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\u30db\u30c3\u30d7\u9577\u3068\u91cd\u306a\u308a\u306b\u306f\u3001\u89e3\u6790\u306e\u72d9\u3044\u4ee5\u5916\u306b\u300c\u91cd\u306d\u5408\u308f\u305b\u3067\u5747\u4e00\u306b\u30ab\u30d0\u30fc\u3067\u304d\u308b\u304b\u300d\u3068\u3044\u3046\u89b3\u70b9\u3082\u3042\u308b\u3002\u7a93\u3092\u4e26\u3079\u3066\u52a0\u3048\u5408\u308f\u305b\u305f\u3068\u304d\u306b\u3001\u6642\u9593\u65b9\u5411\u3067\u5747\u4e00\u306a\u91cd\u307f\u306b\u306a\u308b\u6761\u4ef6\uff08COLA, constant overlap-add\uff09\u3092\u6e80\u305f\u3059\u30db\u30c3\u30d7\u9577\u306e\u9078\u629e\u306f\u3001\u518d\u5408\u6210\uff08\u9006\u5909\u63db\uff09\u3084\u30b9\u30e0\u30fc\u30ba\u306a\u89e3\u6790\u306e\u89b3\u70b9\u3067\u4fdd\u5b88\u7684\u306a\u6307\u91dd\u306b\u306a\u308b\u3002\u30cf\u30f3\u3084\u30cf\u30df\u30f3\u30b0\u7a93\u3067\u306f\u30011\/2\u30841\/4\u306a\u3069\u7279\u5b9a\u306e\u91cd\u306a\u308a\u3067\u90fd\u5408\u304c\u826f\u3044\uff08\u304d\u308c\u3044\u306b\u91cd\u306a\u308b\uff09\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u304a\u308a\u3001\u3053\u3046\u3057\u305f\u6027\u8cea\u3092\u8e0f\u307e\u3048\u3066\u30db\u30c3\u30d7\u9577\u3092\u6c7a\u3081\u308b\u306e\u304c\u5b89\u5168\u7b56\u306b\u306a\u308b\u3002\u4e00\u65b9\u3001\u89e3\u6790\u3060\u3051\u3067\u518d\u5408\u6210\u3092\u4f34\u308f\u306a\u3044\u5834\u5408\u306b\u306f\u3001\u4fe1\u53f7\u306e\u5909\u5316\u901f\u5ea6\u306b\u5fdc\u3058\u3066\u30db\u30c3\u30d7\u9577\u3092\u5e83\u3052\u3001\u8a08\u7b97\u91cf\u3092\u6291\u3048\u308b\u5b9f\u52d9\u7684\u306a\u8abf\u6574\u3082\u884c\u308f\u308c\u308b\u3002[9]\n\n\n\n
STFT\u306e\u7d50\u679c\u306f\u3075\u3064\u3046\u6975\u5ea7\u6a19\uff08\u8907\u7d20\u6570\uff09\u3067\u5f97\u3089\u308c\u3001\u632f\u5e45\uff08\u5927\u304d\u3055\uff09\u3068\u4f4d\u76f8\uff08\u89d2\u5ea6\uff09\u306e\u4e21\u65b9\u306e\u60c5\u5831\u3092\u542b\u3080\u3002\u898b\u3084\u3059\u3055\u306e\u305f\u3081\u3001\u632f\u5e45\u3092\u5bfe\u6570\u30b9\u30b1\u30fc\u30eb\uff08dB\uff09\u306b\u3057\u3066\u6642\u9593\u00d7\u5468\u6ce2\u6570\u306e\u753b\u50cf\uff08\u30b9\u30da\u30af\u30c8\u30ed\u30b0\u30e9\u30e0\uff09\u306b\u3059\u308c\u3070\u3001\u5f37\u3044\u6210\u5206\u304c\u660e\u308b\u304f\uff08\u307e\u305f\u306f\u6fc3\u304f\uff09\u8868\u793a\u3055\u308c\u3001\u3069\u306e\u6642\u523b\u306b\u3069\u306e\u5468\u6ce2\u6570\u304c\u5f37\u304b\u3063\u305f\u304b\u304c\u76f4\u89b3\u7684\u306b\u5206\u304b\u308b\u3002\u97f3\u58f0\u306a\u3069\u3067\u306f\u3001\u30d2\u30c8\u306e\u8074\u611f\u306b\u8fd1\u3065\u3051\u308b\u305f\u3081\u306b\u5468\u6ce2\u6570\u8ef8\u3092\u30e1\u30eb\u5c3a\u5ea6\u306b\u4e26\u3079\u66ff\u3048\u305f\u300c\u30e1\u30eb\u30b9\u30da\u30af\u30c8\u30ed\u30b0\u30e9\u30e0\u300d\u3092\u4f7f\u3046\u3053\u3068\u3082\u3042\u308b\u3002\u305f\u3060\u3057\u3001\u4f4d\u76f8\u3092\u6368\u3066\u3066\u632f\u5e45\u3060\u3051\u3092\u7528\u3044\u308b\u3068\u518d\u5408\u6210\u306b\u8ab2\u984c\u304c\u751f\u3058\u308b\u305f\u3081\u3001\u5fa9\u5143\u304c\u5fc5\u8981\u306a\u7528\u9014\u3067\u306f\u4f4d\u76f8\u306e\u6271\u3044\uff08\u307e\u305f\u306f\u5fa9\u5143\u624b\u6cd5\uff09\u3082\u691c\u8a0e\u304c\u8981\u308b\u3068\u3044\u3046\u7814\u7a76\u7684\u306a\u6307\u6458\u304c\u3042\u308b\u3002[3][10][2]\n\n\n\n
STFT\u3092\u5b9f\u52d9\u3067\u8a2d\u8a08\u3059\u308b\u3068\u304d\u306e\u52d8\u3069\u3053\u308d\u3092\u307e\u3068\u3081\u308b\u3002\u7b2c\u4e00\u306b\u3001\u7a93\u9577\u306f\u300c\u898b\u305f\u3044\u73fe\u8c61\u306e\u6642\u9593\u5e45\u300d\u306b\u5408\u308f\u305b\u308b\u3002\u77ed\u3044\u885d\u6483\u3084\u7d20\u65e9\u3044\u904e\u6e21\u3092\u8ffd\u3046\u306a\u3089\u77ed\u7a93\u3001\u72ed\u3044\u5468\u6ce2\u6570\u5dee\u3092\u5206\u3051\u305f\u3044\u306a\u3089\u9577\u7a93\u304c\u6709\u5229\u3067\u3042\u308b\u3002\u7b2c\u4e8c\u306b\u3001\u7a93\u95a2\u6570\u306f\u6f0f\u308c\u3068\u5206\u89e3\u80fd\u306e\u30d0\u30e9\u30f3\u30b9\u3067\u9078\u3073\u3001\u307e\u305a\u306f\u30cf\u30df\u30f3\u30b0\u3084\u30cf\u30f3\u3092\u57fa\u6e96\u306b\u3001\u6f0f\u308c\u304c\u554f\u984c\u306a\u3089\u30d6\u30e9\u30c3\u30af\u30de\u30f3\u7cfb\u306a\u3069\u3078\u306e\u5909\u66f4\u3092\u691c\u8a0e\u3059\u308b\u3002\u7b2c\u4e09\u306b\u3001\u30aa\u30fc\u30d0\u30fc\u30e9\u30c3\u30d7\u306f50\u301c75%\u3092\u8d77\u70b9\u306b\u3001\u6642\u9593\u65b9\u5411\u306e\u306a\u3081\u3089\u304b\u3055\u3068\u8a08\u7b97\u91cf\u306e\u6298\u308a\u5408\u3044\u3092\u3064\u3051\u308b\u3002\u518d\u5408\u6210\u3084\u5747\u4e00\u52a0\u91cd\u3092\u610f\u8b58\u3059\u308b\u306a\u3089COLA\u6761\u4ef6\u306b\u914d\u616e\u3057\u305f\u30db\u30c3\u30d7\u9577\u3092\u9078\u3076\u3002\u7b2c\u56db\u306b\u3001\u8868\u793a\u306fdB\u30b9\u30b1\u30fc\u30eb\u306e\u30b9\u30da\u30af\u30c8\u30ed\u30b0\u30e9\u30e0\u3067\u50be\u5411\u3092\u628a\u63e1\u3057\u3001\u5fc5\u8981\u306a\u3089\u5468\u6ce2\u6570\u8ef8\u306e\u5909\u63db\uff08\u30e1\u30eb\u306a\u3069\uff09\u3082\u691c\u8a0e\u3059\u308b\u3002\u7b2c\u4e94\u306b\u3001\u5b9f\u88c5\u3067\u306fFFT\u3092\u7528\u3044\u308b\u96e2\u6563STFT\u95a2\u6570\uff08\u4f8b\uff1alibrosa\u3084MATLAB\u306eSTFT\uff09\u3092\u4f7f\u3044\u3001\u7a93\u9577\u30fb\u30db\u30c3\u30d7\u9577\u30fb\u7a93\u95a2\u6570\u30fb\u30aa\u30fc\u30d0\u30fc\u30e9\u30c3\u30d7\u3092\u660e\u793a\u7684\u306b\u8a2d\u5b9a\u3059\u308b\u3002[5][6][8][9][7][4][2][3]\n\n\n\n
\u6700\u5f8c\u306b\u3001STFT\u306e\u9650\u754c\u3082\u6b63\u3057\u304f\u7406\u89e3\u3057\u3066\u304a\u304f\u3002STFT\u306f\u300c\u56fa\u5b9a\u306e\u7a93\u9577\u300d\u3067\u5168\u533a\u9593\u3092\u5206\u6790\u3059\u308b\u305f\u3081\u3001\u901f\u3044\u73fe\u8c61\u3068\u9045\u3044\u73fe\u8c61\u304c\u6df7\u5728\u3059\u308b\u5834\u5408\u3001\u3069\u3061\u3089\u304b\u306b\u4e0d\u5229\u306a\u8a2d\u5b9a\u306b\u306a\u308a\u304c\u3061\u3067\u3042\u308b\u3002\u3053\u306e\u56fa\u5b9a\u5206\u89e3\u80fd\u306e\u9650\u754c\u306f\u539f\u7406\u7684\u306a\u3082\u306e\u3067\u3001\u6642\u9593\u3068\u5468\u6ce2\u6570\u306e\u5206\u89e3\u80fd\u306f\u540c\u6642\u306b\u7121\u9650\u5927\u306b\u306f\u3067\u304d\u306a\u3044\uff08\u4e0d\u78ba\u5b9a\u6027\u539f\u7406\uff09\u3002\u3053\u306e\u6b20\u70b9\u3092\u88dc\u3046\u8003\u3048\u65b9\u3068\u3057\u3066\u3001\u7a93\u306e\u5e45\u3092\u5468\u6ce2\u6570\u306b\u5fdc\u3058\u3066\u5909\u3048\u308b\u30a6\u30a7\u30fc\u30d6\u30ec\u30c3\u30c8\u5909\u63db\u306e\u3088\u3046\u306a\u65b9\u6cd5\u3082\u3042\u308b\u304c\u3001STFT\u306e\u7406\u89e3\u304c\u6642\u9593\u5468\u6ce2\u6570\u89e3\u6790\u306e\u5165\u53e3\u3067\u3042\u308b\u3053\u3068\u306f\u5909\u308f\u3089\u306a\u3044\u3002[11][7]\n\n\n\n
\u4ee5\u4e0a\u306e\u3088\u3046\u306b\u3001\u77ed\u6642\u9593\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306f\u300c\u77ed\u3044\u6642\u9593\u3067\u533a\u5207\u3063\u3066\u3001\u305d\u306e\u90fd\u5ea6\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3059\u308b\u300d\u3053\u3068\u3067\u3001\u3044\u3064\u30fb\u3069\u306e\u5468\u6ce2\u6570\u304c\u5f37\u304b\u3063\u305f\u304b\u30922\u6b21\u5143\u306b\u63cf\u304d\u51fa\u3059\u539f\u7406\u3067\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3002\u7a93\u9577\u30fb\u7a93\u95a2\u6570\u30fb\u30aa\u30fc\u30d0\u30fc\u30e9\u30c3\u30d7\u30fb\u30db\u30c3\u30d7\u9577\u306e\u9078\u629e\u306f\u3001\u6642\u9593\u3068\u5468\u6ce2\u6570\u306e\u898b\u3048\u65b9\u3092\u5de6\u53f3\u3059\u308b\u30cf\u30f3\u30c9\u30eb\u3067\u3042\u308a\u3001\u4fe1\u53f7\u306e\u6027\u8cea\u3068\u76ee\u7684\uff08\u901f\u3044\u5909\u5316\u3092\u6349\u3048\u308b\u306e\u304b\u3001\u8fd1\u3044\u5468\u6ce2\u6570\u3092\u5206\u3051\u305f\u3044\u306e\u304b\uff09\u304b\u3089\u9006\u7b97\u3057\u3066\u6c7a\u3081\u308b\u306e\u304c\u5b9f\u52d9\u7684\u306a\u8a2d\u8a08\u306e\u57fa\u672c\u3068\u306a\u308b\u3002[1][8][9]\n\n\n\n[1] https:\/\/ja.wikipedia.org\/wiki\/%E7%9F%AD%E6%99%82%E9%96%93%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B<\/p>\n\n\n\n[2] https:\/\/en.wikipedia.org\/wiki\/Short-time_Fourier_transform<\/p>\n\n\n\n[3] https:\/\/towardsdatascience.com\/all-you-need-to-know-to-start-speech-processing-with-deep-learning-102c916edf62\/<\/p>\n\n\n\n[4] https:\/\/library.fiveable.me\/advanced-signal-processing\/unit-1\/short-time-fourier-transform-stft\/study-guide\/OprLM7X5xQrmPIAp<\/p>\n\n\n\n[5] https:\/\/librosa.org\/doc\/main\/generated\/librosa.stft.html<\/p>\n\n\n\n[6] https:\/\/jp.mathworks.com\/help\/dsp\/ref\/dsp.stft.html<\/p>\n\n\n\n[7] https:\/\/qiml.radiology.wisc.edu\/wp-content\/uploads\/sites\/760\/2020\/10\/notes_016_stft.pdf<\/p>\n\n\n\n[8] https:\/\/www.numberanalytics.com\/blog\/short-time-fourier-transform-for-signal-analysis<\/p>\n\n\n\n[9] https:\/\/www.dsprelated.com\/freebooks\/sasp\/Choice_Hop_Size.html<\/p>\n\n\n\n[10] https:\/\/www.dafx.de\/paper-archive\/2011\/Papers\/27_e.pdf<\/p>\n\n\n\n[11] http:\/\/www7b.biglobe.ne.jp\/~yizawa\/InfSys1\/basic\/chap11\/index.htm<\/p>\n\n\n\n[12] https:\/\/ys0510.hatenablog.com\/entry\/fourier<\/p>\n\n\n\n[13] https:\/\/appswingby.com\/%E7%9F%AD%E6%99%82%E9%96%93%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B-%E4%BB%8A%E6%9B%B4%E8%81%9E%E3%81%91%E3%81%AA%E3%81%84it%E7%94%A8%E8%AA%9E%E9%9B%86\/<\/p>\n\n\n\n[14] https:\/\/fast-d.hmcom.co.jp\/techblog\/stft-from-zero\/<\/p>\n\n\n\n[15] https:\/\/www.jstage.jst.go.jp\/article\/jasj\/77\/6\/77_396\/_pdf<\/p>\n\n\n\n[16] https:\/\/note.com\/suzukusa\/n\/nc3e5b10cbf85<\/p>\n\n\n\n[17] https:\/\/qiita.com\/takayoshi1968\/items\/636372d464d02699ba4f<\/p>\n\n\n\n[18] https:\/\/labo-code.com\/python\/stft\/<\/p>\n\n\n\n[19] https:\/\/arxiv.org\/pdf\/1504.07372.pdf<\/p>\n\n\n\n[20] https:\/\/www.klv.co.jp\/corner\/fft-in-freq-analysis.html<\/p>\n\n\n\n
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