{"id":4612,"date":"2022-04-19T10:27:25","date_gmt":"2022-04-19T08:27:25","guid":{"rendered":"https:\/\/www.pschatzmann.ch\/home\/?p=4612"},"modified":"2023-06-30T11:35:53","modified_gmt":"2023-06-30T09:35:53","slug":"fast-fourier-transform-fft-with-the-audio-tools-library","status":"publish","type":"post","link":"https:\/\/www.pschatzmann.ch\/home\/2022\/04\/19\/fast-fourier-transform-fft-with-the-audio-tools-library\/","title":{"rendered":"Fast Fourier Transform (FFT) with the Audio Tools Library"},"content":{"rendered":"<p>The <strong>Fast Fourier Transform (FFT)<\/strong> is a mathematical operation that changes the domain (x-axis) of a signal from time to frequency. This is particularly useful for determining the frequency of a signal or for decomposing a signal consisting of multiple frequencies. I had this on my to-do list for quite some time and I finally managed to add this functionality to my <a href=\"https:\/\/github.com\/pschatzmann\/arduino-audio-tools\">Arduino Audio Tools<\/a> library.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.pschatzmann.ch\/wp-content\/uploads\/2022\/04\/FFT-Time-Frequency-View-540-300x210.png\" alt=\"\" width=\"300\" height=\"210\" class=\"alignnone size-medium wp-image-4614\" srcset=\"https:\/\/www.pschatzmann.ch\/wp-content\/uploads\/2022\/04\/FFT-Time-Frequency-View-540-300x210.png 300w, https:\/\/www.pschatzmann.ch\/wp-content\/uploads\/2022\/04\/FFT-Time-Frequency-View-540.png 540w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<h2>Length and Stride<\/h2>\n<p>The <strong>length<\/strong> defines the number of samples that are used to run the FFT. The length must be a value of the power of 2 (e.g. 1024). This parameter impacts<\/p>\n<ul>\n<li>the calculation speed and frequency of calculation<\/li>\n<li>the memory which is needed <\/li>\n<li>the frequency resolution of the result   <\/li>\n<\/ul>\n<p>The <strong>stride<\/strong> defines the number of samples that we use to advance at each step. If we do not define any stride we just consume the samples sequentially:<br \/>\n<img decoding=\"async\" src=\"https:\/\/pschatzmann.github.io\/Resources\/img\/fft1.jpg\" alt=\"FFT1\" \/><\/p>\n<p>If we define a stride, we move ahead in steps as follows<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/pschatzmann.github.io\/Resources\/img\/fft2.jpg\" alt=\"FFT1\" \/><\/p>\n<p>As you can see in the image above the last length-stride samples are reprocessed with each step.<\/p>\n<h2>RealFFT<\/h2>\n<p>In our framework we can use the <a href=\"https:\/\/pschatzmann.github.io\/arduino-audio-tools\/html\/classaudio__tools_1_1_audio_real_f_f_t.html\">AudioRealFFT<\/a> class as copy destination.<br \/>\nYou start the processing by calling the begin method which is expecting <a href=\"https:\/\/pschatzmann.github.io\/arduino-audio-tools\/html\/structaudio__tools_1_1_audio_f_f_t_config.html\">configuration information<\/a> where we define the <strong>length<\/strong> and <strong>stride<\/strong>. We also need to provide the regular <strong>audio parameters<\/strong> (channels, sample_rate, bits_per_sample). Finally we can define a <strong>callback method<\/strong> which will be called when we get a new result.<br \/>\nIn order to determine the result we can use the result() method which provides the best <a href=\"https:\/\/pschatzmann.github.io\/arduino-audio-tools\/html\/structaudio__tools_1_1_audio_f_f_t_result.html\">AudioFFTResult<\/a> or if we want to get the N best values we can call the resultArray() method to which we pass an array of AudioFFTResult.<\/p>\n<p>The <strong>AudioFFTResult<\/strong> contains<\/p>\n<ul>\n<li>the <em>frequency<\/em><\/li>\n<li>the <em>magnitude<\/em> (of the frequency)<\/li>\n<li>the musical note which is corresponding to the frequency (<em>frequencyAsNote()<\/em>)<\/li>\n<\/ul>\n<p>An <a href=\"https:\/\/github.com\/pschatzmann\/arduino-audio-tools\/blob\/main\/examples\/examples-audiokit\/streams-audiokit-fft\/streams-audiokit-fft.ino\">example can be found on Github<\/a><\/p>\n<h2>KissFFT<\/h2>\n<p>Alternatively you can use the <a href=\"https:\/\/github.com\/pschatzmann\/kissfft\">KissFFT Library<\/a> which you will need to <strong>install separately<\/strong>.<br \/>\nJust replace the <code>#include \"AudioLibs\/AudioRealFFT.h\"<\/code> with <code>#include \"AudioLibs\/AudioKissFFT.h\"<\/code> and the <code>AudioRealFFT<\/code> class with the <code>AudioKissFFT<\/code>  in your sketch.<br \/>\nIn the default settings it uses int16 data types, but I did not notice any performance advantage on a ESP32.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Fast Fourier Transform (FFT) is a mathematical operation that changes the domain (x-axis) of a signal from time to frequency. This is particularly useful for determining the frequency of a signal or for decomposing a signal consisting of multiple frequencies. I had this on my to-do list for quite [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":4614,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[20,22],"tags":[39,44],"class_list":["post-4612","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arduino","category-machine-sound","tag-fft","tag-uno"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Fast Fourier Transform (FFT) with the Audio Tools Library - Phil Schatzmann<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.pschatzmann.ch\/home\/2022\/04\/19\/fast-fourier-transform-fft-with-the-audio-tools-library\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fast Fourier Transform (FFT) with the Audio Tools Library - Phil Schatzmann\" \/>\n<meta property=\"og:description\" content=\"The Fast Fourier Transform (FFT) is a mathematical operation that changes the domain (x-axis) of a signal from time to frequency. 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