pwelch ignores peaks in PSD plot

Hello there. I am studying the PSD plots of various aircraft states, and overlapping different estimation methods (green is analytical, blue is FFT and red is pwelch). As you can see, at 0.03 for the PSD of pitch angle there is a peak of power, which is indicated in the analytical plot but is also visible in the FFT plot. I am now trying to smooth out the FFT with the pwelch method, but does not matter how hard I try, the smoothed function will not detect the peak there.

My question is therefore: is this behavior expected, or there is something that I am not seeing that will allow the pwelch smoothed function to represent the peak as well?

[Mathieu NOE]

hello Pietro

does your fft compuation use overlapping and averagin or is it one single buffer fft computation ?

how did you set the pwelch parameters in terms of overlap and frequency resolution (nfft) vs. your fft computation ?

can you compare the delta freq of all methods ?

all the best

[Pietro Campolucci]

hi Mathieu, thanks for the response.

• fft is one buffer
• I am setting a 50% overlap over windows of 5000 samples given 40000 total samples (frequency res is 200)
• what do you mean by delta frequency in this case?

[Mathieu NOE]

hello Pietro

"delta frequency" : I mean , each of you method generates a frequency vector with probably a different step (resolution or delta) . So I was suspecting that the resolution of your pwelch computation was too coarse to show the peak at 0.03 ?

[Pietro Campolucci]

The delta frequency I used is the same for all methods then

[Pietro Campolucci]

also I tried to increase fs for the pwelch wrt to the fft method but the plot just gets shifted down

[Mathieu NOE]

Are you willing to share the code and the data file ?

[Pietro Campolucci]

I am sorry but I am not allowed as it is forbidden unfortunately. However increasing the window size slightly seemed to have a positive effect on the peak detection. However if I increase more the smoothed function gets noisier. I guess that is the best it gets.

[Mathieu NOE]

yeap - maximizing the window size gives you the best frequency resolution, hence you are more able to see a peak emerging. So window size = data length in that case;