(Window Design) Without using a computer, use the window design method with a Hamming window to find an *analytic* expression for the coefficients {h[n]} 38 n=0 of a length-39 FIR filter that approximates an ideal bandpass filter with cutoff frequencies π/4 and 3π/4. Using Matlab or Python, plot the magnitude and phase responses of this filter on a linear scale (not the default logarithmic scale!). From these plots, estimate the passband ripple, the stopband ripple, and the number of zeros that lie on the unit circle (when assessing the stopband and passband ripple, please assume ωs1 = 0.17π, ωp1 = 0.33π, ωp2 = 0.67π, and ωs2 = 0.83π).

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