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}

Linear convolution

Graphical Linear convolution
i m writing in msg language. Its true muje convolution smjne me bhut problem ayi. And even didn't get it for 3 sem . 

lets start. Take two signals x(n) and h(n). We can vertically fold any of the two signals. Consider h(n).  But notice we have to fold by k not n 

therefore we take a dummy variable k. This i shown in the picture below. Now we can fold. Or take the mirror image of h(k). This also i had shown.

Now we multiply x(k) with h(-k) point to point multiplication.

now shift h(-k) by 1 rightwards. This would be h(1-k). Now again multiply h(1-k) by x(k). The result would be y(1). Similarly do with h(2-k) , h(3-k) and so on to give y(2), y(3).

so we obtain y(0), y(1),..………

and now y(n)={y(0), y(1),……………}

i m attaching a video becoz i didn't get folding and shifting easily.so that is my visualization