Question

Which is the commutative property of the LTI System in case of discrete time system?

(a) x[n]+h[n]=h[n]+x[n]

(b) x[n]+h[n]=h[n]*x[n]

(c) x[n]*h[n]=h[n]*x[n]

(d) x[t]*h[t]=h[n]*x[n]

I had been asked this question in an online quiz.

Origin of the question is Properties of LTI Systems in division Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

Right option is (c) x[n]*h[n]=h[n]*x[n]

Easiest explanation: We represent commutative property as: x[t]*h[t]=h[t]*x[t] because it proves that convolution of two signals in either order will be same, with x[n] being the input and h[n] being the impulse response.