Question

Which of the following is introduced in the frequency sampling realization of the FIR filter?

(a) Poles are more in number on unit circle

(b) Zeros are more in number on the unit circle

(c) Poles and zeros at equally spaced points on the unit circle

(d) None of the mentioned

The question was posed to me in a national level competition.

This intriguing question originated from Design of Linear Phase FIR Filters by Frequency Sampling Method in chapter Digital Filters Design of Digital Signal Processing

Answer 1

The correct choice is (c) Poles and zeros at equally spaced points on the unit circle

To elaborate: There is a potential problem for frequency sampling realization of the FIR linear phase filter. The frequency sampling realization of the FIR filter introduces poles and zeros at equally spaced points on the unit circle.