Solve Exercise 8.31 using the WLS design approach.

Exercise 8.31

Design a filter satisfying the following specifications with the minimax approach and show its submatrices of overlapped blocking filtering for \(M=L=2\) and for \(N=1\) :

\[\begin{aligned}\delta_{\mathrm{p}} & =0.01 \\\delta_{\mathrm{r}} & =0.01 \\\Omega_{p_{1}} & =0.48 \frac{\Omega_{\mathrm{s}}}{2} \\\Omega_{p_{2}} & =0.55\frac{\Omega_{\mathrm{s}}}{2} \\\Omega_{r_{1}} & =0.4 \frac{\Omega_{\mathrm{s}}}{2} \\\Omega_{r_{2}} & =0.6 \frac{\Omega_{\mathrm{s}}}{2} \\\Omega_{\mathrm{s}} & =2 \pi \mathrm{rad} / \mathrm{s} .\end{aligned}\]