mcelab\/www_jyo_en2\/jyo_en_2_8_j_2015_f\/index_sj.html\">https:\/\/www.isc.meiji.ac.jp\/~mcelab\/www_jyo_en2\/jyo_en_2_8_j_2015_f\/index_sj.html<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/www.isc.meiji.ac.jp\/~mcelab\/jyo_en2\/2021\/07\/index.htm\">http:\/\/www.isc.meiji.ac.jp\/~mcelab\/jyo_en2\/2021\/07\/index.htm<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/manabitimes.jp\/math\/2280\">https:\/\/manabitimes.jp\/math\/2280<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/arxiv.org\/abs\/2505.02509\">https:\/\/arxiv.org\/abs\/2505.02509<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/b45e01b91b9e2f3afb02c1d48b929d5751c7ce64\">https:\/\/www.semanticscholar.org\/paper\/b45e01b91b9e2f3afb02c1d48b929d5751c7ce64<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.semanticscholar.org\/paper\/9ef5d5ce6041a07a8b6642177a01f6f11470d60b\">https:\/\/www.semanticscholar.org\/paper\/9ef5d5ce6041a07a8b6642177a01f6f11470d60b<\/a><\/li>\n\n\n\n<li><a 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