Question

Find the convolution sum of two sequences x(n)={3,2,1,2} and h(n)={1,2,1,2}

Answer 1

We know that for discrete time system, convolution of two sequence can be given by:

y(n) = x(n) * h(n) = ∑ x[i]h[n-i]

Where * denotes the convolution operator, and

where i ranges from -∞ to +∞

Hence y(n) = [3, 6+2,3+4+1,6+2+2+2,4+1+4,2+2,4]

=>y(n) = [3,8,8,12,9,4,4]

We can also verify the no of samples present in y(n),as

The no of samples in y(n) = x+h-1 = 4+4-1 = 7, which is exactly the no of samples present in the above result.

Answer 2

Answer:Find the convolution sum of two sequences x(n)={2,1,-1,3} and h(n)={1,-1,2}

Step-by-step explanation: