Question

x(n) = a^n u(n) and x(n) = -a^n u(-n-1) have the same X(Z) and ROC.

(a) True

(b) False

I had been asked this question during a job interview.

Question is from The Z-Transform in portion Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Correct answer is (b) False

To explain I would say: a^n u(n) ↔ \(\frac{1}{1-az^{-1}} = \frac{z}{z-a}\); ROC:|z|>|a|

-a^n u(-n-1) ↔ \(\frac{1}{1-az^{-1}} = \frac{z}{z-a}\); ROC:|z|<|a|

Hence, x(n) = a^n u(n) and x(n) = -a^n u(-n-1) have the same X(Z) and differ only in ROC.