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This paper describes a method for estimating the parameters of an autoregressive AR process from a nite number of noisy measurements. The method uses a modi ed set of Yule-Walker equations that lead to a quadratic eigenvalue problem which when solved, gives estimates of the AR parameters and the measurement noise variance.

Weighted averages of brain evoked potentials (EP's) are obtained by weighting each single EP sweep prior to averaging. These weights are shown to maximize the signal-to-noise ratio (SNR) of the resulting average if they satisfy a generalized eigenvalue problem involving the correlation matrices of the underlying signal and noise components. The signal and noise correlation matrices are difficult to estimate and the solution of the generalized eigenvalue problem is often computationally impractical for real-time processing. Correspondingly, a number of simplifying assumptions about the signal and noise correlation matrices are made which allow an efficient method of approximating the maximum SNR weights. Experimental results are given using actual auditory EP data which demonstrate that the resulting weighted average has estimated SNR's that are up to 21% greater than the conventional ensemble average SNR.

This paper describes two new algorithms for tracking the subspace spanned by the principal eigenvectors of the correlation matrix associated with time-domain (i.e. time series) data. The algorithms track the d principal N -dimensional eigenvectors of the data covariance matrix with a complexity of O(Nd 2 ), yet have performance comparable to algorithms having O(N 2 d) complexity. The computation reduction is achieved by exploiting the shift-invariance property of temporal data covariance matrices. Experiments are used to compare our algorithms with other well-known approaches of similar and/or lower complexity. Our new algorithms are shown to outperform the subset of the general approaches having the same complexity. The new algorithms are useful for applications such as subspace-based speech enhancement, and low-rank adaptive filtering.

A new algorithm for doing signal averaging of steady-state visual evoked potentials (VEP's) is described. The subspace average is obtained by finding the orthogonal projection of the VEP measurement vector onto the signal subspace, which is based on a sinusoidal VEP signal model. The subspace average is seen to out-perform the conventional average using a new signal-to-noise-ratio-based performance measure on simulated and actual VEP data.