Design a length L = 50 FIR differentiator using the frequency-sampling method.
(a) Graph the impulse and amplitude responses of the designed differentiator in one plot.
(b) Generate 151 samples of the signal x[n] = 10 cos(0.2πn), 0 ≤ n ≤ 150 and process them through the differentiator designed in (a) to obtain y[n]. Provide stem plots of both x[n] and y[n] for 50 ≤ n ≤ 100 as sub-plots in one figure.
(c) Can you confirm that y[n] corresponds to the samples of the derivative of the signal whose samples are given by x[n]?