Determine the filter H(s) that results by applying the following transformations on a lowpass prototype filter given as Hp(s) =  Plot the corresponding magnitude response. In each case, designate ω 0...

Determine the filter H(s) that results by applying the following transformations on a lowpass prototype filter given as Hp(s) =
 Plot the corresponding magnitude response. In each case, designate ω₀
as the prototype’s 1-dB cutoff frequency.

(a) A lowpass-to-lowpass transformation ω₁
= 3 rad/s.

(b) A lowpass-to-highpass transformation ω₁
= 5 rad/s.

(c) A lowpass-to-bandpass transformation with ω₁
= 3 rad/s and ω₂
= 4 rad/s.

(d) A lowpass-to-bandstop transformation with ω₁
= 4 rad/s and ω₂
= 5 rad/s.