Circular Convolution Using Matlab Program (DSP)

What is Circular Convolution?

Circular Convolution

Circular convolution also know as cyclic convolution to two functions which are aperiodic in nature occurs when one of them is convolved in the normal way with a periodic summation of other function.

A similar situation can be observed can be expressed in terms of a periodic summation of both functions, if the infinite integration interval is reduced to just one period. This situation arises in Discrete Time Fourier Transform(DTFT) and is called as periodic convolution.

Let us consider x to be a function with a defined periodic summation, x_T, where:

If h is any other function for which the convolution x_T * h (Multiply) exists, then the convolution x_T ∗ h is periodic and equal to:

where t_o is an arbitrary parameter and h_T is a periodic summation of h.

The second integral is called the periodic convolution of functions x_T and h_T & is normalized by 1/T.

When x_T is expressed as the periodic summation of another function, x, the same operation may also be referred to as a circular convolution of functions h and x.

Linear Convolution Program Using Matlab

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Matlab Code for Circular Convolution

 

 

 Here is the code

Circular Convolution Matlab Code

MATLAB

clc; close all; clear all; x1=input('Enter the first sequence : '); x2=input('Enter the second sequence : '); N1=length(x1); N2=length(x2); N=max(N1,N2);   if(N2>N1) x4=[x1,zeros(1,N-N1)]; x5=x2; elseif(N2==N1)         x4=x1;         x5=x2; else x4=x1; x5=[x2,zeros(1,N-N2)]; end   x3=zeros(1,N); for m=0:N-1 x3(m+1)=0; for n=0:N-1         j=mod(m-n,N);         x3(m+1)=x3(m+1)+x4(n+1).*x5(j+1); end end   subplot(4,1,1) stem(x1); title('First Input Sequence'); xlabel('Samples'); ylabel('Amplitude'); subplot(4,1,2) stem(x2); title('Second Input Sequence'); xlabel('Samples'); ylabel('Amplitude'); subplot(4,1,3) stem(x3); title('Circular Convolution Using Modulo Operator'); xlabel('Samples'); ylabel('Amplitude');   %In built function y=cconv(x1,x2,N); subplot(4,1,4) stem(y); title('Circular Convolution using Inbuilt Function'); xlabel('Samples'); ylabel('Amplitude');

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clc; close all; clear all; x1=input('Enter the first sequence : '); x2=input('Enter the second sequence : '); N1=length(x1); N2=length(x2); N=max(N1,N2);   if(N2>N1) x4=[x1,zeros(1,N-N1)]; x5=x2; elseif(N2==N1)         x4=x1;         x5=x2; else x4=x1; x5=[x2,zeros(1,N-N2)]; end   x3=zeros(1,N); for m=0:N-1 x3(m+1)=0; for n=0:N-1         j=mod(m-n,N);         x3(m+1)=x3(m+1)+x4(n+1).*x5(j+1); end end   subplot(4,1,1) stem(x1); title('First Input Sequence'); xlabel('Samples'); ylabel('Amplitude'); subplot(4,1,2) stem(x2); title('Second Input Sequence'); xlabel('Samples'); ylabel('Amplitude'); subplot(4,1,3) stem(x3); title('Circular Convolution Using Modulo Operator'); xlabel('Samples'); ylabel('Amplitude');   %In built function   y=cconv(x1,x2,N); subplot(4,1,4) stem(y); title('Circular Convolution using Inbuilt Function'); xlabel('Samples'); ylabel('Amplitude');

 

you can directly execute the code in matlab

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 Here is the Output