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FIR Filter Using Parks-McClellan Algorithm

See attached word document. The problem is taken from 'Digital Signal Processing using Matlab' by Ingle/Proakis.

1. 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.

Question also in attachment

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Solution Summary

The solution includes matlab codes of narrow bandpass filters to filter out the noise component of a digital signal with a sinusoid frequency and zero mean unit variance Guassian noise using Parks-McClellan algorithm . Along with the filters, and the matlab codes also plot the responses of the filters.