a) Show that if the high-pass filter illustrated in Fig. 15.4 is scaled in both magnitude...

a) Show that if the high-pass filter illustrated in Fig. 15.4 is scaled in both magnitude and frequency, the transfer function is the same as Eq. 15.4 with s replaced by s/kf, where kf is the frequency scale factor.

b) In the prototype version of the high-pass filter circuit in Fig. 15.4, ωc = 1 rad/s, R1 = 1Ω, C = 1F, and R2= K ohms. What is the transfer function of the prototype circuit?

c) Using the result in (a), derive the transfer function of the scaled filter.