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25-09-2021 Signals & Systems

Q. 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)]

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Dapzoi Verified
Commented on 2021-09-25 13:03:39 (IST)
Answer: A

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.