00:01
So, let us start with this for that we need to compute the convolution for the given that is y1 of n is equals to x of n convolves to the x of n sorry h of n.
00:17
So, this is what the first part of our question that is a part in that it is given x of n is equals to u of n plus 3 and the second function h of n is equals to u of n minus of 3.
00:37
So, as we need to perform the convolution here.
00:40
So, for that let us apply the formula.
00:44
So, x of k would be equals to u of k plus 3 i am just replacing n by k here simple then obviously h of k would be equals to u of k minus of 3.
00:59
So, i am seeing the above we can write down the h of n minus k as u of n minus k minus of 3.
01:10
So, by using this y of n would be equals to the convolution can be applied and hence it will be summation of minus infinity to infinity x of k times of h of n minus of k.
01:26
So, let us put the values here summation k varying from minus infinity to plus infinity here it would be u of k plus 3 into u of n minus k minus of 3.
01:43
Now, this will be equals to summation of k varying from minus infinity to plus infinity u of k plus 3 u of now this can be replaced by our above function that is n minus k minus of 3 we are just replacing it with this...