where j is √ 01, K is the number of frequency comFernández del RıB o, J. E., and Sarkar, T. K., Comparison ponents, and Am is the complex amplitude at frebetween the Matrix Pencil Method and the Fourier Transquency fm . form Technique for High-Resolution Spectral Estimation, The time function is sampled at N equispaced Digital Signal Processing 6 (1996), 108–125. points, Dt apart. Hence (2.1) r...

Some recent works address the problem of blind source separation with a matrix pencil. In this paper we show that the covariance matrices of the pencil can be computed at the output of a simple linear filter instead of using time-delayed covariance matrices. It is also shown, using block matrix manipulation, that the method might applied when the number of source signals is not equal to the num...

Absfracf-We present a study of a matrix pencil method for estimating parameters (frequencies and damping factors) of exponentially damped and/or undamped sinusoids in noise. Comparison of this method to a polynomial method (SVD-Prony method) shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach but the pencil method i s more efficien...

We consider minimization of a quadratic objective function subject to a sign-indefinite quadratic equality constraint. We derive necessary and sufficient conditions for the existence of solutions to the constrained minimization problem. These conditions involve a generalized eigenvalue of the matrix pencil consisting of a symmetric positivesemidefinite matrix and a symmetric indefinite matrix. ...

In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been us...

A new and simple approach for calculating the eigenstructure of a regular matrix pencil is presented. This proposed approach transforms the generalized eigenvalues problem into a usual eigenvalues problem, and it also can be used to calculate the Weierstrass form of a regular matrix pencil. Mathematics Subject Classification: 93B55

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications. First, the characterization yields a singular value formula for determining the nearest pencil whose eigenvalues lie in a...