Design an M = 25 order FIR Hilbert transformer using the Parks–McClellan algorithm.
a. Graph the impulse and amplitude responses of the designed transformer in one plot.
b. Generate 101 samples of the signal x [ n ]= cos ( 0.3 π n ) , 0 ≤ n ≤ 100 and process them through the transformer designed in
(a) to obtain y [ n ]. Provide stem plots of both x [ n ] and y [ n ] for 25 ≤ n ≤ 75 as sub-plots in one figure.
c. Can you confirm that y [ n ] corresponds to the samples of the Hilbert transform of the signal whose samples are given by x [ n ]?