Nonlinear Signal Processing

The median LMS is proposed to reduce the effects of input noise and to adapt more intelligently in an impulsive environment. Analysis and simulations demonstrate this to be a powerful new adaptive technique.

G. A. Williamson, P. Clarkson, and W. A. Sethares, "Performance characteristics of the adaptive median LMS filter," IEEE Trans. on Signal Processing, Vol. 41, No. 2, pp. 667-680, Feb. 1993.

W. A. Sethares and J. A. Bucklew, "Local stability of the median LMS filter," IEEE Trans. on Signal Processing, Vol. 42, No. 11, pg. 2901-2906, Nov. 94.

Adaptive filtering algorithms applied to the problem of learning nonlinear decision regions. Stochastic averaging theory is generalized to consider stepsize dependent nonlinearities, and is then applied to prove local stability of the proposed algorithms.

J. A. Bucklew and W. A. Sethares, "The covering problem and m- dependent adaptive algorithms," IEEE Trans. on Signal Processing, Vol. 42, No. 10, pg. 2616-2627, Oct. 94.

A new approach to the smoothing of discontinuous signals is suggested. The approach is justified by an extension of the Kalman filter to the nonlinear case.

M. Niedzwiecki and W. A. Sethares, "Smoothing of discontinuous signals: the competitive approach," IEEE Trans. on Signal Processing, Vol. 43, No. 1, pg. 1-12, Jan. 95.

A population-based gradient algorithm that can be guaranteed to converge to the global minimum. Estimates of size of optimal population are obtained via a deterministic averaging approach.

K. L. Blackmore, R. C. Williamson, I. M. Y. Mareels, and W. A. Sethares, "Online Learning via Congregational Gradient Descent," Mathematics of Controls, Systems, and Signals, 10:(4) 331-363, 1997.

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