1.

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»

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→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}\)



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