Question

Which of the following series has an ROC as mentioned below?

(a) α^-nu(n)

(b) α^nu(n)

(c) α^-nu(-n)

(d) α^nu(n)

This question was posed to me in an online interview.

I want to ask this question from Z Transform topic in division Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Right choice is (b) α^nu(n)

Explanation: Let x(n)= α^nu(n)

The z-transform of the signal x(n) is given as

X(z)=X(z)=\(\sum_{n=0}^{\infty} \alpha^n z^{-n} = \sum_{n=0}^{\infty}\alpha z^{-1}n\)

=> X(z)=\(\frac{1}{1-\alpha z^{-1}}\) and ROC is |z|>α which is as given in the question.