Let 'M' be the FIR filter length.

Order of FIR filter $=\mathrm{M}-1=6$

$\therefore \mathrm{M}=7$

Given, Cut-off frequency $\omega_{c}=\frac{\pi}{2} ;$ Gain $C=1$

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

Let Desired Frequency Response of LPF be

$H_{d}\left(e^{j w}\right)=\left\{\begin{array}{cc}{C e^{-j \alpha \omega}} & {|\omega| \leq \omega_{c}} \\ {0} & {\omega_{c} \leq|\omega| \leq \pi}\end{array}\right.$

$\therefore H_{d}\left(e^{j w}\right)=\left\{\begin{array}{cc}{1 e^{-j …