Design a Chebyshev filter with a maximum passband attenuation of $2.5 \mathrm{~dB}$; at $\Omega_p=20 \mathrm{rad} / \mathrm{sec}$ and the stopband attenuation of $30 \mathrm{~dB}$ at $\Omega_s=50 \mathrm{rad} / \mathrm{sec}$.

Solution:

Given,

$ \begin{array}{lll} \Omega_p=20 & \mathrm{rad} / \mathrm{sec} ; & \alpha_p=2.5 \mathrm{~dB} \\ \Omega_s=50 & \mathrm{rad} / \mathrm{sec} ; & \alpha_s=30 \mathrm{~dB} \end{array} $

We know about,

$ \begin{aligned} N & =\frac{\cosh ^{-1} \lambda / \varepsilon}{\cosh ^{-1} 1 / k} \\\\ \lambda & =\sqrt{10^{0.1 \alpha_s}-1}=31.607 \\\\ \varepsilon & =\sqrt{10^{0.1 …