Design a filter with $\mathrm{H}_{\mathrm{d}}\left(\mathrm{e}^{\mathrm{jw}}\right)=\mathrm{e}^{-\mathrm{j} 3 \mathrm{w}},-\pi / 4 \leq \mathrm{w} \leq \pi / 4$

$ 0 \quad, \pi / 4\lt|\mathrm{w}|\lt\pi\\ $

Using Hanning window with $\mathrm{N}=7$

Solution:

$ H_d\left(e^{j \omega}\right)=e^{-j 3 \omega}\\ $

The frequency response is having a term $e^{-j \omega(N-1) / 2}$ which gives $h(n)$ symmetrical about $n=\frac{N-1}{2}=3$, we get a causal sequence.

$ \text { We have, } \begin{aligned}\\ h_d(n) &=\frac{1}{2 \pi} \int_{-\pi / 4}^{\pi / 4} e^{-j 3 \omega} \cdot e^{j \omega …