# Plotting FFT for audio WAV file?

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Avinash Kandalam on 4 Nov 2020
Commented: Mathieu NOE on 9 May 2022
Dear all,
I tried to explain as clear as possible. I want to plot "Raw FFT" file for a "WAV" file. This WAV (audio) file is acquired from a microphone for a period of 1 minute. The goal is to plot frequency distribution (0 Hz - 20 kHz).
1. I want to acquire raw FFT (to see if there are any signal peaks at particular frequency) throughout 1 minute. The WAV (audio) file (only 1) is atttached to this question.
I tried to execute the following code (from previous answers here) and I think it is not the right way. I think what the code shows is basically amplitude vs frequency; but not a typical FFT spectrum.
Million Thanks,
Avinash.
CODE: I tried and most likely wrong. I think as said, it is just amp vs freq, which does not give me clear picture of frequencies which lies in different ranges.
t=linspace(0,length(y1)/fs,length(y1));
Nfft=16777216; %power of 2 and I put a huge number so there are many data points
f=linspace(0,fs,Nfft);
X1=abs(fft(y1,Nfft));
plot(f(1:Nfft/2),X1(1:Nfft/2))
xlabel('Frequency');
ylabel ('Power???');
title ('FFT Spectrum');
OUTPUT: I only zoomed into 0-30 Hz using above code and WAV file attached (ofcourse the wole spectrum is until 20000 Hz) Avinash Kandalam on 4 Nov 2020
@Walter: Thank you for the reply. The content is basically over the signal recorded, there are different sounds happening at different frequencies.
For example, at 30 Hz and 40 Hz, if I see a strong peak (in FFT) then I believe the frequencies produced are mostly at 30 & 50 Hz. Something like this, I want to see my WAV signal to be distinguished. Thanks

Mathieu NOE on 4 Nov 2020
dear friends, here my little contribution to wav file spectral analysis...
enjoy !
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 8192; %
NOVERLAP = round(0.75*NFFT);
w = hanning(NFFT);
% 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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% or
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
Mathieu NOE on 9 May 2022
hello Benjamin
the issue has been found - see Jonas answer