MATLAB function **burst_analysis_beta_envelope(EEG)**
Computes the amplitude envelope of the band-passed filtered continuous data after Hilbert transform.
Next, it extracts beta-band oscillation bursts for fixed criteria: 0.75 quartile of amplitude envelope; also based on parameters minimum duration of burst and separation between bursts.
EEG is an EEG file in the EEGLAB format, an example is uploaded.
More details:
As in our earlier work (e.g. Herrojo Ruiz et al., NeuroImage, 2014), the amplitude envelope A(t) of the instantaneous analytic signal was computed after applying the Hilbert transform to the bandpass-filtered raw data (12–35 Hz; two-way least-squares FIR filter applied with the eegfilt.m routine from the EEGLAB toolbox, Delorme and Makeig, 2004) spanning the full continuous recording of the task performance. Next, from the total beta-band amplitude envelope we extracted data segments corresponding with the epochs locked to the feedback presentation from -9 to 3 s.
Next, MATLAB function **some_plots.m**
Creates two example plots showing the thresholding results on the sample data set EEG_example.set. It also creates a histogram with the distribution of burst durations for one channel in the sample data set.
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MATLAB function **get_timecourse_wavelet(EEG)**
Computes the time-varying spectral power in the beta-band (13-30Hz) after implementing the wavelet time frequency transformation (using Morlet wavelets) based on convolution in the time domain. Calls fieldtrip function ft_freqanalysis.m
Note: the frequency and temporal resolution of the Morlet wavelet is given by the following:
sigma_t = eta / 4 pi f
sigma_f = f/eta
With eta the wavelet family function or number of cycles.
The uncertainty principle imposes the following criterion for Morlet wavelet:
sigma_t sigma_f = 1/ (4 pi) (Mallat, 1999)
Note that the original uncertainty principle is defined for angular frequency, and thus
sigma_t sigma_omega = 1/2
and omega = 2 pi f
Therefore sigma_t sigma_f = 1/ (4 pi)
See mathematical expressions here:
https://osf.io/neq2d/
From: Ruiz MH, Koelsch S, Bhattacharya J. Decrease in early right alpha band phase synchronization and late gamma band oscillations in processing syntax in music. Human brain mapping. 2009 Apr;30(4):1207-25.
See also
Mallat S. A wavelet tour of signal processing. Elsevier; 1999 Sep 14.
Allefeld C. Phase synchronization analysis of event-related brain potentials in language processing (2004). PhD thesis.
Note that most studies have incorrectly adopted the frequency and temporal resolution defined in
Tallon-Baudry C, Bertrand O. Oscillatory gamma activity in humans and its role in object representation. Trends in cognitive sciences. 1999 Apr 1;3(4):151-62.
This paper did not take into account the transformation from angular to ordinary frequency and thus had an erroneous estimation of sigma_t and sigma_f.
