Question

What is the ROC of the z-transform of the signal x(n)= a^nu(n)+b^nu(-n-1)?

(a) |a|<|z|<|b|

(b) |a|>|z|>|b|

(c) |a|>|z|<|b|

(d) |a|<|z|>|b|

I have been asked this question in exam.

Origin of the question is Z Transform topic in portion Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

The correct answer is (a) |a|<|z|<|b|

To explain I would say: We know that,

ROC of z-transform of a^nu(n) is |z|>|a|.

ROC of z-transform of b^nu(-n-1) is |z|<|b|.

By combining both the ROC’s we get the ROC of z-transform of the signal x(n) as |a|<|z|<|b|.