Solution:

Given: M = 7

$w-c = |rad | sec$

Step 1: Obtain desired $T.F. H_d(w)$

$\alpha=\frac{m-1}{2}$

$\alpha=\frac{7-1}{2}=3$

$\therefore H_{d}(\omega)=\left\{\begin{array}{l}{1 e^{j 3 \omega}} \\ {0}\end{array}\right.$

$0 \leq|\omega| \leq 1$ $|\omega| \geq 1$

Step 2: Obtain hd(n)

$h_{d}(n)=\frac{1}{2 \pi} \int_{-\pi}^{\pi} H_{d}\left(e^{j w}\right) e^{j \omega n} d \omega$

$=\frac{1}{2 \pi} \int_{-1}^{1} 1=e^{-j 3 \omega} e^{j \omega n} d \omega$

$=\frac{1}{2 \pi} \int_{-1}^{1} e^{j(n-3)} d \omega$

$=\frac{1}{2 \pi}\left[\frac{e^{j(n-3) w}}{j(n-3)}\right]^{1}_{-1}$

$=\frac{1}{2 \pi}\left[\frac{e^{j(n-3)}-e^{-j(n-3)}}{j(n-3)}\right]$

$h_{d}(n)=\frac{1}{\pi(n-3)} \cdot \sin (n-3)$

Step 3: Obtain h(n)