OPTIMUM TIME VARYING FILTERS FOR TRANSIENT WAVEFORM ANALYSIS
Abstract
This research is concerned with the extraction and analysis of transient waveforms in the presence of noise. A transient signal is a nonstationary signal which is characterized by a distinct onset and a finite duration. This situation occurs, for example, whenever the transient signal is generated by application of a stimulus or other excitation. For the experimental data considered here the transient corresponds to evoked brain potentials resulting from the application of sensory inputs. The primary objective of this research is to improve information extraction from such waveforms thereby improving utilization of the evoked potential as a clinical tool and as an aid in the basic understanding of the functions of the brain. The use of a linear time varying filter is investigated for the estimation of transient signals in the presence of an additive noise process. The filtering operation can be interpreted as a projection of the observations into signal space of reduced dimensionality. Efficient algorithms are developed to reduce computer storage and computation time requirements. The optimal filter depends on knowledge of the signal and noise statistics. However, in practice it is almost always necessary to take into account the imperfect and imprecise knowledge of the a priori information. This leads to modifications of the optimal filter and an extension to Kalman Filtering. Multichannel filters which make use of the measurements from multiple electrode sensors are investigated as a means of obtaining improved estimation. An investigation has been carried out which relates the coupling effects and spatial correlation of visual evoked brain potentials and the electroencephalogram. The coupling factors computed provide an improved quantification of the distinct components of the Event Related Potentials in the individual waveforms. The characterization of the basis functions is also useful for making further improvements in signal extraction procedures. Peak parameters such as signal amplitude and location are important in many applications of signal processing. A least square fitting procedure is described to identify the peak parameters. The effects of noise on the peak location and the amplitude variation are then investigated for various signal-to-noise ratios. Furthermore, location jitter which depends on the signal shape and noise characteristics is quantified here in terms of the radius of curvature at the peak position, the bandwidth, the duration and the signal-to-noise ratio.
Degree
Ph.D.
Subject Area
Electrical engineering
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