instant frequencie Hilbert transformation
The methods are offered, allowing estimating symmetry of a signal: a method of definition of capacity of differential signal; a method of definition of phase shift with the help of Hilbert transformation.
One of the basic diagnostic criteria at analysis of EEG is symmetry. Symmetry of EEG is understood as essential concurrence of frequencies, amplitudes and phases of the signals received from symmetric areas of two hemispheres of a brain. Having revealed presence hemisphere asymmetry of EEG, it is possible to establish localization of pathological processes.
Proceeding from linearity of Fourier transform, display of symmetry will be, that capacity of differential signal will be small in comparison with capacity of EEG of one of abductions. At absence of symmetry capacity of differential signal is commensurable with capacity of EEG of one of abductions. Schedules, illustrating the given positions are resulted.
Thus, definition of capacity of differential signal of symmetric abductions renders the expert the essential help in diagnostics. This method is very evident. The given method can be used at mass screening. With its help even the expert of an average link can eliminate patients with absence of symmetry of EEG and direct them to the expert.
Definition of phase shift is based on representation of signal of EEG by model of an analytical signal on Hilbert. In this case random process looks like: I.e. random process is considered as the harmonious fluctuation modulated on amplitude and a phase by stochastic functions and . Calculation of these functions allows to observe change of amplitude and phase of EEG in time, and also to investigate change in time of instant and average frequencies of fluctuations, if to approach to concept of frequency as derivative full phase of oscillatory process. Such method of the analysis allows characterizing numerically duration and frequency of change of separate rhythms.
Definition of a full phase with the help of integrated transformations of Hilbert, allows receiving some additional information on stability of frequency characteristics, stationarity time and character of transitive modes in oscillatory process. The difference of phases of two abductions of symmetric areas of a brain allows estimating symmetry on a phase