Filtering noise from an audio file

I have a corrupted audio file which contains a message with very loud noise, and I should filter the noise as much as possible. I tried couple of filters, and I could eliminate some of the noises but it's not enough. P.S. The expected audio file is also there, which I plotted it to compare the filtered one with it. Both audio files and the code are provided in the zip file.

clc;
close all;
clear;

[Clean, Fs2] = audioread('expected.m4a');
[sample_data, sample_rate] = audioread('corrupted.m4a');

signal = medfilt1(sample_data,90);      % Applying median filter

%_______________________________________________________________________________%
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

filtered_sound2 = filtfilt(soslp, glp, signal);
%_______________________________________________________________________________%

fs2_d = [filtered_sound2,filtered_sound2];

sound(fs2_d, sample_rate)

subplot(4,1,1);
plot(sample_data);            % Original Signal
title('Original Signal');
xlabel('Time (s)'); ylabel ('Amplitude');

subplot(4,1,2);
plot(filtered_sound2);          % Filtered output
title('Filtered Signal Double');
xlabel('Time (s)'); ylabel ('Amplitude');

subplot(4,1,3);
plot(fs2_d);         % Filtered output
title('Filtered Signal Double');
xlabel('Time (s)'); ylabel ('Amplitude');

subplot(4,1,4);
plot(Clean);                  % Expected output
title('Expected Signal');
xlabel('Time (s)'); ylabel ('Amplitude');

[Jan]

Just some comments: In R2016b I get the warning

 Warning: The first two inputs are interpreted as an SOS matrix
 and G vector. Use column vectors if you meant to specify a
 transfer function.

in the line: filtered_sound2 = filtfilt(soslp, glp, signal);

Producing a stereo sound by fs2_d = [filtered_sound2,filtered_sound2] is not needed. Stay at mono.

[Naser Je]

Yeah I got that as well, I tried this method after refereeing to one of the answers on this "community", other methods didn't give me better results so far.

And regarding the stereo sound, yeah I realized that thanks.

Still hoping someone can help me in this...

[Jan]

If you mention that you took an idea from another thread, add a link also. This helps the readers. It would be useful to know, why you have chosen these filter parameters 1000, 1010, 1, 150.

[Naser Je]

Oh sorry, here is the link to that answer: https://uk.mathworks.com/matlabcentral/answers/357022-can-you-help-remove-the-noise-from-this-audio-file#answer_282048

[Jan]

I'd scale the filtered signal and the expected signal to be in the range [-1, 1] and subtract both from each other. Then you have the pure noise - approximately. Now use FFT to analyze its spectrum. Maybe this allows to improve the filter parameters. I'm not familiar enough with signal processing to help you further.

[Star Strider]

Note that the person who asked that question ended up using wavelets to eliminate the noise, as I originally suggested in my Answer. It is not possible to eliminate broadband noise with only a frequency-selective filter.

The first step of course is to use the fft (link) to see what the frequency content is. That allows you to design your filter effectively.

[Abdulaziz Al-Hasani]

Dear all ,

i would like anyone to have exprience for use the matlab , i need to 3- Design a filter to reduce the noise of a received audio signal

please as you can help me ,

i am looking forward

please contact me in [e-mail]

[Jan]

@Abdulaziz Al-Hasani: Please open a new question and post the details there. Avoid to hijack another thread by posting a new problem in the section for comments.

[mohamed mostafa]

please, how i can design a filter to sperate two voices, my voice and audio of phone.

[zina shalchi]

Hello, I faced the following errors

Error using sound (line 76)

Only one- and two-channel audio supported.

Error in dsp (line 26)

sound(fs2_d, sample_rate)

while trying to implement your code

@Naser Je

would you help

[Lochan Chitnis]

can someone please explain the above code

[Mathieu NOE]

hi

just for the spectral analysis , I used this code. Seems the signal is burried in heavy broadband (white) noise plus two strong tones at 1000 and 2000 Hz

clc
clearvars
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% data
[signal,Fs] = audioread('corrupted.m4a');
% [signal,Fs] = audioread('expected.m4a');

[samples,channels] = size(signal);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 256;    % 
OVERLAP = 0.75;

% spectrogram dB scale
spectrogram_dB_scale = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% if you are dealing with acoustics, you may wish to have A weighted
% spectrums 

% option_w = 0 : linear spectrum (no weighting dB (L) )
% option_w = 1 : A weighted spectrum (dB (A) )
option_w = 0;

%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 1;
if decim>1
    for ck = 1:channels
    newsignal(:,ck) = decimate(signal(:,ck),decim);
    Fs = Fs/decim;
    end
   signal = newsignal;
end
samples = length(signal);
time = (0:samples-1)*1/Fs;

%%%%%% legend structure %%%%%%%%
for ck = 1:channels
    leg_str{ck} = ['Channel ' num2str(ck) ];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : time domain plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1),plot(time,signal);grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz ']);
xlabel('Time (s)');ylabel('Amplitude');
legend(leg_str);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, sensor_spectrum] = myfft_peak(signal,Fs,NFFT,OVERLAP);

% convert to dB scale (ref = 1)
sensor_spectrum_dB = 20*log10(sensor_spectrum);

% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(freq);
    sensor_spectrum_dB = sensor_spectrum_dB+pondA_dB;
    my_ylabel = ('Amplitude (dB (A))');
else
    my_ylabel = ('Amplitude (dB (L))');
end


figure(2),plot(freq,sensor_spectrum_dB);grid on
df = freq(2)-freq(1); % frequency resolution 
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(my_ylabel);
legend(leg_str);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 3 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for ck = 1:channels
    [sg,fsg,tsg] = specgram(signal(:,ck),NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  

    % FFT normalisation and conversion amplitude from linear to dB (peak)
    sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only

    % apply A weigthing if needed
    if option_w == 1
        pondA_dB = pondA_function(fsg);
        sg_dBpeak = sg_dBpeak+(pondA_dB*ones(1,size(sg_dBpeak,2)));
        my_title = ('Spectrogram (dB (A))');
    else
        my_title = ('Spectrogram (dB (L))');
    end

    % saturation of the dB range : 
    % saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
    min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
    sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;

    % plots spectrogram
    figure(2+ck);
    imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
    axis('xy');colorbar('vert');grid on
    df = fsg(2)-fsg(1); % freq resolution 
    title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz / Channel : ' num2str(ck)]);
    xlabel('Time (s)');ylabel('Frequency (Hz)');

end

function pondA_dB = pondA_function(f)
	% dB (A) weighting curve
	n = ((12200^2*f.^4)./((f.^2+20.6^2).*(f.^2+12200^2).*sqrt(f.^2+107.7^2).*sqrt(f.^2+737.9^2)));
	r = ((12200^2*1000.^4)./((1000.^2+20.6^2).*(1000.^2+12200^2).*sqrt(1000.^2+107.7^2).*sqrt(1000.^2+737.9^2))) * ones(size(f));
	pondA = n./r;
	pondA_dB = 20*log10(pondA(:));
end


function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,channels);
    s_tmp((1:samples),:) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end

Answer 1

[matt]

Limit bandwidth to region of highest signal strength in clean audio.

[Clean, Fs2] = audioread('expected.m4a');
[sample_data, sample_rate] = audioread('corrupted.m4a');

Fs = sample_rate;                      



d1 = designfilt('bandpassiir','FilterOrder',20, ...
         'HalfPowerFrequency1',100,'HalfPowerFrequency2',600, ...
         'SampleRate',Fs);

N = length(sample_data);

y1 = filtfilt(d1,sample_data);
%

Audio2 = audioplayer(y1,Fs);
play(Audio2);

f = linspace(0,Fs,N);
figure;
plot(f,abs(fft(sample_data)))
hold on
plot(f,abs(fft(Clean)))
plot(f,abs(fft(y1)))