Filter noise from .wav using FIR or IIR digital filters or FFT filtering method

Hi, Here I got the assigned (noise+sinusoidal)-corrupted audio signal

I need to know the matlab coding for filtering out the noise from the signal by using one of the filter FIR/IIR or FFT.

I just know how to display the unfiltered signal but I don't know to use a filter for removing the noise.

close all; clear all; clc;
%%Analyse the audio
[y, Fs] = audioread('audio_5.wav');

% Plot the Time Domain Representation

t = (0:1/Fs:(length(y)-1)/Fs);
subplot(2,2,1)
plot(t,y)
title('Time Domain - Unfiltered Audio')
xlabel('Time (seconds)')
ylabel('Amplitude')
xlim([0 t(end)])

% Plot the Frequency Domain Representation

m = length(y);
x = fft(y, m);
f = (0:m-1)*(Fs/m);
amplitude = abs(x)/m;
subplot(2,2,2)
plot(f(1:(m/2)),amplitude(1:(m/2)))
title('Frequency Domain - Unfiltered Audio')
xlabel('Frequency')
ylabel('Amplitude')
xlim([0 2000])

Some useful MATLAB functions:

spectrogram

fir1

filter

wavread or audioread

length

wavplay or sound

fft

fftshift

freqz

Answer 1

[Mathieu NOE]

hello

see my demo code below for fft analysis and Butterworth filters

adpt it to your own needs

hope it helps

clc
clear all

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 4096;    % 
OVERLAP = 0.5;

% spectrogram dB scale
spectrogram_dB_scale = 80;  % 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 = 1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% data
% [data,Fs] = audioread('myWAVaudiofile.wav');
[data,Fs] = audioread('Immigran_Hiss.wav');

channel = 1;
signal = data(:,channel);

%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 1;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end
samples = length(signal);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : 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(1),plot(freq,sensor_spectrum_dB,'b');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(my_ylabel);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[sg,fsg,tsg] = specgram(signal,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);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% removal of hiss between t = 0 and t = 1.68 s
% use of bandpass filter to remove noise below 500 and above 2500 Hz
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
data_filtered = data;
t_min = 0;
t_max = 1.68;
ind = 1+fix(t_min*Fs:t_max*Fs-1);

% keep only signal content extracted by bandpass filters 
f_low = 500;
f_high = 2500;
N = 4;
% signal_filtered = zeros(size(signal));
[b,a] = butter(N,2/Fs*[f_low f_high]);
% now let's filter the signal
data_filtered(ind,:) = filtfilt(b,a,data(ind,:));
% save as wav file 
audiowrite('Immigran_Hiss-filt.wav',data_filtered,Fs);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2B : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[sg,fsg,tsg] = specgram(data_filtered(:,1),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(3);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');


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

[Andrew Selley]

Hi, I know this is an old thread but I have a similar assignment.

Can you explain where the figures for NFFT, overlap and tmax and tmin come from?

[Mathieu NOE]

hello Andrew

NFFT is the number of samples used in one fft computation ( a.k.a fft buffer size); usually we do multiple fft computations and average the result to get the so called averaged fft spectrum (converted in dB and eventually dB(A) weighting for acoustic analysis. the number of averages is of course related to the data length; the longer the acquisition, the more averages we can do (this has some benefit to minimize the effect of uncorrelated noises on the fft result);

remember that the resulting fft spectrum will have a frequency resolution df = Fs/NFFT (Fs= sampling rate). So a higher NFFT results in refined frequency resolution, but less buffers = lesser averages = lower time resolution in a time / frequency analysis (spectrogram).

overlap is the amount of overlap between successive buffer ; if overlap = 0.5 it means the next buffer has the first 50 % of data coming from the last 50% of the previous buffer. Thus , having (increasing) the overlap permits to compute more averages in the same amount of time.

So the choice mostly depends if you have a very stationnary signal where you want maximum resolution (maximize NFFT) or if you analyse a rapidely time varying signal (=> try different combinaition of NFFT and larger overlap to get the "best" frequency AND time resolution).

you can easily see the impacts of changing NFFT and overlap on a spectrogram plot

tmax and tmin are simply two values given in this example to apply a filter only on given time interval of the signal. You can of course modify the code for your own needs.

hope it helps

all the best

M