How To Obtain Fourier Series of Human Sound?

Hello everyone, I'm trying to get my voice's fourier series expansion which I take from my microphone. My code is like that:

recorder= audiorecorder(16000,8,2);

drawnow();

pause(1);

recordblocking(recorder, 5);

play(recorder);

data=getaudiodata(recorder);

plot(data)

I can see my voice on the plot but i also need to get it with fourier series and converge it, how can I do it? Thanks.

Answer 1

[Mathieu NOE]

hi

maybe a first package for audio file spectral analysis can alreadu help you ...

enjoy

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 8192;    % 
NOVERLAP = round(0.75*NFFT);
w = hann(NFFT);     % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.

% spectrogram dB scale
spectrogram_dB_scale = 100;  % 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;

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

% [signal,Fs]=wavread('myWAVaudiofile.wav');  %(older matlab)
% or 
[data,Fs]=audioread('myWAVaudiofile.wav'); %(newer matlab)

channel = 1;

signal = data(:,channel);
samples = length(signal);
dt = 1/Fs;
t = (0:dt:(samples-1)*dt);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[sensor_spectrum, freq] = pwelch(signal,w,NOVERLAP,NFFT,Fs);

% 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),semilogx(freq,sensor_spectrum_dB);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,w,NOVERLAP);  

% 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)');


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

[enrique128]

I will take my voice from matlab I don't want to upload .wav file, thanks.

I tried it but it does not meet my requirements because I need to converge with fourier series to my voice.

[Arav Agarwal]

I used this but all this does is run a FFT. How do I actually calculate and scale coefficients so that I can express things like piano sounds using a Fourier Series such as 1.000sin(x) + 0.442sin(2x) + 0.315sin(3x) + 0.083sin(4x) like this guy did in his video. And yes I do want the series to start with 1.000sin(x).