MATLAB: Can you help remove the noise from this audio file

Question

I'm having trouble removing the noise heard from this audio file audio_sample.wav.

I've attempted to use the "butter" function to experiment with removing certain frequencies in an effort to reduce the noise as much as possible.

You will need to have the audio file in the search path your MATLAB is using.

The code will play my "current solution".

Thanks for any help.

%%1)   Load the 'audio_sample.wav' file in MATLAB
[sample_data, sample_rate] = audioread('audio_sample.wav');
% a.  Plot the signal in time and the amplitude of its frequency 
% components using the FFT.
sample_period = 1/sample_rate;
t = (0:sample_period:(length(sample_data)-1)/sample_rate);
subplot(2,2,1)
plot(t,sample_data)
title('Time Domain Representation - Unfiltered Sound')
xlabel('Time (seconds)')
ylabel('Amplitude')
xlim([0 t(end)])
m = length(sample_data); % Original sample length.

n = pow2(nextpow2(m)); % Transforming the length so that the number of 

% samples is a power of 2. This can make the transform computation 

% significantly faster,particularly for sample sizes with large prime 

% factors.
y = fft(sample_data, n);
f = (0:n-1)*(sample_rate/n);
amplitude = abs(y)/n;
subplot(2,2,2)
plot(f(1:floor(n/2)),amplitude(1:floor(n/2)))
title('Frequency Domain Representation - Unfiltered Sound')
xlabel('Frequency')
ylabel('Amplitude')
% b.  Listen to the audio file.
% sound(sample_data, sample_rate)
%%2)  Filter the audio sample data to remove noise from the signal.
order = 7;
[b,a] = butter(order,1000/(sample_rate/2),'low');
filtered_sound = filter(b,a,sample_data);
sound(filtered_sound, sample_rate)
t1 = (0:sample_period:(length(filtered_sound)-1)/sample_rate);
subplot(2,2,3)
plot(t1,filtered_sound)
title('Time Domain Representation - Filtered Sound')
xlabel('Time (seconds)')
ylabel('Amplitude')
xlim([0 t1(end)])
m1 = length(sample_data); % Original sample length.
n1 = pow2(nextpow2(m1)); % Transforming the length so that the number of 
% samples is a power of 2. This can make the transform computation 
% significantly faster,particularly for sample sizes with large prime 
% factors. 
y1 = fft(filtered_sound, n1);
f = (0:n1-1)*(sample_rate/n1);
amplitude = abs(y1)/n1;
subplot(2,2,4)
plot(f(1:floor(n1/2)),amplitude(1:floor(n1/2)))
title('Frequency Domain Representation - Filtered Sound')
xlabel('Frequency')
ylabel('Amplitude')

Answer 1

It is not possible to eliminate broadband noise with a frequency-selective filter. You have to use wavelets to effectively de-noise it.

I got reasonable results with this filter, and using the filtfilt function:

Fs = sample_rate;                                       % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency (Hz)
Wp = 1000/Fn;                                           % Passband Frequency (Normalised)
Ws = 1010/Fn;                                           % Stopband Frequency (Normalised)
Rp =   1;                                               % Passband Ripple (dB)
Rs = 150;                                               % Stopband Ripple (dB)
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);                         % Filter Order
[z,p,k] = cheby2(n,Rs,Ws,'low');                        % Filter Design
[soslp,glp] = zp2sos(z,p,k);                            % Convert To Second-Order-Section For Stability
figure(3)
freqz(soslp, 2^16, Fs)                                  % Filter Bode Plot
filtered_sound = filtfilt(soslp, glp, sample_data);
sound(filtered_sound, sample_rate)

Experiment to get the results you want.