Consider a filter with Butterworth digital lowpass transfer function H(z) obtained by applying the bilinear transform s=c z+1/z−1 to a standard analog Butterowrth lowpass filter of order N.
(a) If the magnitude response of the filter is ∣H(e jω) ∣∣ = 1/(1+9(tan 2)^4)^2for ∣ω∣≤π, what is the filter order N ? What is the value of the parameter c ?
(b) Give a rough plot of the filter magnitude response IH(ejω) ∣∣ for ∣ω∣≤π, specifying the values at ω=0, π/3, 2π/3, π.
