Question

What is the associative property of discrete time convolution?

(a) [x1(n) * x2(n)]*h(n) = x1(n)* [x2(n)*h(n)]

(b) [x1(n) * x2(n)]+h(n) = x1(n) + [x2(n)*h(n)]

(c) [x1(n) + x2(n)]*h(n) = x1(n)* [x2(n)+h(n)]

(d) [x1(n) * x2(n)]h(n) = x1(n) [x2(n)*h(n)]

The question was asked in an online interview.

I need to ask this question from Discrete Time Convolution topic in section Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

Correct answer is (a) [x1(n) * x2(n)]*h(n) = x1(n)* [x2(n)*h(n)]

For explanation: [x1(n)* x2(n)]*h(n)= x1(n)* [x2(n)*h(n)], x1(n) and x2(n) are inputs and h(n) is the impulse response.

This can be proved by considering two x1(n)* x2(n) as one output and then using the commutative property proof.