Question

Find the function whose Z – Transform is \(\frac{1}{z} \).

(a) δ(n)

(b) δ(n+1)

(c) U(n)

(d) U(n+1)

I have been asked this question in semester exam.

Query is from Linear Difference Equations and Z topic in portion Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

Right answer is (b) δ(n+1)

Explanation: δ(n) exists only at n=0 and δ(n+1) exists only at n=1. Therefore while substituting this function, the Z – Transform at every other place becomes zero except at n=1. Therefore the Z-Transform of δ(n+1) is  \(\frac{1}{z}. \)