Question

If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a^-1z)?

(a) |a|r1<|z|<|a|r2

(b) |a|r1>|z|>|a|r2

(c) |a|r1<|z|>|a|r2

(d) |a|r1>|z|<|a|r2

This question was posed to me by my school principal while I was bunking the class.

Enquiry is from Properties of Z Transform in section Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

The correct choice is (a) |a|r1<|z|<|a|r2

To explain I would say: Given ROC of X(z) is r1<|z|<r2

Then ROC of X(a^-1z) will be given by r1<|a^-1z |<r2=|a|r1<|z|<|a|r2