MATLAB: Is spectrum.periodogram not recommended, and how to substitute pwelch in it’s place

median frequencypsdpwelchspectrum.periodogramspectrum.pwelch

A message pops up in Matlab when I use spectrum.periodogram to find the median frequency of a signal, saying that it is not recommended. Why is this? I also get the same message for spectrum.pwelch
I am implementing the solution described by Median Frequency using spectrum.periodogram which is:
psdest = psd(spectrum.periodogram,x,'Fs',1000,'NFFT',length(x)); 
   normcumsumpsd = cumsum(psdest.Data)./sum(psdest.Data);
   Ind = find(normcumsumpsd <=0.5,1,'last');
   fprintf('Median frequency is %2.3f Hz\n',psdest.Frequencies(Ind));
After lots of research I still don't understand the output of the psd well enough so that I can susbstitute spectrum.periodgram. Normally I find my PSD using:
[Pxx,Fx] = pwelch(s,[],[],[],fs);
plot(Fx,10*log10(Pxx))
Ideally I would like to find the median frequency by manipulating the Pxx and Fx values but I am struggling to relate Pxx directly to psdest.Data. I would be grateful if someone could point me in the right direction. Thank you in advance!

Best Answer

Well, first, is your signal a random variable? Or more of a periodic signal (i.e. a sine wave)? If it's periodic, then just a simple FFT will suffice to give you the frequency. You only need to mess with power spectral density if you have a random signal.
As to why periodogram is not recommended... first, let's establish one fact: you can never actual measure power spectral density, because to do that you'd need an infinitely long sample of the data. You can only estimate power spectral density with a finite length sample. And, as it turns out, the periodogram is not a very good estimate. One is problem is that as you take longer and longer data samples, you would expect to get better and better estimates. But this does not happen with periodogram. The estimate remains noisy even for more and more data.
welch's method (pwelch()) is better because as you take more and more data, the estimate gets better. There are other methods, but pwelch is pretty reasonable, and I use it a lot.
Hope this helps. I've also got some tutorials on power spectral density on my website: http://www.mechanicalvibration.com/Random_vibrations.html
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