1.

What is the magnitude response |W(ω)| of a rectangular window function?(a) \(\frac{|sin(ωM/2)|}{|sin(ω/2)|}\)(b) \(\frac{|sin(ω/2)|}{|sin(ωM/2)|}\)(c) \(\frac{|cos(ωM/2)|}{|sin(ω/2)|}\)(d) None of the mentionedThis question was addressed to me in a national level competition.This question is from Design of Linear Phase FIR Filters Using Windows topic in portion Digital Filters Design of Digital Signal Processing

Answer»

The correct OPTION is (a) \(\frac{|sin(ωM/2)|}{|sin(ω/2)|}\)

The explanation: We know that for a rectangular window

W(ω)=\(\sum_{n=0}^{M-1} w(n) e^{-jωn}=e^{-jω(M-1)/2} \frac{sin⁡(\frac{ωM}{2})}{sin⁡(\frac{ω}{2})}\)

THUS the window FUNCTION has a magnitude response

|W(ω)|=\(\frac{|sin(ωM/2)|}{|sin(ω/2)|}\)



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