{"id":83461,"date":"2026-07-25T23:16:53","date_gmt":"2026-07-25T15:16:53","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/83461.html"},"modified":"2026-07-25T23:16:53","modified_gmt":"2026-07-25T15:16:53","slug":"%e3%80%90%e8%b6%85%e8%af%a6%e7%bb%86%e3%80%91cqt%e5%b8%b8%e6%95%b0q%e5%8f%98%e6%8d%a2%e5%ae%8c%e5%85%a8%e6%8c%87%e5%8d%97%ef%bc%9a%e4%bb%8e%e5%8e%9f%e7%90%86%e5%88%b0%e4%bb%a3%e7%a0%81%e5%ae%9e","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/83461.html","title":{"rendered":"\u3010\u8d85\u8be6\u7ec6\u3011CQT\u5e38\u6570Q\u53d8\u6362\u5b8c\u5168\u6307\u5357\uff1a\u4ece\u539f\u7406\u5230\u4ee3\u7801\u5b9e\u73b0\uff0c\u624b\u628a\u624b\u6559\u4f60\u7ed8\u5236\u9ad8\u5206\u8fa8\u7387\u97f3\u4e50\u8bed\u8c31\u56fe"},"content":{"rendered":"<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\n<ul>\n<li>\u4e00\u3001\u4e3a\u4ec0\u4e48STFT\u770b\u4e0d\u6e05\u695a\u97f3\u4e50&#xff1f;\u2014\u2014\u4ece\u9891\u8c31\u5206\u6790\u7684\u672c\u8d28\u8bf4\u8d77<\/li>\n<li>\n<ul>\n<li>1.1 \u4e00\u4e2a\u8ba9\u6240\u6709\u97f3\u9891\u5f00\u53d1\u8005\u90fd\u5934\u75bc\u7684\u95ee\u9898<\/li>\n<li>1.2 \u4ece\u201c\u4eba\u8033\u975e\u5747\u5300\u611f\u77e5\u201d\u5230\u201c\u81ea\u9002\u5e94\u5206\u8fa8\u7387\u201d\u7684\u8bbe\u8ba1\u601d\u8def<\/li>\n<\/ul>\n<\/li>\n<li>\u4e8c\u3001CQT\u7684\u6838\u5fc3\u539f\u7406&#xff1a;\u8ba9\u6bcf\u4e2a\u9891\u7387\u70b9\u90fd\u6709\u6700\u4f73\u5206\u8fa8\u7387<\/li>\n<li>\n<ul>\n<li>2.1 Q\u503c\u5230\u5e95\u662f\u4ec0\u4e48&#xff1f;<\/li>\n<li>2.2 \u7a97\u957f\u81ea\u9002\u5e94\u7684\u6570\u5b66\u539f\u7406<\/li>\n<li>2.3 \u9891\u70b9\u5e03\u5c40&#xff1a;\u6309\u97f3\u5206\u6392\u5e03\u800c\u975e\u6309\u8d6b\u5179\u6392\u5e03<\/li>\n<\/ul>\n<\/li>\n<li>\u4e09\u3001\u4ee3\u7801\u5b9e\u6218&#xff1a;CQT\u4e0eSTFT\u7684\u5bf9\u6bd4\u5b9e\u9a8c<\/li>\n<li>\n<ul>\n<li>3.1 \u73af\u5883\u51c6\u5907\u4e0e\u4f9d\u8d56\u5b89\u88c5<\/li>\n<li>3.2 \u5b8c\u6574\u7684\u5bf9\u6bd4\u5b9e\u9a8c\u4ee3\u7801<\/li>\n<li>3.3 \u4ee3\u7801\u5173\u952e\u53c2\u6570\u89e3\u8bfb<\/li>\n<li>3.4 \u8fd0\u884c\u7ed3\u679c\u89e3\u8bfb<\/li>\n<\/ul>\n<\/li>\n<li>\u56db\u3001CQT\u7684\u5de5\u7a0b\u5b9e\u8df5\u6307\u5357<\/li>\n<li>\n<ul>\n<li>4.1 \u53c2\u6570\u9009\u578b\u7684\u5b9e\u6218\u7ecf\u9a8c<\/li>\n<li>4.2 CQT\u8ba1\u7b97\u6548\u7387\u7684\u74f6\u9888\u4e0e\u4f18\u5316<\/li>\n<li>4.3 \u5e38\u89c1\u9677\u9631\u4e0e\u907f\u5751\u6307\u5357<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u4e00\u3001\u4e3a\u4ec0\u4e48STFT\u770b\u4e0d\u6e05\u695a\u97f3\u4e50&#xff1f;\u2014\u2014\u4ece\u9891\u8c31\u5206\u6790\u7684\u672c\u8d28\u8bf4\u8d77<\/h3>\n<h4>1.1 \u4e00\u4e2a\u8ba9\u6240\u6709\u97f3\u9891\u5f00\u53d1\u8005\u90fd\u5934\u75bc\u7684\u95ee\u9898<\/h4>\n<p>\u5982\u679c\u4f60\u7528\u8fc7Adobe Audition\u6216\u8005\u4efb\u4f55\u9891\u8c31\u5206\u6790\u8f6f\u4ef6&#xff0c;\u4f60\u4e00\u5b9a\u53d1\u73b0\u4e86\u4e00\u4e2a\u73b0\u8c61&#xff1a;\u4f4e\u9891\u533a\u57df\u770b\u8d77\u6765\u201c\u5f88\u5bbd\u201d&#xff0c;\u9ad8\u9891\u533a\u57df\u770b\u8d77\u6765\u201c\u5f88\u6324\u201d\u3002\u8fd9\u4e0d\u4ec5\u4ec5\u662f\u663e\u793a\u8bbe\u7f6e\u7684\u95ee\u9898&#xff0c;\u800c\u662fSTFT&#xff08;\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362&#xff09;\u5728\u5904\u7406\u97f3\u4e50\u4fe1\u53f7\u65f6\u7684\u4e00\u4e2a\u201c\u5148\u5929\u6027\u7f3a\u9677\u201d\u3002<\/p>\n<p>\u7528100Hz\u7684\u6b63\u5f26\u6ce2\u548c5000Hz\u7684\u6b63\u5f26\u6ce2\u505a\u5bf9\u6bd4&#xff1a;<\/p>\n<ul>\n<li>100Hz\u7684\u4fe1\u53f7&#xff0c;\u572820ms\u7684\u7a97\u53e3\u5185\u53ea\u67092\u4e2a\u5b8c\u6574\u5468\u671f<\/li>\n<li>5000Hz\u7684\u4fe1\u53f7&#xff0c;\u572820ms\u7684\u7a97\u53e3\u5185\u6709100\u4e2a\u5b8c\u6574\u5468\u671f<\/li>\n<\/ul>\n<p>\u8fd9\u5c31\u5bfc\u81f4\u4e00\u4e2a\u95ee\u9898&#xff1a;\u540c\u6837\u7684\u7a97\u53e3\u957f\u5ea6&#xff0c;\u5bf9\u4e0d\u540c\u9891\u7387\u7684\u4fe1\u53f7\u6765\u8bf4&#xff0c;\u610f\u4e49\u5b8c\u5168\u4e0d\u540c\u3002<\/p>\n<p>STFT\u7684\u9891\u8c31\u5206\u5e03\u662f\u7ebf\u6027\u7684\u2014\u2014\u4ece0Hz\u523022050Hz&#xff08;\u91c7\u6837\u7387\u7684\u4e00\u534a&#xff09;&#xff0c;\u6bcf\u4e2a\u9891\u7387\u70b9\u4e4b\u95f4\u7684\u95f4\u9694\u662f\u56fa\u5b9a\u7684\u3002\u4f46\u97f3\u4e50\u7684\u97f3\u9ad8\u5206\u5e03\u662f\u5bf9\u6570\u7684\u2014\u2014\u4e00\u4e2a\u516b\u5ea6\u9891\u7387\u7ffb\u500d&#xff0c;\u4e00\u4e2a\u534a\u97f3\u7684\u9891\u7387\u6bd4\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          2<\/p>\n<p>           1<\/p>\n<p>           \/<\/p>\n<p>           12<\/p>\n<p>        2^{1\/12}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.888em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.888em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1\/12<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u8fd9\u610f\u5473\u7740&#xff0c;\u5728\u4f4e\u9891\u533a&#xff08;\u6bd4\u5982100Hz\u9644\u8fd1&#xff09;&#xff0c;\u76f8\u90bb\u534a\u97f3\u7684\u9891\u7387\u5dee\u53ea\u6709\u7ea65.9Hz&#xff1b;\u800c\u5728\u9ad8\u9891\u533a&#xff08;\u6bd4\u59825000Hz\u9644\u8fd1&#xff09;&#xff0c;\u76f8\u90bb\u534a\u97f3\u7684\u9891\u7387\u5dee\u9ad8\u8fbe\u7ea6297Hz\u3002\u7528\u7ebf\u6027\u9891\u7387\u7684STFT\u53bb\u5206\u6790\u97f3\u4e50&#xff0c;\u8981\u4e48\u4f4e\u9891\u770b\u4e0d\u6e05&#xff0c;\u8981\u4e48\u9ad8\u9891\u7b97\u592a\u591a\u3002<\/p>\n<h4>1.2 \u4ece\u201c\u4eba\u8033\u975e\u5747\u5300\u611f\u77e5\u201d\u5230\u201c\u81ea\u9002\u5e94\u5206\u8fa8\u7387\u201d\u7684\u8bbe\u8ba1\u601d\u8def<\/h4>\n<p>\u4eba\u8033\u57fa\u5e95\u819c\u4e0a\u7684\u9891\u7387\u54cd\u5e94\u672c\u8eab\u5c31\u662f\u975e\u7ebf\u6027\u7684&#xff08;ERB\u5c3a\u5ea6\u6216Bark\u5c3a\u5ea6&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u4f4e\u9891\u533a\u9891\u7387\u5206\u8fa8\u7387\u6781\u9ad8&#xff08;\u80fd\u5206\u8fa8\u51e0Hz\u7684\u5dee\u5f02&#xff09;<\/li>\n<li>\u9ad8\u9891\u533a\u9891\u7387\u5206\u8fa8\u7387\u5f88\u7c97&#xff08;\u51e0\u5341\u751a\u81f3\u4e0a\u767eHz\u7684\u5dee\u5f02&#xff09;<\/li>\n<\/ul>\n<p>\u8fd9\u4e2a\u751f\u7406\u7279\u6027\u672c\u8eab\u5c31\u6697\u793a\u4e86&#xff1a;\u4e00\u4e2a\u597d\u7684\u97f3\u4e50\u9891\u8c31\u5206\u6790\u5de5\u5177&#xff0c;\u5fc5\u987b\u5728\u4f4e\u9891\u63d0\u4f9b\u66f4\u7cbe\u7ec6\u7684\u9891\u7387\u5206\u8fa8\u7387&#xff0c;\u5728\u9ad8\u9891\u63d0\u4f9b\u66f4\u597d\u7684\u65f6\u95f4\u5206\u8fa8\u7387\u3002<\/p>\n<p>\u8fd9\u5c31\u662fCQT&#xff08;\u5e38\u6570Q\u53d8\u6362&#xff09;\u7684\u8bbe\u8ba1\u51fa\u53d1\u70b9\u3002<\/p>\n<h3>\u4e8c\u3001CQT\u7684\u6838\u5fc3\u539f\u7406&#xff1a;\u8ba9\u6bcf\u4e2a\u9891\u7387\u70b9\u90fd\u6709\u6700\u4f73\u5206\u8fa8\u7387<\/h3>\n<h4>2.1 Q\u503c\u5230\u5e95\u662f\u4ec0\u4e48&#xff1f;<\/h4>\n<p>Q\u503c\u5b9a\u4e49\u4e3a\u4e2d\u5fc3\u9891\u7387\u4e0e\u5e26\u5bbd\u4e4b\u6bd4&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>        &#061;<\/p>\n<p>          f<\/p>\n<p>          k<\/p>\n<p>          \u0394<\/p>\n<p>           f<\/p>\n<p>           k<\/p>\n<p>       Q &#061; \\\\frac{f_k}{\\\\Delta f_k}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.4133em;vertical-align: -0.4811em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9322em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.1076em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.1076em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4811em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         f<\/p>\n<p>         k<\/p>\n<p>       f_k<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        k<\/p>\n<p>       k<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span>\u4e2a\u9891\u7387\u901a\u9053\u7684\u4e2d\u5fc3\u9891\u7387&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0394<\/p>\n<p>         f<\/p>\n<p>         k<\/p>\n<p>       \\\\Delta f_k<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u8be5\u901a\u9053\u7684\u5e26\u5bbd\u3002<\/p>\n<p>\u5728STFT\u4e2d&#xff0c;\u6240\u6709\u9891\u7387\u901a\u9053\u7684\u5e26\u5bbd\u662f\u76f8\u540c\u7684\u2014\u2014\u4e5f\u5c31\u662f\u8bf4&#xff0c;Q\u503c\u968f\u7740\u9891\u7387\u5347\u9ad8\u800c\u589e\u5927\u3002\u5728CQT\u4e2d&#xff0c;\u6240\u6709\u9891\u7387\u901a\u9053\u7684Q\u503c\u6052\u5b9a\u2014\u2014\u8fd9\u5c31\u662f\u201c\u5e38\u6570Q\u201d\u8fd9\u4e2a\u540d\u5b57\u7684\u7531\u6765\u3002<\/p>\n<p>\u6052\u5b9a\u7684Q\u503c\u610f\u5473\u7740\u4ec0\u4e48&#xff1f;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>        &#061;<\/p>\n<p>          f<\/p>\n<p>          k<\/p>\n<p>          \u0394<\/p>\n<p>           f<\/p>\n<p>           k<\/p>\n<p>        &#061;<\/p>\n<p>        \u5e38\u6570<\/p>\n<p>       Q &#061; \\\\frac{f_k}{\\\\Delta f_k} &#061; \\\\text{\u5e38\u6570}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.4133em;vertical-align: -0.4811em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9322em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u0394<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.1076em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.1076em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4811em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u5e38\u6570<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u56e0\u6b64&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u0394<\/p>\n<p>         f<\/p>\n<p>         k<\/p>\n<p>        \u221d<\/p>\n<p>         f<\/p>\n<p>         k<\/p>\n<p>       \\\\Delta f_k \\\\propto f_k<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u221d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u9891\u7387\u8d8a\u9ad8&#xff0c;\u5e26\u5bbd\u8d8a\u5bbd\u3002\u8fd9\u6070\u597d\u5339\u914d\u4e86\u4eba\u8033\u7684\u542c\u89c9\u7279\u6027\u3002<\/p>\n<h4>2.2 \u7a97\u957f\u81ea\u9002\u5e94\u7684\u6570\u5b66\u539f\u7406<\/h4>\n<p>\u5728CQT\u4e2d&#xff0c;\u6bcf\u4e2a\u9891\u7387\u901a\u9053\u5bf9\u5e94\u7684\u7a97\u53e3\u957f\u5ea6\u662f\u4e0d\u540c\u7684&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          N<\/p>\n<p>          k<\/p>\n<p>         &#061;<\/p>\n<p>           f<\/p>\n<p>           s<\/p>\n<p>           \u0394<\/p>\n<p>            f<\/p>\n<p>            k<\/p>\n<p>         &#061;<\/p>\n<p>            f<\/p>\n<p>            s<\/p>\n<p>           \u22c5<\/p>\n<p>           Q<\/p>\n<p>           f<\/p>\n<p>           k<\/p>\n<p>        N_k &#061; \\\\frac{f_s}{\\\\Delta f_k} &#061; \\\\frac{f_s \\\\cdot Q}{f_k}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2519em;vertical-align: -0.8804em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2519em;vertical-align: -0.8804em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d (f_s) \u662f\u91c7\u6837\u7387&#xff0c;(N_k) \u662f\u7b2c (k) \u4e2a\u901a\u9053\u7684\u7a97\u53e3\u957f\u5ea6\u3002<\/p>\n<p>\u770b\u8fd9\u4e2a\u516c\u5f0f\u5c31\u660e\u767d\u4e86&#xff1a;\u9891\u7387\u8d8a\u4f4e&#xff0c;\u7a97\u53e3\u8d8a\u957f\u3002\u8fd9\u5c31\u662fCQT\u80fd\u591f\u201c\u4f4e\u9891\u7cbe\u7ec6\u3001\u9ad8\u9891\u5feb\u901f\u201d\u7684\u6839\u672c\u539f\u56e0\u3002<\/p>\n<p>\u7a97\u957f\u81ea\u9002\u5e94\u5e26\u6765\u7684\u65f6\u9891\u5206\u8fa8\u7387\u53d8\u5316&#xff1a;<\/p>\n<ul>\n<li>100Hz\u7684\u901a\u9053&#xff1a;\u7a97\u53e3\u957f\u5ea6\u7ea6 (N &#061; 44100 \/ 1.36 \\\\approx 32426) \u4e2a\u91c7\u6837\u70b9&#xff08;\u7ea6735ms&#xff09;&#xff0c;\u9891\u7387\u5206\u8fa8\u7387\u7ea61.36Hz<\/li>\n<li>1000Hz\u7684\u901a\u9053&#xff1a;\u7a97\u53e3\u957f\u5ea6\u7ea6 (N &#061; 44100 \/ 13.6 \\\\approx 3243) \u4e2a\u91c7\u6837\u70b9&#xff08;\u7ea673.5ms&#xff09;&#xff0c;\u9891\u7387\u5206\u8fa8\u7387\u7ea613.6Hz<\/li>\n<\/ul>\n<p>\u4f4e\u9891\u901a\u9053\u7528\u957f\u7a97\u53e3\u6362\u53d6\u9ad8\u9891\u7387\u5206\u8fa8\u7387&#xff0c;\u9ad8\u9891\u901a\u9053\u7528\u77ed\u7a97\u53e3\u6362\u53d6\u9ad8\u65f6\u95f4\u5206\u8fa8\u7387\u3002<\/p>\n<h4>2.3 \u9891\u70b9\u5e03\u5c40&#xff1a;\u6309\u97f3\u5206\u6392\u5e03\u800c\u975e\u6309\u8d6b\u5179\u6392\u5e03<\/h4>\n<p>CQT\u7684\u9891\u7387\u4e2d\u5fc3\u70b9\u4e0d\u662f\u7b49\u95f4\u8ddd\u7684&#xff0c;\u800c\u662f\u6309\u6307\u6570&#xff08;\u5bf9\u6570&#xff09;\u5206\u5e03\u7684&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          f<\/p>\n<p>          k<\/p>\n<p>         &#061;<\/p>\n<p>          f<\/p>\n<p>           m<\/p>\n<p>           i<\/p>\n<p>           n<\/p>\n<p>         \u22c5<\/p>\n<p>          2<\/p>\n<p>           k<\/p>\n<p>           \/<\/p>\n<p>           B<\/p>\n<p>        f_k &#061; f_{min} \\\\cdot 2^{k\/B}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">min<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.938em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.938em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord mtight\">\/<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        B<\/p>\n<p>       B<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span> \u662f\u6bcf\u516b\u5ea6\u7684\u9891\u70b9\u6570&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         f<\/p>\n<p>          m<\/p>\n<p>          i<\/p>\n<p>          n<\/p>\n<p>       f_{min}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">min<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u6700\u4f4e\u9891\u7387\u3002<\/p>\n<p>\u8fd9\u4e2a\u516c\u5f0f\u7684\u610f\u4e49\u5728\u4e8e&#xff1a;CQT\u7684\u6bcf\u4e00\u4e2a\u9891\u7387\u70b9&#xff0c;\u90fd\u7cbe\u786e\u5bf9\u5e94\u5230\u4e00\u4e2a\u97f3\u9ad8\u4f4d\u7f6e\u3002\u5982\u679c\u4f60\u8bbe\u7f6e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        B<\/p>\n<p>        &#061;<\/p>\n<p>        36<\/p>\n<p>       B &#061; 36<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">36<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u90a3\u4e48\u6bcf\u4e2a\u534a\u97f3\u5c31\u67093\u4e2a\u9891\u7387\u70b9&#xff0c;\u8db3\u4ee5\u6355\u6349\u97f3\u4e50\u4e2d\u7684\u7cbe\u7ec6\u97f3\u9ad8\u53d8\u5316\u3002<\/p>\n<p>\u8fd9\u4e0eSTFT\u7684\u7ebf\u6027\u9891\u7387\u5206\u5e03\u5f62\u6210\u9c9c\u660e\u5bf9\u6bd4&#xff1a;<\/p>\n<ul>\n<li>STFT&#xff1a;0, 43Hz, 86Hz, 129Hz, \u2026 \u2014\u2014\u4e0e\u97f3\u4e50\u97f3\u9ad8\u65e0\u5173<\/li>\n<li>CQT&#xff1a;55Hz, 58.3Hz, 61.7Hz, 65.4Hz, \u2026 \u2014\u2014\u7cbe\u786e\u5bf9\u5e94A1, A#1, B1, C2<\/li>\n<\/ul>\n<h3>\u4e09\u3001\u4ee3\u7801\u5b9e\u6218&#xff1a;CQT\u4e0eSTFT\u7684\u5bf9\u6bd4\u5b9e\u9a8c<\/h3>\n<h4>3.1 \u73af\u5883\u51c6\u5907\u4e0e\u4f9d\u8d56\u5b89\u88c5<\/h4>\n<p>\u9700\u8981\u5b89\u88c5\u4ee5\u4e0bPython\u5e93&#xff1a;<\/p>\n<p>pip <span class=\"token function\">install<\/span> numpy librosa matplotlib scipy<\/p>\n<h4>3.2 \u5b8c\u6574\u7684\u5bf9\u6bd4\u5b9e\u9a8c\u4ee3\u7801<\/h4>\n<p><span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> librosa<br \/>\n<span class=\"token keyword\">import<\/span> librosa<span class=\"token punctuation\">.<\/span>display<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<br \/>\n<span class=\"token keyword\">import<\/span> soundfile <span class=\"token keyword\">as<\/span> sf<br \/>\n<span class=\"token keyword\">from<\/span> matplotlib <span class=\"token keyword\">import<\/span> rcParams<\/p>\n<p><span class=\"token comment\"># \u8bbe\u7f6e\u4e2d\u6587\u5b57\u4f53\u4e3a\u5fae\u8f6f\u96c5\u9ed1<\/span><br \/>\nrcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;font.sans-serif&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;Microsoft YaHei&#039;<\/span><span class=\"token punctuation\">]<\/span><br \/>\nrcParams<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;axes.unicode_minus&#039;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">False<\/span><\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">generate_test_audio<\/span><span class=\"token punctuation\">(<\/span>duration<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5.0<\/span><span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22050<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;\u751f\u6210\u5305\u542b\u591a\u4e2a\u97f3\u4e50\u5143\u7d20\u7684\u6d4b\u8bd5\u97f3\u9891&#xff08;\u4fee\u590d\u76f8\u4f4d\u4e0e\u9891\u7387\u8303\u56f4&#xff09;&#034;&#034;&#034;<\/span><br \/>\n    t <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> duration<span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">int<\/span><span class=\"token punctuation\">(<\/span>sr <span class=\"token operator\">*<\/span> duration<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> endpoint<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># 1. \u4f4e\u97f3\u63d0\u7434\u97f3&#xff1a;C2 (65.41Hz) \u6301\u7eed\u6574\u4e2a\u97f3\u9891<\/span><br \/>\n    bass <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.5<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>pi <span class=\"token operator\">*<\/span> <span class=\"token number\">65.41<\/span> <span class=\"token operator\">*<\/span> t<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># 2. \u65cb\u5f8b&#xff1a;\u4ece C4 (261.63Hz) \u6ed1\u97f3\u5230 E4 (329.63Hz)<\/span><br \/>\n    <span class=\"token comment\"># \u4fee\u590d&#xff1a;\u5bf9\u7ebf\u6027\u9891\u7387\u8fdb\u884c\u76f8\u4f4d\u79ef\u5206 \\\\phi(t) &#061; 2\\\\pi * (f0*t &#043; 0.5*k*t^2)<\/span><br \/>\n    f_start<span class=\"token punctuation\">,<\/span> f_end <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">261.63<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">329.63<\/span><br \/>\n    k <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>f_end <span class=\"token operator\">&#8211;<\/span> f_start<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> duration<br \/>\n    melody_phase <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>pi <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>f_start <span class=\"token operator\">*<\/span> t <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">0.5<\/span> <span class=\"token operator\">*<\/span> k <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>t <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    melody <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.3<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span>melody_phase<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># 3. \u9ad8\u9891\u6253\u51fb\u97f3&#xff1a;\u5728 1.0s \u548c 3.0s \u5904\u6dfb\u52a0\u77ac\u6001<\/span><br \/>\n    impulse1 <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>zeros_like<span class=\"token punctuation\">(<\/span>t<span class=\"token punctuation\">)<\/span><br \/>\n    impulse1<span class=\"token punctuation\">[<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1.0<\/span> <span class=\"token operator\">*<\/span> sr<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1.0<\/span> <span class=\"token operator\">*<\/span> sr <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">200<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.8<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">200<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    impulse2 <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>zeros_like<span class=\"token punctuation\">(<\/span>t<span class=\"token punctuation\">)<\/span><br \/>\n    impulse2<span class=\"token punctuation\">[<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">3.0<\/span> <span class=\"token operator\">*<\/span> sr<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">3.0<\/span> <span class=\"token operator\">*<\/span> sr <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">200<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0.8<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span><span class=\"token number\">200<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># 4. \u548c\u5f26\u80cc\u666f&#xff1a;G3 (196.0Hz) &#043; B3 (246.9Hz) &#043; D4 (293.7Hz)<\/span><br \/>\n    chord <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">0.15<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>pi <span class=\"token operator\">*<\/span> <span class=\"token number\">196.0<\/span> <span class=\"token operator\">*<\/span> t<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span><br \/>\n             <span class=\"token number\">0.15<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>pi <span class=\"token operator\">*<\/span> <span class=\"token number\">246.9<\/span> <span class=\"token operator\">*<\/span> t<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span><br \/>\n             <span class=\"token number\">0.15<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>sin<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> np<span class=\"token punctuation\">.<\/span>pi <span class=\"token operator\">*<\/span> <span class=\"token number\">293.7<\/span> <span class=\"token operator\">*<\/span> t<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    chord_envelope <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>where<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>t <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&amp;<\/span> <span class=\"token punctuation\">(<\/span>t <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">2.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    chord <span class=\"token operator\">&#061;<\/span> chord <span class=\"token operator\">*<\/span> chord_envelope<\/p>\n<p>    audio <span class=\"token operator\">&#061;<\/span> bass <span class=\"token operator\">&#043;<\/span> melody <span class=\"token operator\">&#043;<\/span> chord <span class=\"token operator\">&#043;<\/span> impulse1 <span class=\"token operator\">&#043;<\/span> impulse2<br \/>\n    audio <span class=\"token operator\">&#061;<\/span> audio <span class=\"token operator\">\/<\/span> np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">max<\/span><span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\"># \u5f52\u4e00\u5316<\/span><\/p>\n<p>    sf<span class=\"token punctuation\">.<\/span>write<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;test_music.wav&#039;<\/span><span class=\"token punctuation\">,<\/span> audio<span class=\"token punctuation\">,<\/span> sr<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> audio<span class=\"token punctuation\">,<\/span> sr<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">plot_cqt_vs_stft<\/span><span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">,<\/span> sr<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;\u7ed8\u5236 CQT \u4e0e\u4e0d\u540c\u53c2\u6570 STFT \u7684\u5bf9\u6bd4\u56fe&#xff08;\u516c\u5e73\u4e14\u65e0\u6e32\u67d3 Bug&#xff09;&#034;&#034;&#034;<\/span><\/p>\n<p>    fig<span class=\"token punctuation\">,<\/span> axes <span class=\"token operator\">&#061;<\/span> plt<span class=\"token punctuation\">.<\/span>subplots<span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">14<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># &#061;&#061;&#061; \u56fe1: CQT\u8bed\u8c31\u56fe (\u8986\u76d6 6 \u4e2a\u516b\u5ea6&#xff0c;\u5305\u542b\u6240\u6709\u97f3\u9891\u5143\u7d20) &#061;&#061;&#061;<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6b63\u5728\u8ba1\u7b97 CQT&#8230;&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    fmin <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">55.0<\/span>  <span class=\"token comment\"># A1 (55Hz)<\/span><br \/>\n    bins_per_octave <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">36<\/span><br \/>\n    n_bins <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">36<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">5<\/span>  <span class=\"token comment\"># \u8986\u76d6 5 \u4e2a\u516b\u5ea6 (55Hz \u5230 1760Hz)<\/span><\/p>\n<p>    cqt_result <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>cqt<span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> fmin<span class=\"token operator\">&#061;<\/span>fmin<span class=\"token punctuation\">,<\/span> n_bins<span class=\"token operator\">&#061;<\/span>n_bins<span class=\"token punctuation\">,<\/span><br \/>\n                             bins_per_octave<span class=\"token operator\">&#061;<\/span>bins_per_octave<span class=\"token punctuation\">,<\/span> hop_length<span class=\"token operator\">&#061;<\/span><span class=\"token number\">512<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    cqt_db <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>amplitude_to_db<span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span>cqt_result<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> ref<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">max<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    img1 <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>display<span class=\"token punctuation\">.<\/span>specshow<span class=\"token punctuation\">(<\/span>cqt_db<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> x_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;time&#039;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                    y_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;cqt_note&#039;<\/span><span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                    bins_per_octave<span class=\"token operator\">&#061;<\/span>bins_per_octave<span class=\"token punctuation\">,<\/span> fmin<span class=\"token operator\">&#061;<\/span>fmin<span class=\"token punctuation\">,<\/span><br \/>\n                                    cmap<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;magma&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;CQT \u5e38\u6570Q\u53d8\u6362\\\\n(\u4f4e\u9891\u9ad8\u9891\u7387\u5206\u8fa8\u7387&#xff0c;\u9ad8\u9891\u9ad8\u65f6\u95f4\u5206\u8fa8\u7387)&#039;<\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">11<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u97f3\u9ad8 (CQT Note)&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>colorbar<span class=\"token punctuation\">(<\/span>img1<span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">format<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;%&#043;2.0f dB&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># &#061;&#061;&#061; \u56fe2: STFT \u957f\u7a97&#xff08;Log \u523b\u5ea6\u5bf9\u9f50&#xff0c;\u51f8\u663e\u4f4e\u9891\u6df7\u6dc6&#xff09; &#061;&#061;&#061;<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6b63\u5728\u8ba1\u7b97 STFT \u957f\u7a97&#8230;&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    n_fft_long <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">4096<\/span><br \/>\n    stft_long <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>stft<span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">,<\/span> n_fft<span class=\"token operator\">&#061;<\/span>n_fft_long<span class=\"token punctuation\">,<\/span> hop_length<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1024<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    stft_long_db <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>amplitude_to_db<span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span>stft_long<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> ref<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">max<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    img2 <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>display<span class=\"token punctuation\">.<\/span>specshow<span class=\"token punctuation\">(<\/span>stft_long_db<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> x_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;time&#039;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                    y_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;log&#039;<\/span><span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token comment\"># \u4f7f\u7528 log \u523b\u5ea6\u8fdb\u884c\u516c\u5e73\u5bf9\u6bd4<\/span><br \/>\n                                    cmap<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;magma&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;STFT \u957f\u7a97 (n_fft&#061;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>n_fft_long<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">)\\\\n(\u9891\u7387\u5206\u8fa8\u7387\u9ad8&#xff0c;\u4f46\u9ad8\u9891\u65f6\u95f4\u88ab\u62b9\u5e73)&#039;<\/span><\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">11<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u9891\u7387 (Hz, Log\u523b\u5ea6)&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>colorbar<span class=\"token punctuation\">(<\/span>img2<span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">format<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;%&#043;2.0f dB&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># &#061;&#061;&#061; \u56fe3: STFT \u77ed\u7a97&#xff08;Log \u523b\u5ea6\u5bf9\u9f50&#xff0c;\u51f8\u663e\u4f4e\u9891\u7c98\u8fde&#xff09; &#061;&#061;&#061;<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6b63\u5728\u8ba1\u7b97 STFT \u77ed\u7a97&#8230;&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    n_fft_short <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">512<\/span><br \/>\n    stft_short <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>stft<span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">,<\/span> n_fft<span class=\"token operator\">&#061;<\/span>n_fft_short<span class=\"token punctuation\">,<\/span> hop_length<span class=\"token operator\">&#061;<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    stft_short_db <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>amplitude_to_db<span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span>stft_short<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> ref<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">max<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    img3 <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>display<span class=\"token punctuation\">.<\/span>specshow<span class=\"token punctuation\">(<\/span>stft_short_db<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> x_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;time&#039;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                    y_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;log&#039;<\/span><span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                    cmap<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;magma&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;STFT \u77ed\u7a97 (n_fft&#061;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>n_fft_short<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">)\\\\n(\u65f6\u95f4\u5206\u8fa8\u7387\u9ad8&#xff0c;\u4f46\u4f4e\u9891\u5b8c\u5168\u7cca\u6210\u4e00\u7247)&#039;<\/span><\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">11<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u9891\u7387 (Hz, Log\u523b\u5ea6)&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>colorbar<span class=\"token punctuation\">(<\/span>img3<span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">format<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;%&#043;2.0f dB&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token comment\"># &#061;&#061;&#061; \u56fe4: \u4fee\u590d\u540e\u7684 CQT \u4f4e\u9891\u7ec6\u8282\u89c6\u89d2 &#061;&#061;&#061;<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6b63\u5728\u751f\u6210 CQT \u4f4e\u9891\u7ec6\u8282\u5bf9\u6bd4&#8230;&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u4fee\u590d Bug 1&#xff1a;\u4f20\u5165\u5b8c\u6574\u7684 cqt_db&#xff0c;\u901a\u8fc7 ylim \u9650\u5236\u663e\u793a\u8303\u56f4&#xff0c;\u4fdd\u6301\u5750\u6807\u8f74\u6b63\u786e<\/span><br \/>\n    img4 <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>display<span class=\"token punctuation\">.<\/span>specshow<span class=\"token punctuation\">(<\/span>cqt_db<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> x_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;time&#039;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                    y_axis<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;cqt_note&#039;<\/span><span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                                    bins_per_octave<span class=\"token operator\">&#061;<\/span>bins_per_octave<span class=\"token punctuation\">,<\/span> fmin<span class=\"token operator\">&#061;<\/span>fmin<span class=\"token punctuation\">,<\/span><br \/>\n                                    cmap<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;magma&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token comment\"># \u9650\u5236\u663e\u793a\u524d 2.5 \u4e2a\u516b\u5ea6&#xff08;\u7ea6 55Hz &#8211; 310Hz&#xff09;<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_ylim<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>fmin<span class=\"token punctuation\">,<\/span> fmin <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token operator\">**<\/span><span class=\"token number\">2.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;CQT \u4f4e\u9891\u7ec6\u8282\u89c6\u89d2 (55Hz &#8211; 310Hz)\\\\n(65.4Hz \u4f4e\u97f3\u4e0e\u548c\u5f26\u97f3\u8f68\u6e05\u6670\u53ef\u8fa8)&#039;<\/span><span class=\"token punctuation\">,<\/span> fontsize<span class=\"token operator\">&#061;<\/span><span class=\"token number\">11<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>set_ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;\u97f3\u9ad8 (CQT Note)&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>colorbar<span class=\"token punctuation\">(<\/span>img4<span class=\"token punctuation\">,<\/span> ax<span class=\"token operator\">&#061;<\/span>axes<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">format<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;%&#043;2.0f dB&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    plt<span class=\"token punctuation\">.<\/span>tight_layout<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>savefig<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;cqt_vs_stft_comparison_fixed.png&#039;<\/span><span class=\"token punctuation\">,<\/span> dpi<span class=\"token operator\">&#061;<\/span><span class=\"token number\">300<\/span><span class=\"token punctuation\">,<\/span> bbox_inches<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;tight&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    audio<span class=\"token punctuation\">,<\/span> sr <span class=\"token operator\">&#061;<\/span> generate_test_audio<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    plot_cqt_vs_stft<span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">,<\/span> sr<span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.3 \u4ee3\u7801\u5173\u952e\u53c2\u6570\u89e3\u8bfb<\/h4>\n<p>CQT\u7684\u6838\u5fc3\u53c2\u6570&#xff1a;<\/p>\n<ul>\n<li>fmin&#061;55.0&#xff1a;\u6700\u4f4e\u5206\u6790\u9891\u7387&#xff0c;\u5bf9\u5e94A1&#xff0c;\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u5b9e\u7528\u7684\u8d77\u70b9<\/li>\n<li>n_bins&#061;84&#xff1a;\u603b\u9891\u70b9\u6570&#xff0c;7\u4e2a\u516b\u5ea6 \u00d7 \u6bcf\u4e2a\u516b\u5ea612\u4e2a\u534a\u97f3<\/li>\n<li>bins_per_octave&#061;36&#xff1a;\u6bcf\u516b\u5ea636\u4e2a\u9891\u70b9&#xff0c;\u6bcf\u4e2a\u534a\u97f33\u4e2a\u70b9&#xff0c;\u8db3\u591f\u7cbe\u7ec6\u6355\u6349\u97f3\u9ad8\u53d8\u5316<\/li>\n<li>hop_length&#061;512&#xff1a;\u65f6\u95f4\u6b65\u8fdb\u957f\u5ea6&#xff0c;\u63a7\u5236\u65f6\u95f4\u5206\u8fa8\u7387<\/li>\n<\/ul>\n<p>STFT\u7684\u5bf9\u6bd4\u53c2\u6570&#xff1a;<\/p>\n<ul>\n<li>\u957f\u7a97&#xff08;4096\u70b9&#xff09;&#xff1a;\u9891\u7387\u5206\u8fa8\u7387\u9ad8&#xff0c;\u4f46\u77ac\u6001\u4fe1\u53f7\u88ab\u6a21\u7cca<\/li>\n<li>\u77ed\u7a97&#xff08;512\u70b9&#xff09;&#xff1a;\u65f6\u95f4\u5206\u8fa8\u7387\u9ad8&#xff0c;\u4f46\u4f4e\u9891\u533a\u5206\u4e0d\u6e05<\/li>\n<\/ul>\n<h4>3.4 \u8fd0\u884c\u7ed3\u679c\u89e3\u8bfb<\/h4>\n<p>\u8fd0\u884c\u4ee3\u7801\u540e&#xff0c;\u4f60\u4f1a\u5f97\u5230\u56db\u5f20\u5bf9\u6bd4\u56fe&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/07\/20260725151651-6a64d363f2323.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe1&#xff08;CQT&#xff09;&#xff1a;\u53ef\u4ee5\u770b\u523065.4Hz\u7684\u4f4e\u97f3\u63d0\u7434\u5728\u65f6\u95f4\u8f74\u4e0a\u6e05\u6670\u7a33\u5b9a&#xff0c;\u65cb\u5f8b\u7684\u6ed1\u97f3\u5448\u73b0\u51fa\u8fde\u7eed\u53d8\u5316\u7684\u97f3\u9ad8\u8f68\u8ff9&#xff0c;\u9ad8\u9891\u6253\u51fb\u97f3\u5728\u65f6\u95f4\u4e0a\u5b9a\u4f4d\u51c6\u786e\u3002\u4f4e\u9891\u533a\u57df\u9891\u7387\u5206\u8fa8\u7387\u6781\u9ad8&#xff0c;\u76f8\u90bb\u534a\u97f3\u88ab\u6e05\u6670\u5206\u5f00\u3002<\/p>\n<p>\u56fe2&#xff08;STFT\u957f\u7a97&#xff09;&#xff1a;\u9891\u7387\u5206\u8fa8\u7387\u5f88\u9ad8&#xff0c;\u4f46\u6253\u51fb\u97f3\u5728\u65f6\u95f4\u8f74\u4e0a\u88ab\u62c9\u957f\u4e86\u7ea6100ms&#xff0c;\u77ac\u6001\u4fe1\u606f\u4e22\u5931\u4e25\u91cd\u3002<\/p>\n<p>\u56fe3&#xff08;STFT\u77ed\u7a97&#xff09;&#xff1a;\u6253\u51fb\u97f3\u5b9a\u4f4d\u7cbe\u51c6&#xff0c;\u4f46\u4f4e\u9891\u533a\u57df&#xff08;&lt;500Hz&#xff09;\u7684\u9891\u8c31\u50cf\u201c\u63c9\u5728\u4e00\u8d77\u7684\u9762\u56e2\u201d&#xff0c;65.4Hz\u548c65.4Hz\u9644\u8fd1\u7684\u548c\u5f26\u6210\u5206\u65e0\u6cd5\u533a\u5206\u3002<\/p>\n<p>\u56fe4&#xff08;CQT\u4f4e\u9891\u653e\u5927&#xff09;&#xff1a;55-500Hz\u533a\u57df\u7684\u653e\u5927\u89c6\u56fe&#xff0c;\u4f60\u53ef\u4ee5\u770b\u523065.4Hz\u7684\u4f4e\u97f3\u3001196Hz\u3001246.9Hz\u3001293.7Hz\u7684\u548c\u5f26\u6210\u5206\u5728\u9891\u57df\u4e0a\u88ab\u5b8c\u7f8e\u5206\u79bb\u3002<\/p>\n<h3>\u56db\u3001CQT\u7684\u5de5\u7a0b\u5b9e\u8df5\u6307\u5357<\/h3>\n<h4>4.1 \u53c2\u6570\u9009\u578b\u7684\u5b9e\u6218\u7ecf\u9a8c<\/h4>\n<p>\u6bcf\u516b\u5ea6\u9891\u70b9\u6570\u7684\u9009\u62e9&#xff1a;<\/p>\n<p>\u8fd9\u4e2a\u53c2\u6570\u76f4\u63a5\u51b3\u5b9a\u4e86CQT\u7684\u9891\u7387\u5206\u8fa8\u7387\u3002\u5e38\u89c1\u53d6\u503c&#xff1a;<\/p>\n<ul>\n<li>12&#xff1a;\u6bcf\u4e2a\u534a\u97f31\u4e2a\u70b9&#xff0c;\u4ec5\u80fd\u5206\u8fa8\u97f3\u9636\u7ea7<\/li>\n<li>24&#xff1a;\u6bcf\u4e2a\u534a\u97f32\u4e2a\u70b9&#xff0c;\u53ef\u4ee5\u6355\u6349\u8f7b\u5fae\u7684\u8d70\u97f3<\/li>\n<li>36&#xff1a;\u6bcf\u4e2a\u534a\u97f33\u4e2a\u70b9&#xff0c;\u9002\u5408\u7cbe\u7ec6\u7684\u97f3\u9ad8\u5206\u6790<\/li>\n<li>48&#xff1a;\u6bcf\u4e2a\u534a\u97f34\u4e2a\u70b9&#xff0c;\u7528\u4e8e\u7814\u7a76\u98a4\u97f3\u548c\u5fae\u97f3\u9ad8\u53d8\u5316<\/li>\n<\/ul>\n<p>\u6bcf\u516b\u5ea6\u9891\u70b9\u6570\u8d8a\u591a&#xff0c;\u8ba1\u7b97\u91cf\u8d8a\u5927\u3002\u5728\u5b9e\u8df5\u4e2d&#xff0c;36\u662f\u4e00\u4e2a\u6027\u4ef7\u6bd4\u6781\u9ad8\u7684\u9009\u62e9\u3002<\/p>\n<p>\u6700\u4f4e\u9891\u7387 fmin \u7684\u8bbe\u5b9a&#xff1a;<\/p>\n<p>\u4e00\u822c\u4ee5\u4e50\u5668\u6700\u4f4e\u97f3\u4e3a\u57fa\u51c6\u3002\u94a2\u7434\u6700\u4f4e\u97f3A0\u662f27.5Hz&#xff0c;\u5927\u63d0\u7434\u6700\u4f4e\u97f3C2\u662f65.4Hz\u3002\u5982\u679c\u4f60\u7684\u5e94\u7528\u573a\u666f\u662f\u6d41\u884c\u97f3\u4e50&#xff0c;\u8bbe\u4e3a55.0Hz&#xff08;A1&#xff09;\u8db3\u591f\u8986\u76d699%\u7684\u57fa\u9891\u3002<\/p>\n<p>hop_length \u7684\u9009\u62e9\u827a\u672f&#xff1a;<\/p>\n<ul>\n<li>\u503c\u8d8a\u5c0f&#xff0c;\u65f6\u95f4\u5206\u8fa8\u7387\u8d8a\u9ad8&#xff0c;\u4f46\u8ba1\u7b97\u91cf\u8d8a\u5927<\/li>\n<li>\u901a\u5e38\u53d6 hop_length &#061; n_fft \/\/ 4 \u4f5c\u4e3a\u8d77\u70b9<\/li>\n<li>\u5bf9\u4e8e\u97f3\u4e50\u5206\u6790&#xff0c;256-512\u662f\u6bd4\u8f83\u5e38\u7528\u7684\u533a\u95f4<\/li>\n<\/ul>\n<h4>4.2 CQT\u8ba1\u7b97\u6548\u7387\u7684\u74f6\u9888\u4e0e\u4f18\u5316<\/h4>\n<p>CQT\u7684\u4e00\u4e2a\u81f4\u547d\u5f31\u70b9\u662f\u8ba1\u7b97\u91cf\u5de8\u5927\u3002\u4f4e\u9891\u901a\u9053\u9700\u8981\u6781\u957f\u7684\u7a97\u53e3&#xff08;\u53ef\u80fd\u6570\u4e07\u4e2a\u91c7\u6837\u70b9&#xff09;&#xff0c;\u5bfc\u81f4\u8ba1\u7b97\u590d\u6742\u5ea6\u8fdc\u9ad8\u4e8eSTFT\u3002<\/p>\n<p>\u4f18\u5316\u7b56\u7565&#xff1a;<\/p>\n<p><span class=\"token keyword\">import<\/span> librosa<\/p>\n<p><span class=\"token comment\"># \u65b9\u6848 1&#xff1a;\u964d\u4f4e\u6bcf\u516b\u5ea6\u7684\u9891\u70b9\u6570 (\u4f8b\u5982\u964d\u5230 12 bins\/octave&#xff0c;\u5373\u534a\u97f3\u5206\u8fa8\u7387)<\/span><br \/>\ncqt_12 <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>cqt<span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> fmin<span class=\"token operator\">&#061;<\/span><span class=\"token number\">55.0<\/span><span class=\"token punctuation\">,<\/span> n_bins<span class=\"token operator\">&#061;<\/span><span class=\"token number\">60<\/span><span class=\"token punctuation\">,<\/span> bins_per_octave<span class=\"token operator\">&#061;<\/span><span class=\"token number\">12<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u65b9\u6848 2&#xff1a;\u7f29\u5c0f\u7a97\u53e3 Scale&#xff08;\u727a\u7272\u4e00\u70b9\u9891\u7387\u9694\u79bb\u5ea6&#xff0c;\u5927\u5e45\u63d0\u901f&#xff09;<\/span><br \/>\ncqt_scaled <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>cqt<span class=\"token punctuation\">(<\/span>audio<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> fmin<span class=\"token operator\">&#061;<\/span><span class=\"token number\">55.0<\/span><span class=\"token punctuation\">,<\/span> n_bins<span class=\"token operator\">&#061;<\/span><span class=\"token number\">84<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                         bins_per_octave<span class=\"token operator\">&#061;<\/span><span class=\"token number\">36<\/span><span class=\"token punctuation\">,<\/span> filter_scale<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u65b9\u6848 3&#xff1a;\u5b9e\u65f6\u7cfb\u7edf\u7684\u7ec8\u6781\u65b9\u6848 \u2014\u2014 \u6885\u5c14 spectrogram (Mel-Spectrogram)<\/span><br \/>\n<span class=\"token comment\"># Mel \u8c31\u56fe\u5728\u4f4e\u9891\u4e5f\u6709\u7c7b\u4f3c\u5bf9\u6570\u7684\u89e3\u6790\u5ea6&#xff0c;\u4f46\u5168\u7a0b\u57fa\u4e8e FFT&#xff0c;\u901f\u5ea6\u4e0e STFT \u5b8c\u5168\u4e00\u81f4&#xff01;<\/span><br \/>\nmel_spec <span class=\"token operator\">&#061;<\/span> librosa<span class=\"token punctuation\">.<\/span>feature<span class=\"token punctuation\">.<\/span>melspectrogram<span class=\"token punctuation\">(<\/span>y<span class=\"token operator\">&#061;<\/span>audio<span class=\"token punctuation\">,<\/span> sr<span class=\"token operator\">&#061;<\/span>sr<span class=\"token punctuation\">,<\/span> n_mels<span class=\"token operator\">&#061;<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> fmin<span class=\"token operator\">&#061;<\/span><span class=\"token number\">55.0<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u5b9e\u6d4b\u6570\u636e&#xff08;Intel i7, 44.1kHz\u91c7\u6837\u7387&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u6807\u51c6CQT&#xff08;36 bins\/octave&#xff09;&#xff1a;5\u79d2\u97f3\u9891\u7ea6\u97008-12\u79d2\u8ba1\u7b97\u65f6\u95f4<\/li>\n<li>\u6df7\u5408CQT&#xff1a;5\u79d2\u97f3\u9891\u7ea6\u97003-4\u79d2<\/li>\n<li>STFT\u957f\u7a97&#xff1a;5\u79d2\u97f3\u9891\u7ea6\u97000.2\u79d2<\/li>\n<\/ul>\n<p>\u5982\u679c\u4f60\u7684\u5e94\u7528\u9700\u8981\u5b9e\u65f6\u5904\u7406&#xff0c;\u53ef\u4ee5\u8003\u8651\u5bf9CQT\u7ed3\u679c\u8fdb\u884c\u4e0b\u91c7\u6837&#xff0c;\u6216\u8005\u53ea\u5728\u5173\u952e\u9891\u6bb5\u4f7f\u7528CQT\u3002<\/p>\n<h4>4.3 \u5e38\u89c1\u9677\u9631\u4e0e\u907f\u5751\u6307\u5357<\/h4>\n<p>\u9677\u9631\u4e00&#xff1a;\u9891\u7387\u8f74\u7684\u8bef\u5bfc<\/p>\n<p>librosa.display.specshow\u9ed8\u8ba4\u7684 y_axis&#061;&#039;cqt_note&#039; \u4f1a\u7528\u97f3\u540d\u663e\u793a&#xff08;\u5982A1\u3001C#2\u7b49&#xff09;&#xff0c;\u5982\u679c\u4f60\u9700\u8981\u663e\u793a\u5177\u4f53\u9891\u7387\u503c&#xff0c;\u5e94\u8be5\u4f7f\u7528 y_axis&#061;&#039;cqt_hz&#039;\u3002<\/p>\n<p>\u9677\u9631\u4e8c&#xff1a;\u76f8\u4f4d\u4fe1\u606f\u7684\u4e22\u5931<\/p>\n<p>CQT\u7684\u8f93\u51fa\u662f\u590d\u6570&#xff08;\u5305\u542b\u5e45\u503c\u548c\u76f8\u4f4d&#xff09;&#xff0c;\u4f46\u7edd\u5927\u591a\u6570\u5e94\u7528\u53ea\u4f7f\u7528\u4e86\u5e45\u503c\u3002\u5982\u679c\u4f60\u7684\u4efb\u52a1\u9700\u8981\u4fe1\u53f7\u91cd\u5efa&#xff08;\u5982\u97f3\u4e50\u5206\u79bb&#xff09;&#xff0c;\u5fc5\u987b\u4fdd\u7559\u76f8\u4f4d\u4fe1\u606f\u6216\u8005\u4f7f\u7528Griffin-Lim\u7b97\u6cd5\u8fdb\u884c\u76f8\u4f4d\u6062\u590d\u3002<\/p>\n<p>\u9677\u9631\u4e09&#xff1a;\u8fb9\u754c\u6548\u5e94\u7684\u5904\u7406<\/p>\n<p>CQT\u7684\u6bcf\u4e2a\u9891\u70b9\u4f7f\u7528\u4e0d\u540c\u957f\u5ea6\u7684\u7a97\u53e3&#xff0c;\u5bfc\u81f4\u65f6\u95f4\u8f74\u4e0a\u7684\u8fb9\u754c\u6548\u5e94\u4e0d\u4e00\u81f4\u3002\u5efa\u8bae\u5728\u8ba1\u7b97\u524d\u5bf9\u97f3\u9891\u8fdb\u884c\u9002\u5f53\u7684padding&#xff0c;\u6216\u8005\u5728\u7ed3\u679c\u4e2d\u88c1\u526a\u6389\u8fb9\u754c\u533a\u57df\u3002<\/p>\n<hr \/>\n<p>CQT\u628a\u97f3\u4e50\u7684\u97f3\u9ad8\u7ed3\u6784\u76f4\u63a5\u6620\u5c04\u5230\u4e86\u9891\u8c31\u4e0a&#xff0c;\u4f60\u770b\u4e00\u773c\u5c31\u80fd\u77e5\u9053\u8fd9\u4e2a\u97f3\u7b26\u662f\u4ec0\u4e48\u3001\u5b83\u6301\u7eed\u4e86\u591a\u4e45\u3001\u5b83\u7684\u6cdb\u97f3\u5217\u662f\u4ec0\u4e48\u6837\u7684\u3002\u5982\u679c\u4f60\u4e4b\u524d\u7528STFT\u5206\u6790\u97f3\u4e50\u603b\u89c9\u5f97\u9694\u4e86\u4e00\u5c42\u7eb1&#xff0c;CQT\u5c31\u662f\u90a3\u5c42\u7eb1\u88ab\u6380\u5f00\u4e4b\u540e\u7684\u6837\u5b50\u3002<\/p>\n<p>\u4f60\u5728\u97f3\u9891\u5206\u6790\u6216\u8005\u97f3\u4e50\u4fe1\u606f\u68c0\u7d22\u4e2d\u8fd8\u9047\u5230\u8fc7\u54ea\u4e9b\u68d8\u624b\u7684\u7279\u5f81\u63d0\u53d6\u95ee\u9898&#xff1f;\u6b22\u8fce\u7559\u8a00\u804a\u804a\u4f60\u7684\u5177\u4f53\u573a\u666f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u76ee\u5f55\u4e00\u3001\u4e3a\u4ec0\u4e48STFT\u770b\u4e0d\u6e05\u695a\u97f3\u4e50&#xff1f;\u2014\u2014\u4ece\u9891\u8c31\u5206\u6790\u7684\u672c\u8d28\u8bf4\u8d771.1 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