{"id":13223,"date":"2021-06-08T16:03:46","date_gmt":"2021-06-08T10:33:46","guid":{"rendered":"http:\/\/www.pythonpool.com\/?p=13223"},"modified":"2021-06-15T09:50:45","modified_gmt":"2021-06-15T04:20:45","slug":"numpy-ifft","status":"publish","type":"post","link":"https:\/\/www.pythonpool.com\/numpy-ifft\/","title":{"rendered":"Discovering The Numpy ifft Function in Python"},"content":{"rendered":"\n<p>Numpy, which is short for <em>Numerical Python<\/em>, is a library that helps work with multi-dimensional arrays and matrices in python. Using numpy, the arrays in python can be processed at a faster rate. It is an open-source library for performing scientific computations and logical and mathematical operations on python arrays. Numpy has several inbuilt functions, and in this article, we shall be talking about one such function &#8211; <strong>Numpy ifft<\/strong>.<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_74 counter-hierarchy ez-toc-counter ez-toc-transparent ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #990303;color:#990303\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #990303;color:#990303\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#What_is_the_Numpy_ifft_Function\" >What is the Numpy ifft Function?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#About_Inverse_Fourier_Transform\" >About Inverse Fourier Transform<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#Syntax_of_numpy_ifft\" >Syntax of numpy ifft<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#Parameters\" >Parameters:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#Return_value\" >Return value:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#Numpy_ifft_using_python\" >Numpy ifft using python<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#Also_Read\" >Also, Read<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#FAQs\" >FAQ&#8217;s<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-numpy-ifft-function\"><span class=\"ez-toc-section\" id=\"What_is_the_Numpy_ifft_Function\"><\/span>What is the Numpy ifft Function?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>The <em>Numpy ifft<\/em> is a function in python&#8217;s numpy library that is used for obtaining the one-dimensional inverse discrete Fourier Transform. It computes the inverse of the one dimensional discrete Fourier Transform which is obtained by <em>numpy.fft<\/em>. <\/strong><\/p>\n\n\n\n<p><strong>The main application of using the <em>numpy.ifft<\/em> function is for analyzing signals. Here <em>&#8216;ifft&#8217;<\/em> stands for <em>&#8216;Inverse Fast Fourier Transform&#8217;<\/em>. Direct conversion of discrete Fourier Transform into its inverse uses high computation power. So, we use <em>numpy.ifft<\/em> as it performs the inverse at a faster rate.  <\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-about-inverse-fourier-transform\"><span class=\"ez-toc-section\" id=\"About_Inverse_Fourier_Transform\"><\/span>About Inverse Fourier Transform<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Before going into NumPy&#8217;s ifft function, we shall learn first about what is inverse Fourier transform. Fourier Transform converts time signals to their frequency, and <em>Inverse Fourier Transform<\/em> converts it back into their respective time signals.<em> <\/em><\/p>\n\n\n\n<p>Image processing, image <a href=\"http:\/\/www.pythonpool.com\/string-compression-python\/\" target=\"_blank\" rel=\"noreferrer noopener\">compression<\/a>, analyzing signals, audio compression, image reconstruction, etc.<strong>,<\/strong> are the various applications of <strong><em>Inverse Fourier Transform<\/em> in python. By using<em> inverse Fourier transform<\/em>, we convert the signals from their frequency domain to their time domain.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-syntax-of-numpy-ifft\"><span class=\"ez-toc-section\" id=\"Syntax_of_numpy_ifft\"><\/span>Syntax of numpy ifft<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>The syntax of the ifft function in numpy is : <\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><em>fft.ifft(a<strong>,&nbsp;<\/strong>n=None<strong>,&nbsp;<\/strong>axis=-1<strong>,&nbsp;<\/strong>norm=None)<\/em><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-parameters\"><span class=\"ez-toc-section\" id=\"Parameters\"><\/span>Parameters:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>a<\/strong>: It is the input array which has to be transformed.  <\/p>\n\n\n\n<p><strong>n<\/strong>: It is the optional parameter whose value is None by default. It is the length of the transformed axis of the output. If n is not given, then the input length is according to the axis value specified. If n is smaller than the length of the input, then the input is cropped. Else if n is greater, then padding with zero is performed on the input. <\/p>\n\n\n\n<p><strong>axis<\/strong>: This is again an optional parameter that has the value of a negative one by default. If the <strong>n<\/strong> value is not given, then the axis variable is given the value of the axis over which the inverse has to be computed.<\/p>\n\n\n\n<p><strong>norm<\/strong>: It is an optional value that is &#8216;backward&#8217; by default. It indicates the direction of the pair of transforms. The value can be either &#8216;forward,&#8217; &#8216;backward,&#8217; or &#8216;ortho.&#8217; <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-return-value\"><span class=\"ez-toc-section\" id=\"Return_value\"><\/span>Return value:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>out<\/strong> : The output is the transformed complex n dimensional array. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-numpy-ifft-using-python\"><span class=\"ez-toc-section\" id=\"Numpy_ifft_using_python\"><\/span>Numpy ifft using python<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Lets us now implement the ifft function in python. For that, first, we shall import the numpy library.<\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\nimport numpy as np\n<\/pre><\/div>\n\n\n<p>Then, after importing numpy, we will create a one-dimensional array using the numpy <em>array()<\/em> function. <\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\narray = np.array(&#x5B;1,5, 4,3])\n<\/pre><\/div>\n\n\n<p>Here, we shall perform the Fourier transform of the given array first. For that, we shall use <em>fft.fft()<\/em> function present in numpy. <strong>The <em>fft()<\/em> function takes the same parameters as the <em>ifft()<\/em> function. <\/strong><\/p>\n\n\n\n<p><strong>The only difference is that it computes a one dimensional discrete Fourier Transform whereas<em> ifft()<\/em> shall do the inverse of the value obtained by<em> fft()<\/em>.<\/strong><\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\nft  = np.fft.fft(array)\n<\/pre><\/div>\n\n\n<p>Now, to do inverse Fourier transform on the signal, we use the <em>ifft()<\/em> funtion. We use the <em>&#8216;np.fft.ifft()<\/em>&#8216; syntax to access the<em> iffit()<\/em> function. <\/p>\n\n\n\n<p>We shall pass the <em>&#8216;ft&#8217;<\/em> variable as an argument to the <em>ifft()<\/em> function. This will perform the inverse of the Fourier transformation operation. <\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\nift = np.fft.ifft(ft)\n<\/pre><\/div>\n\n\n<p> Now, we shall print both the variables &#8211; <em>&#8216;ft&#8217; <\/em>and<em> &#8216;ift&#8217;<\/em> obtained out of Fourier transformation and inverse Fourier transformation respectively. <\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\nprint(ft)\nprint(ift)\n<\/pre><\/div>\n\n\n<p class=\"has-medium-font-size\"><strong>The output is:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">[13.+0.j -3.-2.j -3.+0.j -3.+2.j]\n[1.+0.j 5.+0.j 4.+0.j 3.+0.j]<\/pre>\n\n\n\n<p>As seen above, when we performed inverse of the Fourier transformation, we got our original array back. <\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">[ 1. + 0.j , 5+0.j , 4+0.j , 3+0.j ] is equal to [ 1, 5, 4, 3 ].<\/pre>\n\n\n\n<p>Here as you can see, the output is in the form of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Complex_number\" target=\"_blank\" rel=\"noreferrer noopener\">complex numbers<\/a>. Complex numbers are in the form of<em> &#8216;a + bi&#8217; <\/em>where a is the real part of the number and b is the imaginary part. <\/p>\n\n\n\n<p>If you don&#8217;t want the answer in complex numbers, we can convert it into an absolute form. For that, we can use the <em>abs() <\/em>function present in the numpy library. <\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\nprint(np.abs(ft))\nprint(np.abs(ift))\n<\/pre><\/div>\n\n\n<p><strong>The output will be:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">[13.          3.60555128  3.          3.60555128]\n[1. 5. 4. 3.]<\/pre>\n\n\n\n<p>However, note that if you cannot use the absolute value obtained from the fft() function for performing inverse, it will not give the same result. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-also-read\"><span class=\"ez-toc-section\" id=\"Also_Read\"><\/span>Also, Read<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ul class=\"wp-block-yoast-seo-related-links\"><li><span style=\"text-decoration: underline;\"><a href=\"http:\/\/www.pythonpool.com\/spectrogram-python\/\">Python Spectrogram Implementation in Python from scratch<\/a><\/span><\/li><li><span style=\"text-decoration: underline;\"><a href=\"http:\/\/www.pythonpool.com\/numpy-sin\/\">Numpy Sin in Python with Illustrated Examples<\/a><\/span><\/li><li><span style=\"text-decoration: underline;\"><a href=\"http:\/\/www.pythonpool.com\/numpy-dot-product\/\">Numpy Dot Product in Python With Examples<\/a><\/span><\/li><li><span style=\"text-decoration: underline;\"><a href=\"http:\/\/www.pythonpool.com\/numpy-ix_\/\">Numpy ix_ Function: Things You Need to Know<\/a><\/span><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-faq-s\"><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQ&#8217;s<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1623059869223\"><strong class=\"schema-faq-question\">rfft() vs fft()<br\/><\/strong> <p class=\"schema-faq-answer\">The key difference between rfft() and fft() is the speeds at which both work. Using rfft() is faster than using fft() because rfft() does not calculate the negative half of the frequency <a href=\"http:\/\/www.pythonpool.com\/spectrogram-python\/\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"text-decoration: underline;\">spectrum<\/span><\/a>. <\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1623082682276\"><strong class=\"schema-faq-question\">scipy.ifft() vs numpy.ifft()<br\/><\/strong> <p class=\"schema-faq-answer\">As the name suggests, the scipy.ifft() function is accessed through the scipy library and the numpy.ifft() function is accessed through the numpy library. The difference is that the scipy.ifft() contains more features than the numpy.ifft() function, and because of that, it is preferred compared to the numpy library. <\/p> <\/div> <\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p>That is all, folks! If you have anything to share, we would love to hear you in the comments.<\/p>\n\n\n\n<p><em>Until then, Keep Learning!<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Numpy, which is short for Numerical Python, is a library that helps work with multi-dimensional arrays and matrices in python. Using numpy, the arrays in &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"Discovering The Numpy ifft Function in Python\" class=\"read-more button\" href=\"https:\/\/www.pythonpool.com\/numpy-ifft\/#more-13223\" aria-label=\"More on Discovering The Numpy ifft Function in Python\">Read more<\/a><\/p>\n","protected":false},"author":20,"featured_media":13283,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[1495],"tags":[4182,4177,4181,4178,4180,4179],"class_list":["post-13223","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-numpy","tag-ifft-numpy","tag-numpy-fft-and-ifft-example","tag-numpy-ifft","tag-numpy-ifft-is-slow","tag-numpy-ifft-of-real-valued-function","tag-numpy-ifft-shifted","infinite-scroll-item"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v20.1 (Yoast SEO v25.0) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Discovering The Numpy ifft Function in Python - Python Pool<\/title>\n<meta name=\"description\" content=\"The Numpy ifft is a function in python&#039;s numpy library which is used for obtaining the one dimensional inverse discrete Fourier Transform.\" \/>\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.pythonpool.com\/numpy-ifft\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Discovering The Numpy ifft Function in Python\" \/>\n<meta property=\"og:description\" content=\"Numpy, which is short for Numerical Python, is a library that helps work with multi-dimensional arrays and matrices in python. 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