Circular Convolution

Logic:

If x₁(n) and x₁(k) are N-point DFT pairs and x₂(n) and x₂(k) are another N-point DFT pairs then the circular convolution is defined as

x₃(n)=x₁(n) (convolve) x₂(n)

x3(n)= summation from n=0 to N-1 of x1(m). x2(n-m); n=0,1,2,......,m-1;

Since there is no command exists in the MATLAB to find circular convolution directly. We use indirect method. We know from the property of DFT that the circular convolution of two finite sequences is equal to the IDFT of the product of individual DFTs.

i.e, x1(n) (circular convolution)x2(n)=IDFT[DFF(x,(n)).DFT(x2,(n))]

Program

clear all; % close all

x1=input ('Enter the first sequence x1(n)');

x2=input ('Enter the second sequence x2(n)');

N=input ('Enter the length of the DFT');

x1k=fft(x1,N); %find the DFT of the first sequence

x2k=fft(x2,N); %find the DFT of the second sequence

x3k=x1k*x2k ; %multiply them

x3=ifft(x3k); % Find the IDFT of the product

disp(x3);