{"id":10780,"date":"2023-05-13T05:02:45","date_gmt":"2023-05-13T09:02:45","guid":{"rendered":"https:\/\/audioapartment.com\/?p=10780"},"modified":"2023-06-10T20:05:16","modified_gmt":"2023-06-11T00:05:16","slug":"what-is-nyquist-frequency","status":"publish","type":"post","link":"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-nyquist-frequency\/","title":{"rendered":"What is Nyquist Frequency? The Key to Perfectly Sampled Sound"},"content":{"rendered":"\n<p>Imagine you&#8217;re in your music studio, bobbing your head to a killer beat, when suddenly, a screeching sound assaults your ears! You realize something has gone terribly wrong with your digital audio. Could it be the mixing? The EQ? The answer could lie in Nyquist Frequency.<strong> But what exactly is Nyquist Frequency, and how does it affect digital audio?<\/strong><\/p>\n\n\n\n<p class=\"quick-answer\"><strong>What is Nyquist frequency?<\/strong> Nyquist frequency is the maximum frequency that can be accurately represented and reproduced in a digital system. It determines the upper limit of audio frequencies that can be captured and played back without introducing distortion or artifacts into the sound.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>What is Nyquist Frequency?<\/strong><\/h2>\n\n\n\n<p>The Nyquist Frequency, named after the Swedish-American engineer Harry Nyquist, is a key concept in the field of digital signal processing and, in particular, digital audio. It refers to the highest frequency that can be accurately represented <a href=\"https:\/\/audioapartment.com\/music-business\/legal\/how-to-clear-a-sample-for-a-song-or-beat-step-by-step-guide\/\">when a signal is digitally sampled<\/a>.<\/p>\n\n\n\n<p>According to Nyquist&#8217;s theorem, in order to accurately capture and <a href=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-distortion\/\" data-type=\"URL\" data-id=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-distortion\/\">reproduce a sound without distortion<\/a> or aliasing, it needs to be sampled at least twice its highest frequency.<strong> The highest frequency that can be accurately represented is the Nyquist Frequency, and it is exactly half of the sampling rate.<\/strong><\/p>\n\n\n\n<p>For example, if you are sampling at a rate of 44.1 kHz (the standard for audio CDs), the highest frequency you can accurately reproduce is 22.05 kHz (which is just above the upper limit of human hearing).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>What happens when the Nyquist frequency is violated in digital audio?<\/strong><\/h2>\n\n\n\n<p>So, what exactly happens when we ignore the Nyquist frequency&#8217;s warnings and allow aliasing to infiltrate our digital audio? Let me break it down for you:<\/p>\n\n\n\n<ul>\n<li><strong>Aliasing distortion<\/strong>: Aliasing causes high-frequency audio signals to masquerade as lower frequencies, leading to a distorted representation of the original sound. <\/li>\n\n\n\n<li><strong>Unpleasant artifacts<\/strong>: Aliasing introduces unpleasant artifacts such as buzzing, hissing, or ghostly echoes. These sonic aberrations distract and detract from the intended musical expression, leaving us scratching our heads in dismay.<\/li>\n\n\n\n<li><strong>Inaccurate frequency representation<\/strong>: When the Nyquist frequency is exceeded, the high-frequency components of the original audio signal &#8220;fold back&#8221; into the lower frequency range. This folding creates false representations of frequencies, causing confusion and disarray in the digital realm.<\/li>\n<\/ul>\n\n\n\n<p>To keep our digital audio pristine, it&#8217;s crucial to honor the Nyquist frequency and ensure that our sampling rate is appropriately set. Let&#8217;s take a look at a small dos and don&#8217;ts data table to guide us on this path:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Do&#8217;s<\/th><th>Don&#8217;ts<\/th><\/tr><\/thead><tbody><tr><td>Set the sampling rate at least twice the Nyquist frequency<\/td><td>Exceed the Nyquist frequency limit<\/td><\/tr><tr><td>Use anti-aliasing filters to remove high-frequency components before sampling<\/td><td>Neglect anti-aliasing measures<\/td><\/tr><tr><td>Maintain a high-quality digital audio chain<\/td><td>Rely on subpar equipment and converters<\/td><\/tr><tr><td>Regularly monitor and analyze the audio for aliasing artifacts<\/td><td>Ignore potential aliasing issues<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><em>Dos and Don&#8217;ts for Nyquist Frequency and Aliasing in Digital Audio<\/em><br><\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>How can we determine the Nyquist frequency in digital audio?<\/strong><\/h2>\n\n\n\n<p>To determine the Nyquist frequency in digital audio, we rely on a simple and elegant formula. The Nyquist frequency (fN) is half the value of <a href=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-sample-rate-unveiling-the-power-of-audio-resolution\/\" data-type=\"URL\" data-id=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-sample-rate-unveiling-the-power-of-audio-resolution\/\">the sampling rate (Fs)<\/a>. Yes, you heard it right\u2014it&#8217;s as straightforward as dividing the sampling rate by two! Allow me to demonstrate with an example:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/audioapartment.com\/wp-content\/uploads\/2023\/06\/a-diagram-showing-the-relationship-of-Nyquist-frequecny-and-sample-rate-wiki-commons-1024x683.jpg\" alt=\"A diagram showing the relationship between Nyquist frequency and sample rate. Source: Wiki Commons\" class=\"wp-image-13792\" title=\"\" srcset=\"https:\/\/audioapartment.com\/wp-content\/uploads\/2023\/06\/a-diagram-showing-the-relationship-of-Nyquist-frequecny-and-sample-rate-wiki-commons-1024x683.jpg 1024w, https:\/\/audioapartment.com\/wp-content\/uploads\/2023\/06\/a-diagram-showing-the-relationship-of-Nyquist-frequecny-and-sample-rate-wiki-commons-300x200.jpg 300w, https:\/\/audioapartment.com\/wp-content\/uploads\/2023\/06\/a-diagram-showing-the-relationship-of-Nyquist-frequecny-and-sample-rate-wiki-commons-768x512.jpg 768w, https:\/\/audioapartment.com\/wp-content\/uploads\/2023\/06\/a-diagram-showing-the-relationship-of-Nyquist-frequecny-and-sample-rate-wiki-commons-60x40.jpg 60w, https:\/\/audioapartment.com\/wp-content\/uploads\/2023\/06\/a-diagram-showing-the-relationship-of-Nyquist-frequecny-and-sample-rate-wiki-commons-600x400.jpg 600w, https:\/\/audioapartment.com\/wp-content\/uploads\/2023\/06\/a-diagram-showing-the-relationship-of-Nyquist-frequecny-and-sample-rate-wiki-commons.jpg 1200w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">A diagram showing the relationship between nyquist frequency and sample rate. Source: wiki commons<\/figcaption><\/figure>\n\n\n\n<p>Let&#8217;s say we have a digital audio system with a sampling rate of 44,100 Hz (44.1 kHz). <strong>To find the Nyquist frequency, we follow these steps:<\/strong><\/p>\n\n\n\n<ol>\n<li>Take the sampling rate (Fs): 44,100 Hz.<\/li>\n\n\n\n<li>Divide it by 2: 44,100 Hz \/ 2 = 22,050 Hz.<\/li>\n<\/ol>\n\n\n\n<p>Voila! The Nyquist frequency, in this case, is 22,050 Hz. It&#8217;s as simple as that!<\/p>\n\n\n\n<p>Now, it&#8217;s important to note that the Nyquist frequency serves as an upper limit, indicating the highest frequency that can be accurately captured and reproduced in the digital domain. Going beyond this frequency risks introducing aliasing and distorting our beloved audio.<\/p>\n\n\n\n<p>Additionally, it&#8217;s worth mentioning that <a href=\"https:\/\/audioapartment.com\/instruments-and-equipment\/what-is-a-daw\/\" data-type=\"URL\" data-id=\"https:\/\/audioapartment.com\/instruments-and-equipment\/what-is-a-daw\/\">modern digital audio equipment <\/a>often operates at a standard sampling rate of 44.1 kHz (CD quality), 48 kHz (common for digital media), or higher for <a href=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-hi-fi-audio-high-fidelity-audio\/\" data-type=\"URL\" data-id=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-hi-fi-audio-high-fidelity-audio\/\">high-resolution audio<\/a>. These standard rates have been established to maintain compatibility across different platforms and provide a balance between audio quality and file size.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Can Nyquist frequency be manipulated in digital audio?<\/strong><\/h2>\n\n\n\n<p>While the sampling rate determines the Nyquist frequency itself and acts as a fundamental limit for accurate digital audio reproduction, there are indeed techniques and tools available that allow us to manipulate the perception of frequency in the digital domain. <\/p>\n\n\n\n<figure class=\"wp-block-pullquote\"><blockquote><p>With careful processing, we can shape the frequency content of a sound, effectively altering the perceived frequencies&#8230;<\/p><\/blockquote><\/figure>\n\n\n\n<p><strong>Let&#8217;s delve into these fascinating methods:<\/strong><\/p>\n\n\n\n<ul>\n<li><strong>Digital Signal Processing (DSP): <\/strong><a href=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-digital-signal-processing\/\" data-type=\"URL\" data-id=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-digital-signal-processing\/\">Through the power of DSP<\/a>, we can employ various algorithms and techniques to modify and manipulate audio signals. With careful processing, we can shape the frequency content of a sound, effectively altering the perceived frequencies without violating the Nyquist frequency.<\/li>\n\n\n\n<li><strong>Equalization (EQ):<\/strong> EQ allows us to<a href=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-eq-in-audio\/\" data-type=\"URL\" data-id=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-eq-in-audio\/\"> boost or attenuate specific frequency ranges<\/a> in an audio signal. By emphasizing or reducing certain frequencies, we can create a desired tonal balance and shape the overall sound to our liking.<\/li>\n\n\n\n<li><strong>Pitch-shifting<\/strong>: With pitch-shifting techniques, we can alter <a href=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-pitch-in-music\/\" data-type=\"URL\" data-id=\"https:\/\/audioapartment.com\/techniques-and-performance\/what-is-pitch-in-music\/\">the perceived pitch of a sound<\/a> without affecting the Nyquist frequency. This can be particularly useful for creative purposes, such as creating harmonies or changing the key of a musical composition.<\/li>\n\n\n\n<li><strong>Time-stretching<\/strong>: Time-stretching enables us to modify the duration of an audio signal without significantly affecting the perceived pitch or violating the Nyquist frequency. This technique proves valuable when adjusting the tempo or duration of a piece of music.<\/li>\n\n\n\n<li><strong>Sampling rate conversion<\/strong>: Although altering the sampling rate directly affects the Nyquist frequency, we can employ sampling rate conversion algorithms to change the sampling rate while maintaining the integrity of the audio signal. This allows us to manipulate the Nyquist frequency indirectly by adjusting the sampling rate.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Comparison of Sampling Rates and Nyquist Frequencies in Digital Audio<\/strong><\/h2>\n\n\n\n<p>The relationship between sampling rates and Nyquist Frequencies gives us profound insights into the design of our digital audio systems. It helps us understand the trade-offs between audio quality and data size and why sometimes higher isn&#8217;t always better.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Sampling Rate (kHz)<\/th><th>Nyquist Frequency (kHz)<\/th><\/tr><\/thead><tbody><tr><td>44.1<\/td><td>22.05<\/td><\/tr><tr><td>48<\/td><td>24<\/td><\/tr><tr><td>96<\/td><td>48<\/td><\/tr><tr><td>192<\/td><td>96<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><em>Comparison of Sampling Rates and Nyquist Frequencies in Digital Audio<\/em><\/figcaption><\/figure>\n\n\n\n<div class=\"wp-block-group ne-video-section is-layout-constrained wp-block-group-is-layout-constrained\"><div class=\"wp-block-group__inner-container\">\n<p>If you want even more tips and insights, watch this video called <em>&#8220;Audio Basics: The Nyquist Theorem&#8221;<\/em> from the Cato Zane YouTube channel.<\/p>\n\n\n<!--presto-player:video_id=39--><figure class=\"wp-block-video presto-block-video  presto-provider-youtube\" style=\"--plyr-color-main: var(--presto-player-highlight-color, #18a5a5); --presto-player-logo-width: 150px; \">\n    <presto-player  id=\"presto-player-1\" src=\"\/\/www.youtube.com\/embed\/09z7Y9CBY5w?iv_load_policy=3&amp;modestbranding=1&amp;playinline=1&amp;showinfo=0&amp;rel=0&amp;enablejsapi=1\" media-title=\"Audio Basics: The Nyquist Theorem\" css=\"\" class=\"presto-video-id-39 presto-preset-id-5 skin-modern\" skin=\"modern\" icon-url=\"https:\/\/audioapartment.com\/wp-content\/plugins\/presto-player\/img\/sprite.svg\" preload=\"\" poster=\"\" playsinline  >\n        \n\n    <\/presto-player>\n<\/figure>        <script>\n            var player = document.querySelector('presto-player#presto-player-1');\n            player.video_id = 39;\n                                                player.preset = {\"id\":5,\"name\":\"Youtube Optimized\",\"slug\":\"youtube\",\"icon\":\"youtube\",\"skin\":\"modern\",\"play-large\":true,\"rewind\":true,\"play\":true,\"fast-forward\":true,\"progress\":true,\"current-time\":true,\"mute\":true,\"volume\":true,\"speed\":true,\"pip\":false,\"fullscreen\":true,\"captions\":false,\"reset_on_end\":true,\"auto_hide\":true,\"captions_enabled\":false,\"save_player_position\":false,\"sticky_scroll\":false,\"sticky_scroll_position\":\"bottom right\",\"on_video_end\":\"select\",\"play_video_viewport\":false,\"hide_youtube\":false,\"lazy_load_youtube\":true,\"hide_logo\":false,\"border_radius\":0,\"caption_style\":\"\",\"caption_background\":\"\",\"is_locked\":true,\"cta\":[\"\"],\"watermark\":[\"\"],\"search\":[\"\"],\"email_collection\":[\"\"],\"created_by\":1,\"created_at\":\"2023-05-02 23:48:56\",\"updated_at\":\"2023-05-02 23:48:56\",\"deleted_at\":\"\",\"show_time_elapsed\":false};\n                                                                player.chapters = [];\n                                                                player.overlays = [];\n                                                                player.tracks = [];\n                                                                player.branding = {\"logo\":\"\",\"color\":\"#18a5a5\",\"logo_width\":150,\"player_css\":\"\"};\n                                                                player.blockAttributes = {\"id\":39,\"src\":\"https:\\\/\\\/www.youtube.com\\\/watch?v=09z7Y9CBY5w\",\"preset\":5,\"video_id\":\"09z7Y9CBY5w\",\"visibility\":\"public\",\"color\":\"#00b3ff\",\"mutedPreview\":{\"enabled\":false,\"captions\":false},\"mutedOverlay\":{\"enabled\":false,\"src\":\"\",\"width\":200,\"focalPoint\":{\"x\":0.5,\"y\":0.5}},\"mutedOverlayType\":\"text\",\"mutedOverlayText\":\"Click to play\",\"mutedOverlayImageWidth\":200,\"playsInline\":true,\"chapters\":[],\"overlays\":[],\"tracks\":[],\"title\":\"Audio Basics: The Nyquist Theorem\"};\n                                                                                            player.skin = \"modern\";\n                                                                player.analytics = false;\n                                                                player.automations = true;\n                                                                player.provider = \"youtube\";\n                                                                player.video_id = 39;\n                                                                                                                        player.provider_video_id = \"09z7Y9CBY5w\";\n                                                                player.youtube = {\"noCookie\":false,\"channelId\":\"\",\"show_count\":false};\n                                    <\/script>\n        <\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Frequently asked questions (FAQ)<\/h2>\n\n\n\n<p>Do you still have questions about Nyquist frequency in digital audio? Below are some of the most commonly asked questions.<\/p>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1682228188531\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><strong>Why is the Nyquist frequency important in digital audio?<\/strong><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The Nyquist frequency is crucial because it sets the upper limit for accurately capturing and reproducing audio in a digital system. Exceeding this frequency can lead to aliasing and distortion, compromising the fidelity of the sound.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1682228196889\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><strong>How does the Nyquist frequency relate to the sampling rate?<\/strong><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The Nyquist frequency is directly linked to the sampling rate. The sampling rate must be at least twice the Nyquist frequency to avoid aliasing. This ensures that the digital system captures enough data points to accurately represent the original analog signal.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1682228199668\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><strong>Can the Nyquist frequency be higher than the highest frequency of interest in a recording?<\/strong><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>No, it cannot. The Nyquist frequency should always be higher than the highest frequency of interest in the recording. This allows for accurate representation and faithful reproduction of the audio content.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h2>\n\n\n\n<p>We&#8217;ve strummed our way through the sonorous world of Nyquist Frequency. Have I hit the right frequency with this article? Let me know in the comments section below.<strong> I read and reply to every comment. <\/strong>If this post struck a chord with you, consider sharing it with a friend, and don&#8217;t forget to check out the full ensemble of tips and tricks on audio production. Thanks for reading, and keep hitting the right frequencies!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Key Takeaways<\/strong><\/h3>\n\n\n\n<p>This article covered the intricacies of the Nyquist Frequency and its importance in the digital audio domain. Here are some key takeaways:<\/p>\n\n\n\n<ul>\n<li>The Nyquist Frequency, named after Harry Nyquist, is half of the sampling rate of a digital audio system.<\/li>\n\n\n\n<li>It is the highest frequency that can be accurately captured and reproduced by a digital audio system without distortion or aliasing.<\/li>\n\n\n\n<li>Understanding the Nyquist Frequency is vital for ensuring the fidelity of digital audio, as neglecting it can lead to distortions and a poor audio experience.<\/li>\n\n\n\n<li>Sampling rates and Nyquist Frequencies are interlinked. A higher sampling rate will result in a higher Nyquist Frequency, allowing for the accurate reproduction of higher-frequency sounds.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Helpful resources<\/h3>\n\n\n\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Nyquist_frequency\" target=\"_blank\" rel=\"noopener\">Nyquist Frequency<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/musicweb.ucsd.edu\/~trsmyth\/digitalAudio171\/Nyquist_Sampling_Theorem.html\" target=\"_blank\" rel=\"noopener\">Nyquist Sampling Theorem<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/homes.esat.kuleuven.be\/~spchlab\/AudioDemonstrations\/Sampling.htm\" target=\"_blank\" rel=\"noopener\">Digitizing Audio Signals<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Discover Nyquist frequency in digital audio\u2014its importance, manipulation techniques, and avoiding aliasing. Dive into the world of sonic precision!<\/p>\n","protected":false},"author":3,"featured_media":10784,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[716],"tags":[685],"_links":{"self":[{"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/posts\/10780"}],"collection":[{"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/comments?post=10780"}],"version-history":[{"count":0,"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/posts\/10780\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/media\/10784"}],"wp:attachment":[{"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/media?parent=10780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/categories?post=10780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/audioapartment.com\/wp-json\/wp\/v2\/tags?post=10780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}