Question

What is the frequency response of a system with input h(n) and window length of M?

(a) \(\sum_{n=0}^{M-1} h(n)e^{jωn}\)

(b) \(\sum_{n=0}^{M} h(n)e^{jωn}\)

(c) \(\sum_{n=0}^M h(n)e^{-jωn}\)

(d) \(\sum_{n=0}^{M-1} h(n)e^{-jωn}\)

I have been asked this question in homework.

The origin of the question is Design of Linear Phase FIR Filters by Frequency Sampling Method topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

The correct choice is (d) \(\sum_{n=0}^{M-1} h(n)e^{-jωn}\)

The explanation is: The desired output of an FIR filter with an input h(n) and using a window of length M is given as

H(ω)=\(\sum_{n=0}^{M-1} h(n)e^{-jωn}\)