Question

What is the number of filter coefficients that specify the frequency response for h(n) anti-symmetric?

(a) (M-1)/2 when M is even and M/2 when M is odd

(b) (M-1)/2 when M is odd and M/2 when M is even

(c) (M+1)/2 when M is even and M/2 when M is odd

(d) (M+1)/2 when M is odd and M/2 when M is even

The question was asked in quiz.

My question comes from Design of FIR Filters in portion Digital Filters Design of Digital Signal Processing

Answer 1

Correct answer is (b) (M-1)/2 when M is odd and M/2 when M is even

The explanation is: We know that, for a anti-symmetric h(n) h(M-1/2)=0 and thus the number of filter coefficients that specify the frequency response is (M-1)/2 when M is odd and M/2 when M is even.