Question

Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are

(a) The same

(b) Reciprocal of each other

(c) Negative of each other

(d) Complements of each other

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

The question is from The Z-Transform topic in section Digital Control Systems of Control Systems

Answer 1

The correct option is (b) Reciprocal of each other

To explain: x1(n) is the signal in the discrete domain and X1(z) is the signal in the z domain, RoC Rx

       z Reciprocals x2(n) = x1(-n) X1(1/z), RoC 1/ R