Question

The zeros of the system function of comb filter are located at ______________

(a) Inside unit circle

(b) On unit circle

(c) Outside unit circle

(d) None of the mentioned

I have been asked this question in an international level competition.

I'd like to ask this question from Structures for FIR Systems in division Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

The correct choice is (b) On unit circle

For explanation: The system function of the comb filter is given by the equation

H1(z)=\(\frac{1}{M}(1-z^{-M} e^{j2πα})\)

Its zeros are located at equally spaced points on the unit circle at

zk=e^j2π(k+α)/M k=0,1,2….M-1