{"id":4821,"date":"2021-08-03T10:08:08","date_gmt":"2021-08-03T04:38:08","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=4821"},"modified":"2025-11-29T21:19:47","modified_gmt":"2025-11-29T15:49:47","slug":"what-is-the-convolution-theorem","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-the-convolution-theorem\/","title":{"rendered":"What is the Convolution Theorem?"},"content":{"rendered":"\n<p>The convolution theorem states that f1(t) and f2(t) are two time functions which are zero for t&lt;0 and if Laplace transform are F1(s) and F2(s)then the transform of convolution of f1(t) and f2(t) is the product of individual transforms F1(s) and F2(s).<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"331\" height=\"85\" src=\"https:\/\/lh3.googleusercontent.com\/gxzhXC_IzCN5x_VB_QRYNPHxz6rK1zGFgFQiYMvp5f8gCrlPF_G7GOVqAcJuFt-qloQf15xrru7F0ddb4c8lNxbSDlp1_h-4WPcxgyw2wGZAvBvjQp44KwYZgEB7oSM3yeeAyMMu\"><\/p>\n\n\n\n<p>The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Laplace_transform\" target=\"_blank\" rel=\"noreferrer noopener\">Laplace transform<\/a> is<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"349\" height=\"37\" src=\"https:\/\/lh5.googleusercontent.com\/ChUvOQ07Pw66pYWSH3IzGZqNm4-E2JFsA9HN_mAiwZr-UHK-jSt0dVhqRcuExRJES-RY8MuGjJdKeilsAPx3iQKJYWnOv45VZueMMsdoDkokw8Fcq8pc54Y8yOypIZDYYrGC1iEt\"><\/p>\n\n\n\n<p>The Laplace Transformation transforms convolution into multiplication.<\/p>\n\n\n\n<p>The graphical presentation of the convolution integral helps in the understanding of every step in the convolution procedure. According to the definition integral, the convolution procedure involves the following steps:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The interval in which convolution is equal to zero is identified by applying the convolution duration property.<\/li>\n\n\n\n<li>Firstly, fold one of the signals which is simpler amongst two along the vertical axis. Then this signal represents one signal in the time scale.<\/li>\n\n\n\n<li>Now shift the signal from left to right and vary parameters from -\u221e to +\u221e. Then check for the overlapping area in the two signals.\u00a0<\/li>\n\n\n\n<li>Then find the integral product of those signals in the respective given intervals.<\/li>\n<\/ul>\n\n\n\n<p>In a network analysis we apply convolution theorem. With the help of Laplace transform we proceed as convolution in the time domain is multiplication in S domain. This makes the calculation a bit easier.<\/p>\n\n\n\n<p><strong>Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-zigbee\/\" target=\"_blank\" rel=\"noreferrer noopener\">What is ZigBee?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.goseeko.com\/blog\/what-are-encoders-and-decoders\/\" target=\"_blank\" rel=\"noreferrer noopener\">Encoders and Decoders<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-uart\/\" target=\"_blank\" rel=\"noreferrer noopener\">Working of UART<\/a> <a href=\"https:\/\/dpa.stamforduniversity.edu.bd\/\">https:\/\/dpa.stamforduniversity.edu.bd\/<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-fft\/\" target=\"_blank\" rel=\"noreferrer noopener\">Classification of FFT<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-fourier-transform\/\" target=\"_blank\" rel=\"noreferrer noopener\">Fourier Transform and its properties<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The convolution theorem states that the transform of convolution of f1(t) and f2(t) is the product of individual transforms F1(s) and F2(s).<\/p>\n","protected":false},"author":28,"featured_media":4830,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[37],"tags":[],"class_list":["post-4821","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electronics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is the Convolution Theorem? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"The convolution theorem states that the transform of convolution of f1(t) and f2(t) is the product of individual transforms F1(s) and F2(s).\" \/>\n<meta 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