Charles W. Therrien

A new 2-D fast RLS algorithm

A two-dimensional fast recursive least-squares algorithm is presented using a geometrical formulation based on the mathematical concepts of vector space, orthorgonal projection, and subspace decomposition. By appropriately ordering the 2-D data, the algorithm provides an exact least-squares solution to the deterministic normal equations. The method is further extended to the general FIR (finite impulse response) Wiener filter and the ARMA (autoregressive moving-average) modeling. The size and shape of the support region for both the MA and AR coefficients of the filter can be chosen arbitrarily.<<ETX>>

Design of 2-D FIR filters by nonuniform frequency sampling

A method for the frequency-sampling design of two-dimensional FIR filters with nonuniformly spaced samples is presented. By imposing some mild constraints on sample location in the 2-D frequency plane, the method always provides a unique design solution. Important characteristics of the method are design flexibility through the use of nonuniform samples and computational efficiency. This method is compared with the uniform sampling, inverse discrete Fourier transform (DFT) approach and also with a general method for filter design called arbitrary sampling. The method presented is shown to require much less computation than the arbitrary sampling approach, which may lead to possible degenerate cases where there is no unique solution for the filter. The method proposed does not lead to such degeneracies and possesses more flexibility than the uniform sampling method. Examples are given in order to compare the new method with the uniform sampling method. >

Multichannel 2-D AR spectrum estimation

Spectral estimation for multiple 2-D signals by autoregressive modeling is discussed. The procedure computes the entire spectral matrix of autospectra and cross spectra for the set of 2-D signals. Specific differences between AR models for this problem and those for lower dimensional problems are discussed. Experimental results are presented. >

A direct algorithm for computing 2-D AR power spectrum estimates

An algorithm for computing the parameters in a 2-D autoregressive spectral estimate without prior estimation of the correlation is described. The algorithm utilizes the multichannel form of the Burg algorithm and the relation between multichannel and 2-D AR modeling. The procedure permits computation of the spectral matrix for several channels of 2-D data; models with support in different quadrants are combined to form the spectral estimate. >

Optimal filtering with multirate observations

This paper considers the problem of optimal filtering for several channels of observations occurring at different sampling rates. The problem is formulated in general terms with arbitrary sampling rates for the observations. The set of observation sequences (channels) are jointly cyclostationary and the resulting optimal filters are linear and periodically time-varying (LPTV). A formula for the period of the system is given and the explicit forms of the Wiener-Hopf equations and the estimation error variance are derived. Simulation results are presented for estimation of a signal with known correlation function in noise using two observation sequences with sampling rates differing from that of the underlying signal to be estimated.

Least squares optimal filtering with multirate observations

The paper addresses the problem of optimal filtering from a least squares perspective when multiple observation sequences are available with differing sampling rates. In such cases, the processes are jointly cyclostationary and the resulting linear optimal filters are periodically time-varying. The data matrices for this problem have an interesting structure and we develop the form of the resulting least squares multirate Wiener-Hopf equations. Filtering results are illustrated for a typical example and issues of computation and amount of training data needed are investigated.

Issues in multirate statistical signal processing

The statistical analysis of random signals and noise is traditionally carried out under the assumption of wide sense stationarity. In the processing of signals through systems at multiple data rates, even local stationarity is not always a valid assumption. While a stationary discrete-time signal that is down-sampled at a multiple of the original sampling rate retains wide sense stationarity, the same may not be true for a signal that is interpolated and processed at a higher rate. Such multirate signals however exhibit cyclostationarity and can be optimally processed by periodically time-varying systems. This paper discusses some issues in the theory of multirate random signals, and suggests some structures for optimal filtering for combinations of these signals.

Multirate filtering and estimation: the multirate Wiener filter

In this paper we address the problem of estimating a random process from two observed signals at different sampling rates. In particular, we consider the case where one of the observed signals is sampled at half the rate of the other. The optimal filter for this problem is derived as a linear filter with periodically varying coefficients. We provide quantitative expressions for the reduction in mean-square error due to added observations at the lower sampling rate.

An iterative Prony method for ARMA signal modeling

A new iterative version of the Prony method is presented and shown to be exceptionally effective in finding ARMA models for acoustic data in the time domain. The method is based on a quadratic type of gradient algorithm, where it is shown that the gradient and Hessian are easily computed from the data. The new algorithm is found experimentally to have excellent convergence behavior. The performance of the algorithm is demonstrated and compared with that of the original Prony method and with that of the Steiglitz and McBride (1965) iterative prefiltering algorithm on some recorded acoustic data. >

A hidden Markov model approach to the classification of acoustic transients

A system for the detection and classification of acoustic transients based on hidden Markov model (HMM) methods is described. The system was tested using two different sets of data. The results from these tests are summarized and compared to some other known algorithms and to the performance of human beings. The effect of observation noise on the training and classification process is also discussed, and results using different noise-correction techniques are presented.<<ETX>>