Assignment:
A digital signal y(k) contains a sinusoid of frequency π/2 and a zero mean unit variance Guassian noise w(k), i.e.
y(k) = 2cos(π k/2) + w(k)
We want to filter out the noise component using 50-th order casual and linear phase FIR filter
(a) Using Parks-McClellan algorithm, design a narrow bandpass filter with Passband width of no more than 0.02π and Stopband attenuation of at least 30dB. Note that no other parameters are given, and you have to choose the remaining parameters for the remez function to satisfy the given requirements. Provide a plot of the log-magnitude response in dB of the designed filter.
(b) Generate 200 samples of the sequence y(k) and process through the filter designed in part (a) to obtain the output z(K). Provide subplots of y(k) and z(k) for 100 ≤ k ≤ 200 on one plot and comment on the results.
Provide complete and step by step solution for the question and show calculations and use formulas.