Different outputs from spectrogram and pwelch

When analysing an acoustic signal, I would expect to get the same results presented in a spectrogram or a PSD analysis, when using the same input variables.

However, this is not the case with my example data (xbit.mat), attached.

%Read audio file
load('xbit.mat');
Fs=96000; %sample rate
xbit=detrend(xbit);
cal=-163.287; %calibration value

% FFT inputs
window=Fs;         
nfft=Fs;         
overlap=Fs/2;   

% Spectrogram
Calibration=10^((abs(cal))/20); % calibration value for specific device used to record data
xbit_cal=xbit*Calibration;
figure(1)
subplot(2,1,1)
[S,F,T,P] = spectrogram(xbit_cal,window,overlap,nfft,Fs,'yaxis');
surf(T,F,10*log10(P),'edgecolor','none');
colorbar;
view(0,90);
ylim([50 24000])
set(gca,'YScale','log','TickDir','out');
clim([0 120]);
ylabel('Frequency');
xlabel('Time')
ylabel(colorbar,'Intensity','VerticalAlignment','bottom','Rotation',270,'FontSize',12)

% PSD analysis
[pxx,f]=pwelch(xbit,window,overlap,nfft,fs); %perform PSD analysis 
%signal, window/segment length, overlap, nfft
pxx_dB=10*log10(pxx)-cal; %convert to dB re 1µPa and calibrate
subplot(2,1,2)
semilogx(f,pxx_dB)
ylabel('Intensity')
xlabel('Frequency')

Answer 1

[Louise Wilson]

There was a mistake in my code which I have now rectified. The results for the spectrogram and spectra now match.

Answer 2

[Mrutyunjaya Hiremath]

1. Spectrogram Scaling: In your spectrogram analysis, you are converting the spectrogram power values to dB and applying calibration (cal) using P=((10*log10(P))-cal);. This could lead to the differences in the value ranges between the spectrogram and PSD.
2. PSD Scaling: In your PSD analysis, you are calculating the PSD values using pwelch, which already provides the power spectral density values in dB. However, you are applying an additional calibration (pxx_dB=10*log10(pxx)-cal;) to the PSD values. This might be causing the PSD values to be shifted.

To maintain consistency and facilitate a direct comparison between the spectrogram and PSD, you should avoid applying additional calibrations and dB conversions to both the spectrogram and PSD values. Here's how you can modify your code:

% ... (previous code)

% Spectrogram
figure(1)
subplot(2,1,1)
[S,F,T,P] = spectrogram(xbit,window,overlap,nfft,Fs,'yaxis');
surf(T,F,P,'edgecolor','none');
colorbar;
view(0,90);
ylim([50 24000])
set(gca,'YScale','log','TickDir','out');
clim([0 120]);
ylabel('Frequency');
xlabel('Time')
ylabel(colorbar,'Intensity','VerticalAlignment','bottom','Rotation',270,'FontSize',12)

% PSD analysis
pxx=pwelch(xbit,window,overlap,nfft); %perform PSD analysis 
pxx_dB=10*log10(pxx); % convert to dB re 1µPa
subplot(2,1,2)
plot(pxx_dB)
ylabel('Intensity')
xlabel('Frequency')

By removing the cal calibration and dB conversions from both the spectrogram and PSD calculations, you should get a more accurate representation of the value ranges between the two analyses. This will allow you to compare the spectrogram and PSD more directly.

[Louise Wilson]

Thanks for your answer!

This does not help me though because I need to apply the calibration value for the values to be valid?

Surely there is a solution to apply it consistently to both outputs, which should be done once they are converted to dB? (since the calibration value is in dB)