Question

Which of the following is the backward design equation for a low pass-to-high 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=\(\frac{Ω’_S}{Ω_u}\)

I got this question during a job interview.

My question comes from Frequency Transformations in the Analog Domain topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Correct option is (b) ΩS=\(\frac{Ω_u}{Ω’_S}\)

To elaborate: If Ωu is the desired pass band edge frequency of new high pass filter, then the transfer function of this new high pass filter is obtained by using the transformation s→Ωu/s. 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=\(\frac{Ω_u}{Ω’_S}\) .