A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feed-forward memory connections, wideband array processing, and in problems with a multi-input, multi-output network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...

This paper introduces a new algorithm for blind equalization which uses a set of cost functions. Each of them guarantees a closed form solution of the equalization problem and approximates the ideal MSE (mean square error) solution. On the basis of an iterative process the best approximation is selected. Application of this algorithm is not limited to linear equalizers operating at symbol rate. As a possible generalization to include other areas (such as system identification, decision-feedback equalization or fractionally spaced equalization), an extension to fractional tap space equalizers is outlined.

A method for whitening a polynomial matrix is described, including the calculation of the eigenvalue polynomials and eigenvector polynomials of an FIR polynomial matrix. The multichannel blind deconvolution problem is briefly described and FIR polynomial matrix whitening is applied to the problem. Benefits of the whitening technique are demonstrated through simulation. Data prewhitening or the use of an exact least squares adaptation is necessary in any problem of moderate complexity. The group theoretic aspects of FIR polynomial matrix algebra are discussed. 1. INTRODUCTION AND MOTIVATION A method for whitening a multichannel linear system is presented. Multiple input and multiple output linear systems are considered. A two input and two output system would be written as H = h 11 h 21 h 12 h 22 : (1) The h ij 's are FIR filters which each represent an acoustic multi-path transfer function from source i to sensor j. Referring to Figure 1, a two-sensor, two-source problem can...

Current methods of estimation of the univariate spectral density are reviewed and some improvements are suggested. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements rather than competes with the popular ARIMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Two new algorithms for fast computation of the autoregressive spectral density function are presented. A new style of plotting the spectral density function is suggested. Exploratory spectral analysis of a number of hydrological time series is performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in riverflow time series is discussed with long riverflow, treering and mud varve series. A comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. The software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca in the directory pub\mhts.

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