Polynomial Matrix Spectral Factorization

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(PDF) On algorithmization of Janashia-Lagvilava matrix spectral ...

In this paper, we extend the basic idea of the Janashia–Lagvilava algorithm to adapt it for the spectral factorization of positive-definite polynomial matrices on the real line. This extension

Various polynomial matrix factorisations have been addressed, such as the Smith–Macmillan form [19], or polynomial matrix factors that are paraunitary (PU) or lossless [20–33]. Typically, the

Controller Design Using Polynomial Matrix Description

For the theory of common multiples and divisors of matrix polynomials from the spectral analysis point of view, see Gohberg et al. (1978a, 1978b, 1981, 1982a), also the book Gohberg et al.

Abstract: A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on

Such a polynomial possesses the spectral factorization (3) with \(Y = X{\kern 1pt} *\); see, e.g., [21, 30] or [].. The conditions (21) ensure that the spectrum of the quadratic matrix

On factorization of matrix polynomials
About the Newton iteration for spectral factorization
arXiv:2112.01143v1 [math.CA] 2 Dec 2021

In multiwavelet theory, scalar or matrix spectral factorization plays a key role. Finding spectral factors of para-Hermitian polynomial matrices (which are product filters in

Numerical algorithms for the canonical J-factorization of polynomial matrices with respect to the imaginary axis are given. The factorization problems for the non-regular

All the procedures above are either directly programmed or can be easily composed from the functions of Polynomial Toolbox for Matlab, which is a third-party Matlab toolbox for

arXiv:2112.01143v1 [math.CA] 2 Dec 2021

Download scientific diagram | Polynomial-Matrix Spectral factorization via feedback. from publication: Control theoretical approach to multivariable spectral factorisation problem | It is

Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to functions useful in control theory systems, basis functions in numerical methods or

In this paper, algorithms are developed for the problems of spectral factorization and sum of squares of polynomial matrices with n indeterminates.

The J-spectral factorization of para-Hermitian polynomial matrices has important applications in control and systems theory, as described first in Wiener (1949).See e.g.

polynomial matrices over the real line, over the imaginary axis and over the unit circle. 1 Introduction Positive transfer functions play a fundamental role in sys-tems and control theory:

An elementary proof of the polynomial matrix spectral factorization theorem – Volume 144 Issue 4 Skip to main content Accessibility help We use cookies to distinguish you

D.A. Bini and A. Bottcher, Polynomial factorization through Toeplitz matrix computations, Linear Algebra Appl. 366 (2003) 25–37. Google Scholar D. Bini, G. Del Corso, G. Manzini and L.

The determinant of a polynomial with matrix coefficients may be independent of Z. Applied to matrix filters, this may mean that an inverse filter may have only a finite number of powers in Z

The Toeplitz method of spectral factorization is based on special properties of Toeplitz matrices In this chapter we introduce the Toeplitz matrix to perform spectral

Keywords: spectral factorization, Toeplitz matrices, Euler-Frobenius polynomials, Daubechies wavelets. AMS subject classification: 12D05, 15A23. 1. Introduction Our recent

Kwakernaak H. and Šebek M. (1994). Polynomial J-Spectral Factorization. IEEE Trans. Autom. Control, 39(2), 315-328. [Collection of several algorithms for the J-spectral factorization of a

In this paper, algorithms are developed for the problems of spectral factorization and sum of squares of polynomial matrices with n indeterminates, and a natural interpretation

In this factorization, S is a symmetric matrix and G is a square, stable, and minimum-phase system with unit (identity) feedthrough. G‘ is the conjugate of G, which has transfer function

By using the PEVD algorithm, the multichannel spectral factorization problem is simply broken down to a set of single channel problems which can be solved by means of existing one

Multichannel spectral factorization algorithm using polynomial matrix eigenvalue decomposition Abstract: In this paper, we present a new multichannel spectral factorization algorithm which

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex

Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design.

It is shown how with analogy to analogue theory, that the problem of control polynomial-matrix spectral factorization can be solved using negative feedback. This recursive method is

In this paper, we extend the basic idea of the Janashia–Lagvilava algorithm to adapt it for the spectral factorization of positive-definite polynomial matrices on the real line.

J-spectral factorization of polynomial matrices, we propose an algorithmic solution to hyperbolic QR factorization of a rank de cient constant matrix. Application to reduced-order H 1 ltering is

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis

In this paper, recently published results on matrix spectral factorization is reviewed, and their connection to wavelet matrices is revealed.

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