The warping effect of the bilinear transformation also affects the phase of the transformed filter. Consider a filter with transfer function G(s) = e^−5s.

(a) Find the transformed discrete frequencies ω(rad) correspond-ing to 0 ≤ Ω ­≤ 20 (rad/sec) using a bilinear transformation with K = 1. Plot ­versus ω

(b) Discretize the continuous frequencies 0 ≤ ­Ω ≤ 20(rad/sec) to compute values of G(jΩ) and use MATLAB functions to plot the phase of G(jΩ).

(c) Find the function

H(e^jω) = G(jΩ)|_{Ω = tan(ω/2)},

and plot its unwrapped phase using MATLAB for the discrete frequencies corresponding to the analog frequencies to 0 ≤ Ω ­≤ 20(rad/sec). Compare the phases of G(jΩ) and of H(e^jω).