Spectral analysis of multichannel time series is a common procedure
in many areas of biomedical signal
processing. Particularly in the analysis of multichannel EEG signals,
various spectral parameters are of
great interest. The analysis of coherence of EEG signals is a
useful tool for examining the functional
relationship between different brain structures. This information can
be useful in disease related research
e.g. localization of epileptic foci, as well as in cognitive studies
of normal brain.
In many applications the vector autoregressive (VAR) model is estimated
in order to compute the
spectral density matrix S, ordinary, and partial coherences. The partial
coherence is a measure of the joint
variance of two channels at a particular frequency, after the influence
of all other channels has been
removed. Unfortunately, the most commonly used algorithm requires much
more computations for partial
coherences than for ordinary coherences and therefore many researchers
limit their analysis to ordinary
coherences only.
We introduce here an algorithm for computing partial coherences directly
from the matrix coefficients
of the VAR model. The new algorithm does not require computing of the
spectral density matrix S. Instead of
computation of the inverse of the matrix S followed by computation
of k*(k-1)/2 minors of matrix S for each
frequency, it requires only one inverse of a real symmetric residual
matrix for all frequencies. All other
computations are the same as in the traditional algorithm. This significantly
reduces the number of
computations, improving both speed and accuracy.
(Supported by NIH grant NS 33732)