PWELCH vs PSD

I am trying to update some code that uses the deprecated function PSD to use PWELCH instead; however, I am getting completely different results when I am using what seems to be the same parameters. Does anyone know why? Here are what I believe to be the equivalent function calls:

[pxx,f] = pwelch(data, hanning(1024), [], 1024, 250);
   [pxx,f] = psd(data,1024,250,hanning(1024));

Where: data = signal in a vector

hanning(1024) = window vector
   1024 = nfft, number of points in the fft
   250 = Fs, the sampling rate
   [ ] = noverlap, defaults to 50% window overlap

Matlab has removed all help information for the PSD function, and instead says to use its functional equivalent pwelch, so I don’t have anyway of looking up what the original documentation says about the function’s inputs and outputs. Could the outputs be scaled differently? Is the PSD calculated differently between the two functions?

ANSWER

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The result of psd is not correctly scaled, therefore you should use pwelch. For spectral density, the result should be scaled by the sampling frequency, which is not performed by psd.

If you look at the two results, the f vector should be the same. If you take the ratio of two pxx, you can that most samples, the differ by a factor of 125, which is basically half of sampling frequency. This is because the resulting spectrum is one-sided. The two end points differs by a factor of 250.

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