Question

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

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

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

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

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

This question was addressed to me in a job interview.

Query is from Frequency Transformations topic in section Digital Filters Design of Digital Signal Processing

Answer 1

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

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

s→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}\)