1. Problem 8.1. For part (d) use a Blackman window rather than a Bartlett window.

2. We wish to design an FIR bandpass filter satisfying the following specifications:

\begin{matrix}−0.02 < |H(ω)| < 0.02, & 0 ≤ |ω| ≤ 0.2π \\ −0.95 < |H(ω)| < 1.05, & 0.3π ≤ |ω| ≤ 0.7π \\ −0.001 < |H(ω)| < 0.001, & 0.75π ≤ |ω| ≤ π \end{matrix}

Design this filter using a Kaiser window.

(a) Find β for the Kaiser window to meet the passband and stopband attenuations.

(b) Find the length M of the filter to meet the transition band widths.

(c) Find and plot the impulse response h(n) of the filter.

(d) Plot the gain |H(ω)| of the filter and show that it meets the specifications.

3. Repeat Problem 3 using the Remez algorithm for designing an equiripple FIR filter (the remez() function if MATLAB).