1.

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»

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=\(\frac{Ω_u}{Ω’_S}\) .



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