Circular Convolution with Zero Padding

In this post you would see how to get the result of Linear Convolution using Circular Convolution method with the help of an example - Circular Convolution with Zero Padding

Circular Convolution with Zero Padding

Example: If x(n) = {1, 2, 3, 1} & h(n) = {1, 1, 1}, find output response y(n) using Circular Convolution with zero padding method.

Solution: Since x(n) = {1, 2, 3, 1} & h(n) = {1, 1, 1}

Therefore, length of x(n), L = 4 

           and length of h(n), M = 3

We know that for Linear Convolution, length of y(n) = L + M - 1

Therefore, in this case, length of y(n) = 4 + 3 - 1 = 6

Now, to get the result of Linear Convolution using Circular Convolution method, we need to write appropriate number of zeros in x(n) and h(n) to make their lengths equal to the length of y(n).

i.e., x(n) = {1, 2, 3, 1, 0, 0} - Here two zeros are written to make length of x(n) equal to 6

   & h(n) = {1, 1, 1, 0, 0, 0} - Here three zeros are written to make length of h(n) equal to 6

Now, perform Circular Convolution on the above two signals.Here matrix multiplication method is used.

Therefore, y(n) = {1, 3, 6, 6, 4, 1}. 

This output would be similar to the output obtained with Linear Convolution method.

Hence we can say that "Circular Convolution with Zero Padding" method is used to get the result of Linear convolution of two signals using Circular Convolution method.

Click here to find VIDEO on Circular Convolution with Zero Padding:

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