Question

If the filter has anti-symmetric unit sample response with M even, then what is the value of Q(ω)?

(a) cos(ω/2)

(b) sin(ω/2)

(c) 1

(d) sinω

The question was posed to me in an online interview.

Question is taken from Design of Optimum Equi Ripple Linear Phase FIR Filters topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (b) sin(ω/2)

To explain I would say: If the filter has a anti-symmetric unit sample response, then we know that

h(n)= -h(M-1-n)

and for M even in this case, Q(ω)=sin(ω/2).