Question

If A=\(\frac{-Ω_1^2+Ω_u Ω_l}{Ω_1 (Ω_u-Ω_l)}\) and B=\(\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}\), then which of the following is the backward design equation for a low pass-to-band pass transformation?

(a) ΩS=|B|

(b) ΩS=|A|

(c) ΩS=Max{|A|,|B|}

(d) ΩS=Min{|A|,|B|}

I have been asked this question in quiz.

I'm obligated to ask this question of Frequency Transformations in the Analog Domain topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (d) ΩS=Min{|A|,|B|}

Explanation: If Ωu and Ωl are the upper and lower cutoff  pass band frequencies of the desired band pass filter and Ω1 and Ω2 are the lower and upper cutoff  stop band frequencies of the desired band pass filter, then the backward design equation is

ΩS=Min{|A|,|B|}

where, A=\(\frac{-Ω_1^2+Ω_u Ω_l}{Ω_1 (Ω_u-Ω_l)}\) and B=\(\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}\).