Question

Find the convolution of x1[n] = {1, 2, 3, 4} and x2[n] = {2, 1, 2, 1}.

(a) Y[n] = {14, 10, 14, 10}

(b) Y [n] = {14, 16, 14, 16}

(c) Y [n] = {14, 16,-14,-16}

(d) Y [n] = {14,-16,-14, 16}

This question was addressed to me in semester exam.

I would like to ask this question from Convolution : Impulse Response Representation for LTI Systems in division Time Domain Representation for LTI Systems of Signals and Systems

Answer 1

The correct answer is (b) Y [n] = {14, 16, 14, 16}

Best explanation: By using convolution sum we get x1[n]*x2[n] = {14, 16, 14, 16}. This can be verified using tabular method of convolution.