On Signal Dependent Basis Functions, Estimation of Event Related Potentials and Multiple Window Spectrum Analysis

Abstract: The three parts of this thesis are different examples of utilization of signal dependent basis functions in the estimation procedure. The first part surveys a number of parametric methods applied to estimation of single ERP (P300). The basis functions of the sERP are the damped sinusoids where the frequency and damping factor are estimated from the signal. The algorithms for white noise disturbance are known, and they are here also developed for coloured noise disturbance. Evaluations are made for simulated sERP conditions, i.e., short data sequences with low-frequency content and low signal-to-noise ratio. The algorithms are also applied to real data measurements. In the second part, a new system for automatic tracking of the depth of anaesthesia is proposed. The amplitude and latency of the Nb-trough are used as tracking parameters. Signal dependent basis functions are obtained by filtering a long average in a bandpass-filterbank. The basis functions are adapted to a shorter average, and the waveform of the AEP is estimated. The system detects changes in the state of consciousness with a maximum delay of 52 s. A multiple window method where the windows are matched to a peaked power density spectrum is proposed in the third part. The advantage of the method is that model assumptions of the measured spectrum are unnecessary. The windows are derived as Karhunen-Loeve basis functions of a known peaked power density spectrum. With a penalty function, the optimization procedure can be constrained with resulting control of sidelobes. Suppression of sidelobes outside the predetermined resolution bandwidth will prevent leakage from frequencies outside the mainlobe width.