We are given BachWithNoise.wav audio file, and the follwoing code.

Given:

% Remove noise from recording

clear all

% Edit following to point to location of the file on your system

fname = 'desktop/Bach/BachWithNoise.wav';

[y,Fs]=audioread(fname);

%% Power Spectral Density

windLength = 2048;

wind = hamming(windLength);

[Pyy,f]=pwelch(y(:,1),wind,[],[],Fs);

plot(f,10*log10(Pyy))

xlabel('Frequency (Hz)')

ylabel('Pyy (dB)')

title('PSD of Signal with High Frequency Noise')

Summary Description: Given a recording with added noise (BachWithNoise.wav), design a digital filter to restore the audio recording Required software: MATLAB or octave optional: computer with audio output (useful to play the original and filtered audio signals) . You have obtained an audio recording from the early 1700's. Unfortunately, the recording instrumentation of the time was rather primitive. Consequently the recording contains a considerable amount of noise. The audio recording is a two channel waveform, audio file format (wav), file (f,-44,100 Hz) that contains the musical signal plus the high frequency noise. Your task is to find a method that recovers the musical signal while minimizing the noise. You know a couple of facts about the recording. First, the highest frequency component from all the instruments in the musical signal is 15 kHz. Second, the musical signal and noise are uncorrelated. Use power spectral density estimation, i.e., MATLAB function pwelch, to identify the frequency ranges of the music and noise. See sample MATLAB script Project Bach.m". Based on the results from PSD analysis, design a filter to remove the noise while retaining as much of the recording bandwidth as possible Since phase distortion has a detrimental impact on audio signals, a linear phase filter should be used Also, since the signal is much longer than the filter, an overlap-add method could be used to implement the filtering process. (Hint: fftfilt) Your report should contain the matlab script, the PSD's of the original recording and the filtered signal the frequency response of the filter (magnitude and phase), and the approximate signal-to-noise ratios (in dB) for each channel. If your matlab script does not include the code used to obtain the filter coefficients, then document each step in that process. You may use the MATLAB publish feature to create your report. Make sure all documentation and figures are included in the report