Question

What is the ROC of z-transform of finite duration anti-causal sequence?

(a) z=0

(b) z=∞

(c) Entire z-plane, except at z=0

(d) Entire z-plane, except at z=∞

The question was asked by my college professor while I was bunking the class.

My enquiry is from Z Transform in chapter Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Right choice is (d) Entire z-plane, except at z=∞

Explanation: Let us an example of anti causal sequence whose z-transform will be in the form X(z)=1+z+z^2 which has a finite value at all values of ‘z’ except at z=∞. So, ROC of an anti-causal sequence is entire z-plane except at z=∞.