second, to satisfy the following specifications.

$0,707 \leq\left|H\left(e^{jw}) | \leq 1.0 : 0 \leq w \leq 0.2 \pi\right.\right.$

$\mathrm{H}\left(\mathrm{e}^{\mathrm{jw}}) | \leq 0.08 \quad : 0.4 \pi \leq \mathrm{w} \leq \pi\right.$

Given:

Desired Pass-band edge $\omega_{p}=0.2 \pi$

Desired Stop-band edge $\omega_{s}=0.4 \pi$

Gain at Pass-band edge $A_{p}=0.707$

Gain at Stop-band edge $A_{s}=0.08$

$\mathrm{T}=1 \mathrm{sec}$

Step 1: Pre-warp Analog Frequency:

By Bilinear Transformation (BLT)

$\Omega=\frac{2}{T} \tan \frac{\omega}{2}$

$\therefore \Omega_{p}=\frac{2}{1} \tan \frac{\omega_{p}}{2}=2 \tan \frac{0.2 \pi}{2}=0.6498$

$\Omega_{s}=\frac{2}{1} \tan \frac{\omega_{s}}{2}=2 \tan \frac{0.4 \pi}{2}=1.4531$

Step 2: …