Procedure of circular convolution

Circular Convolution

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solving circular convolution is just like solving graphical linear convolution.

three easy steps:
1. Fold
2. Shift 
3. Multiply 
And get the answers

Let the two sequences be x1(n)={1, 1, 2, 2}
x2(n)={1, 2, 3, 4}

for x(-n) enter the elements in counter clockwise direction. Multiply it to x2(n). Don't change x2(n). The result u will get after element by element multiplication and adding all the elements of result will be x3(0). You can check it by formula.

Then rotate the ring by 1 unit in clockwise direction. It will be x1(1-n). Multiply x1(1-n) by x2(n). Remember x2(n) will not change. The result after multiplication and adding all the elements of result is x3(2).

same will happen with x1(2-n) and x1(3-n)

Therefore the result is

x3(n)={15, 17, 15, 13}