{"id":5150,"date":"2021-08-31T11:24:27","date_gmt":"2021-08-31T05:54:27","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=5150"},"modified":"2026-02-17T01:29:07","modified_gmt":"2026-02-16T19:59:07","slug":"what-is-circular-convolution","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-circular-convolution\/","title":{"rendered":"What is Circular Convolution?"},"content":{"rendered":"\n<p>The Circular Convolution can be performed using two methods: concentric circle method and matrix multiplication method. Assuming x<sub>1<\/sub>(n) and x<sub>2<\/sub>(n) as two finite sequences of length N. <\/p>\n\n\n\n<p>Now let us consider X<sub>1<\/sub>(K) and X<sub>2<\/sub>(K) as the inverse DFTs of sequences x<sub>1<\/sub>(n) and x<sub>2<\/sub>(n). The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Discrete_Fourier_transform\" target=\"_blank\" rel=\"noreferrer noopener\">DFT <\/a>for the sequences is<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"183\" src=\"https:\/\/lh4.googleusercontent.com\/mVsl4_YLUZgBKK4_TrFUW994PqtcwWbrMoyxXIeQooDJbe7MW_LPXBH1GQzzhOHpbMWqMtjAf6jTu00Q86ARouqUH5wI7_jRrO6zxlyygjrw11Ng_YGKJ022GVvYYaW7Z9uI9lVa=s0\"><\/p>\n\n\n\n<p>Let&nbsp; x<sub>3<\/sub>(n) be one more sequence with DFT X<sub>3<\/sub>(K). The relation between the three finite duration sequences is given as<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"27\" src=\"https:\/\/lh6.googleusercontent.com\/fMtDHhS74HCETTcqC_gMSNRiFW8ZIJNkHiGenLn34QaSVl32rSvcX89yeYSJIs1iPCi6_Fc4fzVhBbeuAoGOrqc80St-NfGt1byi9qmXEE1j16VfUuSh96vSE6N016DiRy2LD1cW=s0\"><\/p>\n\n\n\n<p>After taking inverse discrete <a href=\"https:\/\/www.goseeko.com\/blog\/what-is-fourier-transform\/\" target=\"_blank\" rel=\"noreferrer noopener\">Fourier transform<\/a> of above sequences we have<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"243\" height=\"98\" src=\"https:\/\/lh3.googleusercontent.com\/M4OZLiZ2SA_ZCtcOHvZqYRaO5HgEMIKiVYemCO16CkX8IzKv1vM17BlpezkIbG__XYqabVRBUxHxcuONpGAT9aaVPR0ctW8vcamb_A1h7HoEpxvALeLynTH8p8twUCuRWIRQSxYN=s0\"><\/p>\n\n\n\n<p>The above equation can also be written as<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"497\" height=\"74\" src=\"https:\/\/lh5.googleusercontent.com\/wqs78LqkofO2wH5ZpGX71JvIndSTAvpTtBKv2KLbXESY4o2_DNoIQDOjwoRq_K1NG_X4a6DpiIwFbL4NurJ5g_cqLgB3j3YGjad2ob25zNYVzgmKr_QGQQqx4irUM8Nu1cdWxGPE=s0\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Methods of Circular Convolution<\/strong><\/h2>\n\n\n\n<p>The two basic methods normally used for circular convolution are \u2212<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Concentric circle method,<\/li>\n\n\n\n<li>Matrix multiplication method.<\/li>\n<\/ul>\n\n\n\n<p><strong>Concentric Circle Method<\/strong><\/p>\n\n\n\n<p>We firstly assume two finite length sequences x<sub>1<\/sub>(n) and x<sub>2<\/sub>(n). Now using the below steps we can easily circular convolve the two sequences.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Firstly, we take two concentric circles. Then at the circumference of this circle we plot N samples of x<sub>1<\/sub>(n) with equal distance between each point. This plot is then done in an anticlockwise direction.<\/li>\n\n\n\n<li>In the inner circle we plot N samples of x<sub>2<\/sub>(n) in clockwise direction. Then the starting point is kept the same as in x<sub>1<\/sub>(n).<\/li>\n\n\n\n<li>Then we multiply the corresponding samples. The result of multiplication is added to obtain the final value.&nbsp;<\/li>\n\n\n\n<li>At last the value of the inner circle is to be rotated in an anticlockwise direction with one sample at a time.<\/li>\n<\/ul>\n\n\n\n<p><strong>Matrix Multiplication Method<\/strong><\/p>\n\n\n\n<p>Here we represent the given sequences x<sub>1<\/sub>(n) and x<sub>2<\/sub>(n) in matrix form.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The NXN matrix is formed by repeating one of the sequences. This is then achieved by making a circular shift of one sample.<\/li>\n\n\n\n<li>Then the Second sequence forms a column matrix.<\/li>\n\n\n\n<li>Finally the result of circular convolution is calculated by multiplying these two matrices.<\/li>\n<\/ul>\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:\/\/jhanpa.lgoms.org\/\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><a href=\"https:\/\/jhanpa.lgoms.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/jhanpa.lgoms.org\/<\/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 Circular Convolution can be performed using two basic methods which are concentric circle method and matrix multiplication method.<\/p>\n","protected":false},"author":28,"featured_media":5183,"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-5150","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 Circular Convolution? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"The Circular Convolution can be performed using two basic methods which are concentric circle 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