DTF
Determination of EEG propagation in brain
DTF
As a first step a MultiVariate
AutoRegressive (MVAR) model is
fitted [14] to the data.
All the data channels are treated as one process and are analyzed
simultaneously. The data epoch properties are described by means of the
fitted MVAR model parameters A(i):
 or in another form:
 Transforming the model to
frequency domain we get:
 which can be presented as
 From the above equation one can see that MVAR can be treated as a black-box model with the noises at the input and the signal as the output: 
All the information about the
spectral properties and interrelation between channels is contained in
the H( f ) -- transfer matrix of the
model. From the transfer matrix power spectrum, ordinary, multiple and
partial coherences can be easily calculated.
Power spectrum:  Ordinary coherences:
 Partial coherences (give only direct relations between signals):  Multiple coherences (give relation between one signal and all the other signals of the set):  Moreover causal relations between channels can be described using Directed Transfer Function (DTF). The DTF is constructed from transfer matrix of the MVAR model [1]. The normalized (to all the inflows to channel i) version is defined as:  The non-normalized version:  Note: both formulas describe transmission from channel j to channel i in the frequency domain. By means of DTF the transmissions between channels are shown as functions of frequency. The quality of the model fitting is essential to get reliable estimates. The balance has to be kept between number of model parameters and the number of data points, therefore the data epoch cannot be too short. |
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