Question

For a stable system which of the following is correct?

(a) |z| < 1

(b) |z| = 1

(c) |z| > 1

(d) |z| ≠ 1

The question was asked in a job interview.

My doubt stems from Properties of ROC topic in section Laplace Transform and System Design of Signals and Systems

Answer 1

The correct choice is (a) |z| < 1

Explanation: We know that, for the system to be stable, the ROC should include the unit circle.

|z| = 1, represents the unit circle but does not include it.

|z| > 1, represents the region outside the unit circle. In other words, it excludes the region of the unit circle.

|z| ≠ 1 does not represent a unit circle.