Question

A single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.

(a) True

(b) False

I had been asked this question by my school teacher while I was bunking the class.

My question is based upon State-Space System Analysis and Structures in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

The correct option is (a) True

The best explanation: If h(n) is the impulse response of the single input-single output system, and h1(n) is the impulse response of the transposed system, then we know that h(n)=h^1>(n). Thus, a single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.