Spectral estimation of of EEG/MEG time series data
The spectral estimation toolbox for FieldTrip, the specest module, contains a consistent set of functions for spectral estimation and decomposition of electrophysiological data. These specest functions allow other projects (such as SPM) to reuse the implemented methods separate from FieldTrip and facilitates external contributions to FieldTrip by separating the user interface from the functionality.
The lowlevel functions are combined in the specest toolbox which is selfcontained and does not depend on other FieldTrip functions. It is available for download here.
Specest Functions

 Wavelet convolution in the timedomain by multiplication in the frequency domain. Wavelets used are complex sinusoids multiplied with a windowing function (e.g. Slepian, Hanning, Hamming,…).

 Nontime resolved spectral estimation by tapering the data with a windowing function (e.g. Slepian, Hanning, Hamming,…) prior to compution the Fourier transform.

 Spectral estimation by bandpass filtering the data prior to computing the Hilbert transform.

 Wavelet convolution in the timedomain by multiplication in the frequency domain. Wavelets used are Morlet wavelets.

 Wavelet convolution in the timedomain using Morlet wavelets.
Definition of the functioncalls (API)
The functions should be called as
[spectrum, ntaper, freqoi, timeoi] = ft_specest_mtmconvol(dat, time, key1, value1, ...) [spectrum, ntaper, freqoi] = ft_specest_mtmfft (dat, time, key1, value1, ...) [spectrum, freqoi, timeoi] = ft_specest_hilbert (dat, time, key1, value1, ...) [spectrum, freqoi, timeoi] = ft_specest_wavelet (dat, time, key1, value1, ...) [spectrum, freqoi, timeoi] = ft_specest_tfr (dat, time, key1, value1, ...)
Where dat consists of a matrix of dimensionality Nchan x Ntime, and time is a 1xNtime vector containing the time indices in seconds. The time vector is used to compute the sampling rate, and to determine, in the case of mtmfft, where t=0 resides with respect to dat.
Each function can take a set of common and functionspecific additional arguments in keyvalue pairs. Which additional arguments a function can take is described in the reference documentation: ft_specest_mtmconvol, ft_specest_mtmfft, ft_specest_hilbert, ft_specest_wavelet, ft_specest_tfr.
Definition of Phase
In the case of ft_specest_mtmconvol, the phase at the peak of an oscillation in the data is defined to be 0, and the trough of an oscillation in the data is defined to be π/π, progressing counterclockwise around the circle.
In the case of ft_specest_mtmfft, the average phase of the data segment is from the perspective that an oscillation in the data has a phase of 0, i.e. is at it's peak (following the same convention as ft_specest_mtmconvol), at timepoint t=0.
For ft_specest_hilbert how phase is defined at the peak and at the trough of an oscillation in the data depends on the type of filter and the filter order that is used to bandpass filter the data, prior to computing the Hilbert transform.
For ft_specest_wavelet and ft_specest_tfr how phase is defined at the peak and at the trough of an oscillation in the data depends on the width of the Gaussian that is used.