(a) Design a digital Chebyshev filter for the given specifications using bilinear transformation (Use $\mathrm{T}=1 \mathrm{sec}$ ) $$ \begin{aligned} & 0.8 \leq\left[H\left(e^{j \omega}\right) \leq 1\right] \quad 0 \leq \omega \leq 2 \pi \\ & {\left[H\left(e^{j \omega}\right)\right] \leq 0.2 \quad 0.6 \pi \leq \omega \leq \pi} \end{aligned} $$
Explanation
The bilinear transformation is used to convert the analog filter transfer function to a digital filter transfer function. It maps the s-plane to the z-plane and is given by $s = \frac{2}{T} \frac{1 - z^{-1}}{1 + z^{-1}}$. The analog Chebyshev filter transfer function is used as the starting point and the bilinear transformation is applied to obtain the digital filter transfer function.
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