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Which property of an LTI system does the following equation prove h[n]*h1[n]=∂[n]?

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in Signals and Systems by (1.2m points)
Which property of an LTI system does the following equation prove h[n]*h1[n]=∂[n]?

(a) Invertibility

(b) Stability

(c) Associativilty

(d) Commutative

I had been asked this question during an interview for a job.

My question is taken from Properties of LTI Systems topic in division Time-Domain Analysis of CT Systems of Signals and Systems

1 Answer

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by (42.1k points)
Right choice is (a) Invertibility

To explain I would say: This equation proves that the condition that h1[n] must satisfy to be the impulse response of the inverse system in case of discrete time LTI system. Thus this gives the necessary condition for the invertibility property of an LTI system.

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