Plotting amplitude of individual frequencies over time.

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Fred Hollingsworth on 19 Nov 2020
Commented: Star Strider on 19 Nov 2020
Hi,
I'm coming back to MATLAB after a long time away.
I need to plot the amplitude of an individual frequency over the length of an audio file. I'm currently reading in the audio file, and then using an FFT on it for another part of my analysis. However, I don't know how to specific a frequency to plot the amplitude of, rather than see the spectral characteristics of all frequencies at once.
Any help & code examples would be very appreciated.

Star Strider on 19 Nov 2020
The pspectrum function can likely do what you want. Use the 'spectrogram' type and choose the x-axis column that corresponds to your frequency-of-interest to see it evolve over time.
Using and adapting one of the examples in the documentation:
fs = 3000;
t = 0:1/fs:1-1/fs;
randn(size(t))/100;
x2 = exp(2j*pi*100*cos(2*pi*2*t)) + randn(size(t))/100;
[p,f,t] = pspectrum(x2,fs,'spectrogram');
figure
waterfall(f,t,p');
xlabel('Frequency (Hz)')
ylabel('Time (seconds)')
wtf = gca;
wtf.XDir = 'reverse';
view([30 45])
Freq = 500;
figure
plot(t, p(500,:)')
xlabel('Time')
ylabel('Amplitude')
title(sprintf('Frequency = %5d',Freq))
.

Fred Hollingsworth on 19 Nov 2020
Thank you! This is exactly what I needed!
Star Strider on 19 Nov 2020
As always, my pleasure!

Mathieu NOE on 19 Nov 2020
hello
this is a typical case were my little code snipset can be useful !!
if you need to refine the frequency resolution, increase NFFT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 1024; %
NOVERLAP = round(0.75*NFFT);
w = hanning(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 = 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 = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% or
channel = 1;
signal = data(:,channel);
samples = length(signal);
dt = 1/Fs;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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

R2020b

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