Question

If h(n) is the impulse response of an LTI system T and h1(n) is the impulse response of the inverse system T^-1, then which of the following is true?

(a) [h(n)*h1(n)].x(n)=x(n)

(b) [h(n).h1(n)].x(n)=x(n)

(c) [h(n)*h1(n)]*x(n)=x(n)

(d) [h(n).h1(n)]*x(n)=x(n)

This question was posed to me in an international level competition.

My question is from Inverse Systems and Deconvolution topic in division Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

Correct answer is (c) [h(n)*h1(n)]*x(n)=x(n)

For explanation I would say: If h(n) is the impulse response of an LTI system T and h1(n) is the impulse response of the inverse system T^-1, then we know that h(n)*h1(n)=δ(n)=>[h(n)*h1(n)]*x(n)=x(n).