The transfer function [H(s)=frac{kappa}{left(s^{2}+1.4256 s+1.23313 ight)(s+0.6265)}] corresponds to a lowpass normalized Chebyshev filter with passband ripple (A_{mathrm{p}}=0.5)

The transfer function

\[H(s)=\frac{\kappa}{\left(s^{2}+1.4256 s+1.23313\right)(s+0.6265)}\]

corresponds to a lowpass normalized Chebyshev filter with passband ripple \(A_{\mathrm{p}}=0.5\) \(\mathrm{dB}\).

(a) Determine \(\kappa\) such that the filter gain at DC is 1 .

(b) Design a highpass digital filter with cutoff frequency \(\omega_{p}=\frac{\pi}{3} \mathrm{rad} / \mathrm{s}\), sampling frequency \(\omega_{\mathrm{s}}=\pi \mathrm{rad} / \mathrm{s}\), and passband ripple of \(0.5 \mathrm{~dB}\) using the bilinear transformation.

(c) Suggest a possible realization for the resulting transfer function.