Question

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

(a) cos(ω/2)

(b) sin(ω/2)

(c) 1

(d) sinω

The question was asked at a job interview.

This interesting question is from Design of Optimum Equi Ripple Linear Phase FIR Filters topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Correct answer is (c) 1

For explanation: If the filter has a symmetric unit sample response, then we know that

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

and for M odd in this case, Q(ω)=1.