S. Kung

A Toeplitz approximation approach to coherent source direction finding

In this paper, the Toeplitz Approximation Method (TAM) of stochastic system identification is applied to the linear equal spaced array narrowband source direction finding problem. The proposed algorithm provides high resolution direction finding capability and is designed for an arbitrary noise, multipath signal environment. As such, it extend existing capability in fields such as passive sonar, radar and communications. A comparitive simulation between TAM and the MUSIC method, using spatial smoothing, is presented which are based on low signal-noise-ratio (SNR) data and a multipath environment.

Toeplitz eigensystem solver

In this paper, a novel algorithm for computing the minimum eigenvalue and associated eigenvector is presented. This algorithm is a derivative of the inverse iteration method which requires a linear system to be solved in each iteration. Taking advantage of the Toeplitz structure, a pipelined Toeplitz system solver can be applied to solve the Toeplitz system in O(N) time units with O(N) processors. This brings the total computing time for solving the Toeplitz minimum eigenvalue down to O(KN) time units where K is the number of iterations. This algorithm makes it possible to perform real time processing of the Pisarenkos high resolution spectrum estimate.

Some notes on valuation theory in linear systems

In recent years, there has been an increasing interest in the pole-zero structure of multivariable sytems, at both finite and infinite frequencies. However, in most present approaches there is a certain asymmetry (which we shall elaborate below) in the treatment of the finite and infinite points. In this paper, we shall indicate how the language of valuation theory can be used to give a more uniform treatment of finite and infinite frequencies and more generally of polynomial and rational matrices.

A new predictive efficiency criterion for approximate stochastic realization

The problem addressed in this paper is that of realizing a minimum phase ARMA model for a stochastic process, from noisy measurements or estimates of its covariance lags. The new algorithm proposed in this paper optimizes the covariance approximation in terms of the predictive efficiency of the current state vector for the future of the output process. Reasons for preferring the new approximation criterion to canonical correlation analysis are presented, and illustrated with the help of a counter example. Simulations indicate that the new method is capable of high resolution estimates, as compared with existing methods.

Highly parallel architectures for solving linear equations

An important impact of the fast growing VLSI device technology will be the massive capability of parallel processing which will in turn greatly affect the trend of modern signal processing technology. For the new trend it will be a necessity to have revolutionary architectural design concepts such as topological mapping between algorithm and architecture, simple and regular data flow etc [1]. In this paper, based on a natural topology of the computing structure, a novel computational wave-front notion is introduced for describing and and validating data flow in locally connected networks. The parallel architectures include the linear system, with and without pivoting, and the least-square solver using Givens method. We believe that this set of linear system architectures will play a central role in modern signal processing.

A Matrix Data Flow Language/Architecture for Parallel Matrix Operations Based on Computational Wavefront Concept

This paper focuses on revolutionary parallel architecture and language concepts for a class of matrix operations which are fundamental for signal processing computations. Based on the notion of computational wavefront, a data flow language for matrix array processors is developed and a new processor architecture tailored to this language is proposed. Simulations were done in global and local levels and both of them report encouraging success.

Improved Pisarenko's sinusoidal spectrum estimate via SVD subspace approximation methods

This paper presents two numerically stable Pisarenko type spectrum estimators based on a subspace approximation approach. A sinusoidal signal plus noise model is assumed. By using the singular value decomposition, the covariance matrix is decomposed into a signal subspace which represents the signal component; and a noise subspace which represents the noise contributions. The first method makes use of a signal subspace structure which characterizes the signal covariance matrix by a linear system triple (A, b, c). Then the frequencies of the signal sinusoids are solved as the eigenvalues of the A matrix. The second method utilizes a Toeplitz structure of the noise subspace. Then a subspace approximation procedure is taken to find an estimate of this noise subspace. The frequency estimates are then solved as the roots of the defining sequence of this Toeplitz noise subspace matrix. Simulation results are furnished to illustrate the advantages of these proposed new methods.

A unification of system equivalence definitions

The concept of system equivalence was introduced by Rosenbrock to generalize the notion of system similarity to nonstate-space models, i.e., to systems described by polynomial operators. The idea of equivalence is relatively natural: given two descriptions of the same physical system by two different observers, we would like to assert whether these descriptions are the same from a coordinate-free point of view. In this paper, system equivalence is studied from both the polynomial and the state-space points of view. Previous definitions of system equivalence are connected together, and an alternative definition is proposed. This new approach is based on constructing complete information sets for a given differential system by expanding its usual input/ output map. This idea generalizes the earlier concept of maximal-strict system equivalence introduced by Morf.

Highly concurrent Toeplitz eigen-system solver for high resolution spectral estimation

In this paper, we develop a highly concurrent Toeplitz Eigen-System Solver (TES) for computing the minimum eigenvalue and associated eigenvector of a N by N symmetric Toeplitz matrix. Conventionally, solving an eigen-system will require O(N3) times with sequential machine; or O(N2) time with O(N) processing units. By exploring the Toeplitz structure and adopting a Rayleigh quotient iteration, the TES can solve for the desired minimum eigenvalue in O(KN) time with N processors and K iterations. The development of TES offers a fast algorithm to implement the Pisarenkos high resolution spectral estimation technique.

Analysis and implementation of the adaptive notch filter for frequency estimation

This paper enhances some theoretical and implementation aspects of a constrained autoregressive moving average model, the notch filter model developed in [1] for the estimation of sinusoidal signals in additive, uncorrelated noise, colored or white. This model is shown to approximate the actual signal plus noise model. In addition, the parameter estimates obtained by minimization of the output power of the notch filter approximate the maximum likelihood estimate of the model parameters. The relationship of the notch filtering approach to the existing autoregressive and Pisarenke methods is established. Next, a scheme to combine fast convergence and unbiased estimation is suggested. Lastly, certain implementation aspects of the filter are considered and the method is shown to be amenable to parallel processing.