Question

H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable:

(a) Poles must be inside the unit circle and zeros must be outside the unit circle

(b) Poles and zeroes must be inside the unit circle

(c) Poles and zeroes must be outside the unit circle

(d) Poles must be outside the unit circle and zeros must be inside the unit circle

The question was posed to me in exam.

The doubt is from The Z-Transform in chapter Digital Control Systems of Control Systems

Answer 1

Correct option is (b) Poles and zeroes must be inside the unit circle

The best I can explain: For H(z) to be stable the poles must be inside the unit circle and for the inverse of H(z) to be stable the poles of it must be inside the unit circle.