Question

x(n)*δ(n-n0)=?

(a) x(n+n0)

(b) x(n-n0)

(c) x(-n-n0)

(d) x(-n+n0)

This question was addressed to me during an interview.

This interesting question is from Analysis of Discrete time LTI Systems in division Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Right choice is (b) x(n-n0)

Easy explanation: x(n)*δ(n-n0)=\(\sum_{k=-{\infty}}^{\infty} x(k)\delta(n-k-n_0)\)

=x(k)|k=n-n0

=x(n-n0)