Question

Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z-domain, their region of convergences are _______________

(a) The same

(b) Reciprocal of each other

(c) Negative of each other

(d) Complementary

This question was addressed to me in quiz.

I'd like to ask this question from Concept of Convolution topic in section Signal Transmission Through Linear Systems of Signals and Systems

Answer 1

Correct choice is (b) Reciprocal of each other

For explanation: x1(n) has z-transform X1(z)

The ROC = Rx (say)

 Again, x2(n) = x1(-n) has z-transform X1(1/z)

The ROC = 1/Rx

Hence they are reciprocals.