Question

The  z-transform of δ[n-k]>0 is __________

(a) Z^k, Z>0

(b) Z^-k, Z>0

(c) Z^k, Z≠0

(d) Z^-k, Z≠0

The question was posed to me by my college director while I was bunking the class.

Question is taken from Properties of Z-Transforms in division Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Correct option is (d) Z^-k, Z≠0

To explain: Performing z-transform on δ[n-k], we get,

X (z) = \(∑_{n=0}^∞ x[n]z^{-n}\)

= Z^-k, Z≠0.