Question

What is the equation for the frequency ωk in the frequency response of an FIR filter?

(a) \(\frac{π}{M}\)(k+α)

(b) \(\frac{4π}{M}\)(k+α)

(c) \(\frac{8π}{M}\)(k+α)

(d) \(\frac{2π}{M}\)(k+α)

I have been asked this question in my homework.

I'd like to ask this question from Design of Linear Phase FIR Filters by Frequency Sampling Method topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right choice is (d) \(\frac{2π}{M}\)(k+α)

The best explanation: In the frequency sampling method for FIR filter design, we specify the desired frequency response Hd(ω) at a set of equally spaced frequencies, namely

ωk=\(\frac{2π}{M}(k+α)\)

where k=0,1,2…M-1/2 and α=0 0r 1/2.