Question

The desired frequency response is specified at a set of equally spaced frequencies defined by the equation?

(a) \(\frac{\pi}{2M}\)(k+α)

(b) \(\frac{\pi}{M}\)(k+α)

(c) \(\frac{2\pi}{M}\)(k+α)

(d) None of the mentioned

I have been asked this question in an interview for internship.

The origin of the question is Structures for FIR Systems in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct option is (c) \(\frac{2\pi}{M}\)(k+α)

Easiest explanation: To derive the frequency sampling structure, we specify the desired frequency response at a set of equally spaced frequencies, namely ωk=\(\frac{2\pi}{M}\)(k+α), k=0,1…(M-1)/2 for M odd

k=0,1….(M/2)-1 for M even

α=0 or 0.5.