Real-time identification of parameters of the ARMA model of the human EEG waveforms

Electroencephalogram (EEG) can provide important information about the functioning of the human brain. In particular, the EEG waveforms manifest certain changes due to application of drugs, such as general anesthetics. Measurement of the changes in the EEG waveforms in real time, may therefore be used to determine the global effects of the administered drug. Among numerous mathematical techniques used in the analysis of the EEG waveforms, perhaps, the fast Fourier transform (FFT) is the most widely used. Recently some researchers have suggested the use of the autoregressive moving average (ARMA) model for the EEG analysis. In this method the coefficients of the ARMA model are identified and used to describe the waveform. We consider a first order ARMA model, and use the Extended Least Squares (ELS) and its recursive version (RELS) for parameter estimation. The identified parameters are then used to describe the time-domain or the frequency-domain properties of the EEG waveforms. Since the parameters of the model may change with time, a forgetting factor is incorporated in the RELS algorithm to allow for tracking of time varying parameters. The advantage of recursive estimation of the coefficients of the ARMA model over the non-recursive estimation and the FFT method, is substantial reduction in computation as well as its capability to track the time varying process.