{"id":447,"date":"2025-07-11T18:44:56","date_gmt":"2025-07-11T10:44:56","guid":{"rendered":"https:\/\/blog.keruone.cn\/?p=447"},"modified":"2025-07-11T18:44:56","modified_gmt":"2025-07-11T10:44:56","slug":"thought-of-fft","status":"publish","type":"post","link":"https:\/\/blog.keruone.cn\/index.php\/2025\/07\/11\/thought-of-fft\/","title":{"rendered":"FFT\u8c03\u8bd5\u6709\u611f"},"content":{"rendered":"<h1>FFT\u8c03\u8bd5\u6709\u611f<\/h1>\n<blockquote><p>\n  \u5728\u7535\u8d5b\u96c6\u8bad\u671f\u95f4\uff0c\u8c03\u8bd5FFT\u7684\u4ee3\u7801\u65f6\u6709\u611f\u800c\u53d1\u3002\n<\/p><\/blockquote>\n<p>\u5728\u7535\u8d5b\u96c6\u8bad\u671f\u95f4\uff0c\u6211\u4eec\u4e3b\u653b\u4fe1\u53f7\u7c7b\u9898\u76ee\uff0cFFT\u662f\u5176\u4e2d\u4e00\u4e2a\u91cd\u8981\u7684\u5de5\u5177\u3002\u5728\u8c03\u8bd5FFT\u7684\u4ee3\u7801\u65f6\uff0c\u6e10\u6e10\u6709\u4e86\u4e00\u4e9b\u4ee5\u524d\u6ca1\u6709\u7684\u611f\u53d7\uff0c\u6216\u8005\u8bf4\u5bf9\u4ee5\u524d\u6a21\u7cca\u7684\u611f\u53d7\u6709\u4e86\u66f4\u6df1\u7684\u7406\u89e3\u3002<br \/>\n&#8211; > \u7406\u8bba\u4e2d\u8bf4\u70c2\u4e86\u7684\u9891\u7387\u5728\u6b64\u57fa\u672c\u4e0d\u63d0\uff0c\u672c\u6587\u4e3b\u8981\u4ece\u66f4\u7b26\u5408\u5e38\u4eba\u7406\u89e3\u7684\u89d2\u5ea6\u6765\u5206\u6790\u4e00\u4e0bFFT\u7684\u4e00\u4e9b\u95ee\u9898\u3002<\/p>\n\n<hr \/>\n<h2>1. FFT\u7684\u4e0b\u6807\u548c\u6700\u5c0f\u5206\u8fa8\u7387<\/h2>\n<p>\u5176\u5b9e\uff0cFFT\u7684\u4e0b\u6807\u5c31\u662f\u8fd9\u6b21FFT\u7684\u6700\u5c0f\u5206\u8fa8\u7387\uff0c\u800c\u5bf9\u5e94\u7684\u5e45\u503c\u5c31\u662f\u5728\u8be5\u6700\u5c0f\u5206\u8fa8\u7387\u7684\u500d\u6570\u5904\u9891\u7387\u5bf9\u5e94\u7684\u5e45\u503c\u3002<br \/>\n\u800c\u6700\u5c0f\u5206\u8fa8\u7387\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<code>delta_f = maxIndex \/ N * fs<\/code><\/p>\n<p>\u4f46\u867d\u7136\u7b97\u662f\u8fd9\u4e48\u7b97\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u7531\u4e8e\u4e0d\u540c\u8bbe\u5907\u7684\u5dee\u5f02\uff0c\u5b9e\u9645\u7684\u6700\u5c0f\u5206\u8fa8\u7387\u53ef\u80fd\u4f1a\u6709\u504f\u5dee\u3002\u8fd9\u5bf9\u4f4e\u9891\u7684\u5f71\u54cd\u5176\u5b9e\u4e0d\u5927\uff0c\u56e0\u4e3a\u4f4e\u9891\u5206\u91cf\u7684\u5468\u671f\u5b9e\u5728\u591f\u957f\uff0c\u8bef\u5dee\u4e0d\u4f1a\u592a\u5927\u3002\u4f46\u662f\u5bf9\u4e8e\u9ad8\u9891\u5206\u91cf\u6765\u8bf4\uff0c\u5468\u671f\u77ed\uff0c\u8bef\u5dee\u5c31\u4f1a\u6bd4\u8f83\u660e\u663e\u3002<\/p>\n<p>\u8fd9\u5176\u5b9e\u4e5f\u662f\u7406\u8bba\u63a8\u5bfc\u548c\u5b9e\u9645\u843d\u5730\u7684\u5dee\u5f02\u3002\u7406\u8bba\u4e0a\uff0cFFT\u7684\u4e0b\u6807\u662f\u4e00\u4e2a\u7406\u60f3\u7684\u5206\u8fa8\u7387\uff0c\u4f46\u662f\u5b9e\u9645\u4e2d\uff0c\u7531\u4e8e\u8bbe\u5907\u7684\u9650\u5236\uff0c\u53ef\u80fd\u4f1a\u6709\u504f\u5dee\u3002<\/p>\n<p>\u5bf9\u6b64\uff0c\u5176\u5b9e\u6211\u7684\u5904\u7406\u65b9\u6cd5\u4e5f\u5f88\u7b80\u5355\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u6bd4\u5982\u6211\u4eec\u73b0\u5728\u6700\u4f4e\u5206\u8fa8\u7387\u9884\u8ba110Hz\uff0c\u90a3\u6b64\u65f6\u5bf9\u5e94\u7684\u4e0b\u6807\u5c31\u662f1\u3002\u90a3\u4e48\u572810kHz\u65f6\uff0c\u4e0b\u6807\u7406\u8bba\u4e0a\u5e94\u8be5\u662f1000\uff0c\u4f46\u662f\u5b9e\u9645\u4e2d\u53ef\u80fd\u4f1a\u6709\u504f\u5dee\uff0c\u6bd4\u5982990~1010\u3002\u8fd9\u65f6\uff0c\u5c31<strong>\u5fae\u8c03<\/strong>\u91c7\u6837\u7684<strong>\u5468\u671f<\/strong>\uff0c\u4f7f\u5f97\u5bf9\u5e9410kHz\u7684\u4e0b\u6807\u521a\u597d\u57281000\u5904\u3002<\/p>\n<h2>2. FFT\u9891\u8c31\u6cc4\u9732\u539f\u56e0<\/h2>\n<h3>2.1 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alt=\"\u4f4e\u9891\u91c7\u6837\u6709\u504f\u5dee\" \/><\/div><br \/>\n1. \u8f93\u5165\u4fe1\u53f7\u9891\u7387\u8f83\u9ad8\uff0c\u91c7\u6837\u9891\u7387\u51c6\u786e\uff1a<br \/>\n<div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blog.keruone.cn\/wp-content\/uploads\/2025\/07\/\u9ad8\u9891-\u91c7\u6837\u5468\u671f\u504f\u5dee0-\u5ef6\u62d3\u7ed3\u679c.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/blog.keruone.cn\/wp-content\/uploads\/2025\/07\/\u9ad8\u9891-\u91c7\u6837\u5468\u671f\u504f\u5dee0-\u5ef6\u62d3\u7ed3\u679c.png\" 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src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/blog.keruone.cn\/wp-content\/uploads\/2025\/07\/\u4fe1\u53f7\u6c49\u660e\u7a97.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\u7a97\u51fd\u6570\u7684\u4f5c\u7528\" \/><\/div><br \/>\n&#8211; \u52a0\u7a97\u540e\u5ef6\u62d3\u4fe1\u53f7\u4ea4\u754c\u5904\u6bd4\u8f83\uff1a<br \/>\n<div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blog.keruone.cn\/wp-content\/uploads\/2025\/07\/\u52a0\u7a97\u5ef6\u62d3\u4fe1\u53f7\u4ea4\u754c\u5904\u6bd4\u8f83.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/blog.keruone.cn\/wp-content\/uploads\/2025\/07\/\u52a0\u7a97\u5ef6\u62d3\u4fe1\u53f7\u4ea4\u754c\u5904\u6bd4\u8f83.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\u52a0\u7a97\u540e\u5ef6\u62d3\u4fe1\u53f7\u4ea4\u754c\u5904\u6bd4\u8f83\" \/><\/div><\/p>\n<ol>\n<li>\n<p><strong>\u91c7\u6837\u9891\u7387\u7684\u5fae\u8c03<\/strong><br 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href=\"https:\/\/blog.csdn.net\/huibianyu\/article\/details\/40187261\">\u535a\u5ba2<\/a>\u53ef\u4ee5\u6765\u7f16\u5199ap-fft\u7684\u76f8\u5173\u7b97\u6cd5<br \/>\n\u6211\u518dmatlab\u4e0a\u8fdb\u884c\u4e86\u4eff\u771f\u5bf9\u6bd4\uff0c\u5206\u522b\u662f2048\u70b9FFT\u30011024\u70b9FFT\u548c2047\u4e2a\u91c7\u6837\u70b9\u7684ap-fft\uff0c\u7ed3\u679c\u5982\u4e0b\uff1a<br \/>\n<div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/blog.keruone.cn\/wp-content\/uploads\/2025\/07\/ap-fftfft\u5bf9\u6bd4\u56fe.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/blog.keruone.cn\/wp-content\/uploads\/2025\/07\/ap-fftfft\u5bf9\u6bd4\u56fe.png\" 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