Question

Which of the following is a low pass-to-band stop transformation?

(a) s→\(\frac{s(Ω_u-Ω_l)}{s^2+Ω_u Ω_l}\)

(b) s→\(\frac{s(Ω_u+Ω_l)}{s^2+Ω_u Ω_l}\)

(c) s→\(\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}\)

(d) none of the mentioned

This question was posed to me by my college professor while I was bunking the class.

This intriguing question comes from Frequency Transformations topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (c) s→\(\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}\)

Best explanation: If Ωu and Ωl are the upper and lower cutoff  pass band frequencies of the desired band stop filter, then the transformation to be performed on the normalized low pass filter is

s→\(\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}\)