Question

When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero.

(a) True

(b) False

This question was addressed to me in unit test.

My enquiry is from Structures for FIR Systems in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct choice is (a) True

To explain I would say: When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero. Consequently, the corresponding resonant filters can be eliminated and only the filters with nonzero gains need be retained.