Question

If a system has N different poles, then the system can have ______________

(a) N ROC’s

(b) (N-1) ROC’s

(c) (N+1) ROC’s

(d) 2N ROC’s

The question was posed to me during a job interview.

Question is from Properties of ROC in section Laplace Transform and System Design of Signals and Systems

Answer 1

Right answer is (c) (N+1) ROC’s

The explanation: Let us consider 2 poles. For 2 poles, we will have 3 ROC conditions. Hence, if a system has N poles then the system will have (N+1) ROC’s.