Design an ideal low-pass filter with N = 11 with frequency response,

$$ H_d\left(e^{j v}\right)= \begin{cases}1, & \text { for }-\frac{\pi}{2} \leq \omega \leq \frac{\pi}{2} \\ 0, & \text { for } \frac{\pi}{2} \leq|\omega| \leq \pi\end{cases} $$

Solution:

$ H_d(\omega)=\left\{\begin{array}{lc}\\ 1, & \text { for }-\frac{\pi}{2} \leq \omega \leq \frac{\pi}{2} \\\\ 0, & \text { for } \frac{\pi}{2} \leq|\omega| \leq \pi\\ \end{array}\right. $

The filter coefficients are given by,

$ \begin{aligned} h_d(n) & =\frac{1}{2 \pi} \int_{-\pi}^\pi H_d(\omega) e^{j \omega n} d \omega \\\\ & =\frac{1}{2 \pi} \int_{-\pi …