{"id":39232,"date":"2025-10-21T09:35:17","date_gmt":"2025-10-21T14:35:17","guid":{"rendered":"https:\/\/www.dmcinfo.com\/?p=39232"},"modified":"2025-12-23T09:44:56","modified_gmt":"2025-12-23T14:44:56","slug":"dsp-low-pass-iir-filter-calculator","status":"publish","type":"post","link":"https:\/\/www.dmcinfo.com\/blog\/39232\/dsp-low-pass-iir-filter-calculator\/","title":{"rendered":"DSP Low-Pass IIR Filter Calculator\u00a0"},"content":{"rendered":"\n<p>There are countless DSP (Digital Signal Processing) techniques out there, and many of them can look intimidating at first glance. In this calculator, we\u2019ll keep things simple and focus on the most practical and widely used case in embedded firmware: a first-order low-pass filter, with a gain of 1. This filter is similar to the classic RC (resistor-capacitor) analog filter and is sometimes called a digital RC filter.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-calculate-filter-coefficient\">Calculate Filter Coefficient<\/h2>\n\n\n\n<p>The first step to implement this filter is to calculate the filter coefficient, which depends on the sample rate and desired cut-off frequency.&nbsp;<\/p>\n\n\n\n<p>The formula to calculate this coefficient is from <a href=\"https:\/\/en.wikipedia.org\/wiki\/Low-pass_filter#Simple_infinite_impulse_response_filter\" target=\"_blank\" rel=\"noreferrer noopener\">Wikipedia<\/a>:&nbsp;<img decoding=\"async\" width=\"175\" height=\"65\" class=\"wp-image-39248\" style=\"width: 150px; vertical-align:middle;\" src=\"https:\/\/cdn.dmcinfo.com\/wp-content\/uploads\/2025\/10\/21091347\/dsp-filter-formula.png\" alt=\"filter coefficient formula\"><\/p>\n\n\n\n<p>Where <img decoding=\"async\" width=\"25\" height=\"28\" class=\"wp-image-39250\" style=\"width: 25px; vertical-align:middle;\" src=\"https:\/\/cdn.dmcinfo.com\/wp-content\/uploads\/2025\/10\/21091723\/fc-formula.png\" alt=\"fc from a formula\"> is the filter cut-off frequency, and <img decoding=\"async\" width=\"35\" height=\"33\" class=\"wp-image-39252\" style=\"width: 35px; vertical-align:middle;\" src=\"https:\/\/cdn.dmcinfo.com\/wp-content\/uploads\/2025\/10\/21091828\/delta-t-formula.png\" alt=\"delta t formula\"> is the sampling period (but it is easier to enter it as a Sampling Frequency, Fs).&nbsp;<\/p>\n\n\n\n<div style=\"border:1px solid black; padding: 20px; \"> \n    <h2>First Order IIR Low\u2011Pass Filter Coefficient Calculator<\/h2> \n    <div>\n        <label for=\"fs\"><\/label>Enter sampling frequency (Fs, Hz): <\/label> \n        <input type=\"number\" id=\"fs\" value=\"100000\" min=\"1\" step=\"1\"> \n    <\/div>\n    <div>\n        <label for=\"fc\">Enter desired cutoff frequency (fc, Hz): <\/label> \n        <input type=\"number\" id=\"fc\" value=\"2000\" min=\"1\" step=\"1\"> \n    <\/div>\n    <div style=\"padding: 10px; \">\n        <button id=\"calcBtn\">Calculate Filter Coeficient<\/button> \n    <\/div>\n    <div> \n      <div>Coeficient <b>a<\/b>: <span id=\"ka\">\u2014<\/span><\/div> \n      <div>Coeficient b (for reference, b = 1 \u2212 a): <span id=\"kb\">\u2014<\/span><\/div> \n      <div>Eqvivalent RC filter time constant (for reference): <span id=\"krc\">\u2014<\/span><\/div> \n    <\/div> \n<\/div> \n\n<script> \nconst TAU = Math.PI*2;\n\nfunction coeffs(Fs, fc)\n{ \n  const dt = 1\/Fs; \n  const a = (TAU*dt*fc)\/(TAU*dt*fc + 1); \n  const b = 1 - a; \n  const RC = dt*((1-a)\/a); \n  return {a,b,RC}; \n} \n\nfunction fmtRC(RC)\n{ \n  if (!isFinite(RC) || RC <= 0) return '\u2014'; \n  if (RC >= 1) return `${RC.toPrecision(3)} s`; \n  if (RC >= 1e-3) return `${(RC*1e3).toPrecision(3)} ms`; \n  return `${(RC*1e6).toPrecision(3)} \u00b5s`; \n} \n\nfunction render()\n{ \n  const Fs = parseFloat(document.getElementById('fs').value); \n  const fc = parseFloat(document.getElementById('fc').value); \n  if(!(Fs>0 && fc>0 && fc<Fs\/2))\n  { \n    alert('Please ensure Fs>0 and 0<fc<Fs\/2'); \n    return; \n  } \n\n  const {a,b,RC} = coeffs(Fs,fc); \n  document.getElementById('ka').textContent = a.toPrecision(6); \n  document.getElementById('kb').textContent = b.toPrecision(6); \n  document.getElementById('krc').textContent = fmtRC(RC); \n}\n\ndocument.getElementById('calcBtn').addEventListener('click', render); \n<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-filter-implementation\">Filter Implementation<\/h2>\n\n\n\n<p>Knowing the filter coefficient&nbsp; <strong>a<\/strong>, it is pretty easy to implement our filter:&nbsp;<\/p>\n\n\n\n<p><strong>filter_output = filter_output + a * (new_sample - filter_output)&nbsp;<\/strong><\/p>\n\n\n\n<p>Where:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>filter_output <\/strong>is a variable that must survive between calls, it can be a static variable, something global, etc.&nbsp;&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>a<\/strong> is a coefficient we just calculated above&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>new_sample<\/strong> is a new ADC sample&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>The filter calculations should be called on every sample, so it may be a good idea to implement them inside the ADC interrupt. However, you can also run the filter on an array of values\u2014whatever works best for your architecture.&nbsp;<\/p>\n\n\n\n<p>Don\u2019t forget that the filter calculations should generally use real (float) values!&nbsp;<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Learn more about DMC\u2019s&nbsp;<a href=\"https:\/\/www.dmcinfo.com\/services\/embedded-development-and-embedded-programming\/\">Embedded Development and Programming<\/a>&nbsp;services and&nbsp;<a href=\"https:\/\/www.dmcinfo.com\/contact\">contact us<\/a>&nbsp;for your next project!<\/strong><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are countless DSP (Digital Signal Processing) techniques out there, and many of them can look intimidating at first glance. In this calculator, we\u2019ll keep things simple and focus on the most practical and widely used case in embedded firmware: a first-order low-pass filter, with a gain of 1. This filter is similar to the [&hellip;]<\/p>\n","protected":false},"author":37,"featured_media":39268,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[754],"tags":[],"class_list":["post-39232","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-embedded-development-programming"],"yoast_head":"<title>DSP Low-Pass IIR Filter Calculator\u00a0 | DMC, Inc.<\/title>\n<meta name=\"description\" content=\"Calculate the filter coefficient for your digital signal processing needs with DMC, Inc.&#039;s user-friendly DSP calculator.\" \/>\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.dmcinfo.com\/blog\/39232\/dsp-low-pass-iir-filter-calculator\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" 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