Given the specifications $\alpha_p=3 \mathrm{~dB} ; \alpha_s=16 \mathrm{~dB} ; f_p=1 \mathrm{KH}_2$ and $f_s=2 \mathrm{KHz}$. Determine the order of the filter using the Chebyshev approximation. Find $H(s)$.

Solution:

From the given data we can find,

$ \begin{aligned} & \Omega_p=2 \pi \times 1000 \mathrm{~Hz}=2000 \pi \mathrm{rad} / \mathrm{sec} \\ & \Omega_s=2 \pi \times 2000 \mathrm{~Hz}=4000 \pi \mathrm{rad} / \mathrm{sec} \end{aligned} $

Step: 1

$ \begin{aligned} N \geq \frac{\cosh ^{-1} \sqrt{\frac{10^{0.1 \alpha_s}-1}{10^{0.1 \alpha_p}-1}}}{\cosh ^{-1} \frac{\Omega_s}{\Omega_p}} & =\cosh ^{-1} \frac{\sqrt{\frac{10^{1.6}-1}{10^{0.3}-1}}}{\cosh …