Non-Gaussian statistical signal processing is important when signals and/or noise deviate from the ideal Gaussian model. Stable distributions are among the most important non-Gaussian models. They share defining characteristics with the Gaussian distribution, such as the stability property and central limit theorems, and in fact include the Gaussian distribution as a limiting case. To help engineers better understand the stable models and develop methodologies for their applications in signal processing. A tutorial review of the basic characteristics of stable distributions and stable signal processing is presented. The emphasis is on the differences and similarities between stable signal processing methods based on fractional lower-order moments and Gaussian signal processing methods based on second-order moments. >

Signal processing with fractional lower order moments: stable processes and their applications

A new method for analysis of electroencephalogram (EEG) signals using empirical mode decomposition (EMD) and Fourier-Bessel (FB) expansion has been presented in this paper. The EMD decomposes an EEG signal into a finite set of band-limited signals termed intrinsic mode functions (IMFs). The mean frequency (MF) for each IMF has been computed using FB expansion. The MF measure of the IMFs has been used as a feature in order to identify the difference between ictal and seizure-free intracranial EEG signals. It has been shown that the MF feature of the IMFs has provided statistically significant difference between ictal and seizure-free EEG signals. Simulation results are included to illustrate the effectiveness of the proposed method.

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Discrimination between ictal and seizure-free EEG signals using empirical mode decomposition

Develops a new iterative reweighted least squares algorithm for the design of optimal L/sub p/ approximation FIR filters. The algorithm combines a variable p technique with a Newton's method to give excellent robust initial convergence and quadratic final convergence. Details of the convergence properties when applied to the L/sub p/ optimization problem are given. The primary purpose of L/sub p/ approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained L/sub 2/ approximation filters. The new method can also be applied to the complex Chebyshev approximation problem and to the design of 2D FIR filters. >

Iterative reweighted least-squares design of FIR filters

An adaptive FIR filter based on the least mean p-power error (MPE) criterion is investigated. First, some useful properties of MPE function are studied. Three main results are as follows: 1) MPE function is a convex function of filter coefficients; so it has no local minima. 2) When input process and desired process are both Gaussian processes, then MPE function has the same optimum solution as the conventional Wiener solution for any p. 3) When input process and desired process are non-Gaussian processes, then MPE function may have better optimum solution than Wiener solution. Next, a least mean p-power (LMP) error adaptive algorithm is derived and some application examples are presented. Consequently, when the signal is corrupted by an impulsive noise, the adaptive algorithm with p=1 is preferred. Furthermore, when the signal is corrupted by noise or interference, the adaptive algorithm with proper choice of p may be preferred. >

Least mean p-power error criterion for adaptive FIR filter

Fast communication: EEG signal analysis using FB expansion and second-order linear TVAR process

Signal Processing via Fourier-Bessel Series Expansion

Signal processing via Fourier-Bessel series expansion

L p normed minimization with applications to linear predictive modeling for sinusoidal frequency estimation

Lp normed model based filter design

Current results in fast algorithm computational complexity analysis, computer architecture design, and VLSI hardware advances with applications to digital signal processing

Jim Schroeder

Papers

Signal Processing via Fourier-Bessel Series Expansion

Signal processing via Fourier-Bessel series expansion

L p normed minimization with applications to linear predictive modeling for sinusoidal frequency estimation

Lp normed model based filter design

Current results in fast algorithm computational complexity analysis, computer architecture design, and VLSI hardware advances with applications to digital signal processing