Question

Which of the following is the backward design equation for a low pass-to-low pass transformation?

(a) ΩS=\(\frac{Ω_S}{Ω_u}\)

(b) ΩS=\(\frac{Ω_u}{Ω’_S}\)

(c) Ω’S=\(\frac{Ω_S}{Ω_u}\)

(d) ΩS=\(\frac{Ω’_S}{Ω_u}\)

The question was posed to me in an interview.

The origin of the question is Frequency Transformations in the Analog Domain topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (d) ΩS=\(\frac{Ω’_S}{Ω_u}\)

For explanation: If Ωu is the desired pass band edge frequency of new low pass filter, then the transfer function of this new low pass filter is obtained by using the transformation s → s / Ωu. If ΩS and Ω’S are the stop band frequencies of prototype and transformed filters respectively, then the backward design equation is given by

ΩS=\(\frac{Ω’_S}{Ω_u}\) .