Question

The poles of a digital filter with linear phase response can lie

(a) Only at z =0

(b) Only on the unit circle

(c) Only inside the unit circle but not at z =0

(d) On the left side of Real (z) =0 line

This question was posed to me in final exam.

This intriguing question comes from Difference Equations topic in chapter Digital Control Systems of Control Systems

Answer 1

Right choice is (b) Only on the unit circle

The best I can explain: For stable systems the poles in z plane must lie inside or on the unit circle and Minimum number of delay elements = (Maximum power of z)-(minimum power of z).