(a) Design a linear phase FIR filter to meet the given magnitude response specifications. $$ \begin{aligned} H\left(e^{j \omega}\right) & =e^{-j 5 \omega} & & \pi / 2 \leq|\omega| \leq \pi \\ & =0, & & \text { otherwise } \end{aligned} $$ Use a suitable window that provides at least 40 dB sidelobe attenuation. (15)
Explanation
The linear phase FIR filter can be designed using the window method. The Kaiser window is used to provide at least 40 dB sidelobe attenuation. The Kaiser window is given by $w(n) = I_0 \left(\alpha \sqrt{1 - \left(\frac{\sin(\pi n / N)}{\pi n / N}\right)^2}\right)$, where $I_0$ is the modified Bessel function of order 0 and $\alpha$ is a parameter that controls the sidelobe attenuation.
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