# I am trying to clean up the corruption and recover the original soundtrack but it turns out way less than my expectation

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S Suhaimi on 4 Dec 2023
Edited: S Suhaimi on 5 Dec 2023
% Step 1: Identify the system's impulse response h[n]
% Padding the shorter signal to make it the same length as the longer one for FFT
length_difference = length(xtraining)-length(straining);
% Compute the FFT of the padded training sequence and the xtraining sequence
X_xtraining = fft(xtraining);
% Compute the frequency response of the system H(f)
H_f = X_xtraining ./ X_straining;
% Compute the impulse response of the system h[n] using inverse FFT
h_f = ifft(H_f);
% Select the first 9 elements of the impulse response for the FIR filter
hFILTER = h_f(1:9);
disp(hFILTER) % Display the impulse response
% Step 2: Recover the specific sequence from y[n]
% Pad the impulse response to the length of y for FFT
length_difference2 = length(y) - length(hFILTER);
% Compute the FFT of the corrupted signal y and the padded impulse response
Y_f = fft(y);
% Compute the filtered signal in the frequency domain
S_f = Y_f ./ H_f;
% Convert the filtered signal back to time domain
s_plus_cos = ifft(S_f);
% Step 3: Detect the single tone frequency f
% Take FFT of the signal y
Y = fft(y);
% Compute the magnitude spectrum of Y
magnitude_spectrum = abs(Y);
% Find the index of the peak in the magnitude spectrum
[~, index_of_peak] = max(magnitude_spectrum);
% Compute the frequency resolution of the FFT
frequency_resolution = fs / length(y);
% Calculate the single tone frequency using its FFT index
single_tone_frequency = (index_of_peak - 1) * frequency_resolution;
% Display the single tone frequency
disp(single_tone_frequency);
% Assign the detected frequency to f
f = single_tone_frequency;
% Step 4: Design a "notch" filter to filter out the single tone sinusoid
% Create the coefficients for a second-order notch filter
hNOTCH = [1, -2*cos(2*pi*f/fs),1];
% Apply the notch filter to the signal
recovered_audio = conv(s_plus_cos,hNOTCH);
% Play the recovered audio
sound(recovered_audio,fs)
% This is the distorted version: sound(y,fs)
% The quality that the sound supposed to produce: sound(stest,fs)

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