Question

What is the ROC of the signal x(n)=δ(n-k), k>0?

(a) z=0

(b) z=∞

(c) Entire z-plane, except at z=0

(d) Entire z-plane, except at z=∞

I had been asked this question by my college professor while I was bunking the class.

I'd like to ask this question from Z Transform topic in section Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Correct choice is (c) Entire z-plane, except at z=0

To explain I would say: We know that, the z-transform of a signal x(n) is X(z)=\(\sum_{n=-\infty}^{\infty} x(n)z^{-n}\)

Given x(n)=δ(n-k)=1 at n=k

=> X(z)=z^-k

From the above equation, X(z) is defined at all values of z except at z=0 for k>0.

So ROC is defined as Entire z-plane, except at z=0.