FOOOF model, and PSD units

emokh1986 · November 25, 2024, 12:48pm

However, I have another related question and hope you could guide me. What is the formula for FOOOF? I have , for example, these parameters:
aperiodic_params: [-9.18, 1.02]
peak_params:[8.91, 1.69, 1.14; 18.35, 0.80, 1.40]
Is the fitted function like this:
10^(-9.18) * f^(1.02) + 1.69exp(-1/2((f-8.91)/1.14)^2 ) + 0.80exp(-1/2((f-18.35)/1.40)^2 )
or something else?

In addition, I have particularly problem with the units of PSD. Please look at these three plots of the same PSDs:
The FOOOF parameters are for which units? In addition, It is starnge to me, why the units in Log(Power) plots are largly negative (around -100).

Thank you in advance for guiding me!

Raymundo.Cassani · November 25, 2024, 1:08pm

For the formula, that is right, there is an aperiodic (with certain parameters) and peaks are added to it. This is how it is computed in Brainstorm:

github.com

brainstorm-tools/brainstorm3/blob/ba154f9a940ef0dc1358304758b80797e46d0be7/toolbox/process/functions/process_fooof.m#L1256-L1283


      
          function model_fit = build_model(freqs, ap_pars, ap_type, pk_pars, peak_function)
          %     Builds a full spectral model from parameters.
          %
          %     Parameters
          %     ----------
          %       freqs : 1xn array
          %           Frequency values for the power spectrum, in linear scale.
          %       ap_pars : 1xm array
          %           Parameter estimates for aperiodic fit.
          %       pk_pars : kx3 array, where k = No. of peaks.
          %           Guess parameters for peak fits.
          %       pk_type : {'gaussian', 'cauchy', 'best'}
          %           Which types of peaks are being fitted.
          %
          %       Returns
          %       -------
          %       model_fit : 1xn array
          %           Model power spectrum, in log10-space
          
              ap_fit = gen_aperiodic(freqs, ap_pars, ap_type);

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For the parameters, the are explained with full details in the FOOOF tutorial:
https://neuroimage.usc.edu/brainstorm/Tutorials/Fooof#Accessing_FOOOF_model_parameters

Moreover, at the end of that tutorial there is the link to the publication that presented FOOOF, then you look for further information.

They are for the log10(power) as the parameters are given in [Bells] (also described in the tutorial link above).

This is right, a dB is 10*log10(power), and since power is in [microVolts^2]

Luc · November 25, 2024, 2:40pm

+1 to everything @Raymundo.Cassani has said above! Just one small point is that the exponent parameter in the equation has an implied negative, leading to an exponential decay (negative signs are often dropped when reporting by convention).

emokh1986 · December 9, 2024, 8:19am

@Raymundo.Cassani
@Luc
Please look at this figure. I used a graphical calculator to plot the FOOOF function according to its parameters. But the final plot is not completely fit on what Brainstorm (FOOOF) has drawn:
the FOOOF model (red curve on the left) is not fit to the black curve (on the right). I have checked it and understood that the problem is not because of aperiodic (that is exactly fitted to the FOOOF aperiodic plot). Is there a problem with my formula?

Thank you in advance

Raymundo.Cassani · December 9, 2024, 2:02pm

The peak calculation is wrong. From the FOOOF tutorial:
https://neuroimage.usc.edu/brainstorm/Tutorials/Fooof#Accessing_FOOOF_model_parameters

peaks: a struct containing every peak’s channel of origin, center frequency (in Hz), amplitude (in B, Bells, or log[Power]), and standard deviation/gamma (in Hz); if peaks were sorted by frequency band, another column would show the name of the frequency band the peak is located in.

The amplitude of the peak is already in Bells [B], so you would need to multiply it by 10 to get dB, i.e., no need to apply log10 on the peaks.

emokh1986 · December 16, 2024, 9:48am

Thank you @Raymundo.Cassani and @Luc . it is now clear for me.

tmedani · December 16, 2024, 7:15pm

@emokh1986 thanks for the feedback!