A MULTICHANNEL TIME-VARYING FILTER FOR ESTIMATING NONSTATIONARY SIGNALS IN NOISE (EVOKED POTENTIAL, SIGNAL PROCESSING, ELECTROENCEPHALOGRAM, IMPLEMENTATION)
Abstract
This thesis discusses the theoretical design, practical implementation, and performance of a multichannel time-varying estimator for nonstationary signals in noise. The estimator takes the form of the optimum linear digital filter derived under the criterion of minimum mean-square error between the output of the filter and the signal being estimated (which is present in one of the channels). The original contributions of this research are twofold: (1) a robust implementation theory for digital optimum linear filters and (2) a new estimate of the transient signal characteristically evoked by the human brain in response to an effective sensory stimulus. By developing an improved single response estimate of this evoked potential (EP), it is hoped that researchers will achieve a better understanding of the human brain. Design of the filter requires knowledge of the cross-correlation matrices of the received data from the different channels and of the cross-correlation matrices between the desired signal and the signals in the other channels. The cross-correlations may be known a priori, estimated from ensembles of responses a posteriori, or estimated from models of the random processes. Problems with the large dimensionality and ill-conditioned nature of the matrix estimates are discussed in detail. Practical implementations are considered and a minimum norm least squares (MNLS) solution to the optimum filter matrix equation is derived. The MNLS implementation involves a tradeoff between signal resolution and noise reduction. It is especially suited to a posteriori optimum filtering problems because the models and estimates used to design the optimum filter are often somewhat different from the statistics of the input signal and noise processes. Several filters are designed for simulated and human visual EP data. Filters are also designed for a nonstationary communications problem. Filter performance is evaluated using the criteria of mean-square error, signal bias, noise reduction, and output signal-to-noise ratio. The extension to multiple channels is shown to improve performance considerably and to provide valuable spatial and component information.
Degree
Ph.D.
Subject Area
Electrical engineering
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