scholarly journals Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization

2019 ◽  
Vol 39 (4) ◽  
pp. 2006-2041
Author(s):  
Vasil Kolev ◽  
Todor Cooklev ◽  
Fritz Keinert
Keyword(s):  
Spectral Factorization ◽  
Matrix Spectral Factorization

scholarly journals A New Method of Matrix Spectral Factorization

2011 ◽  
Vol 57 (4) ◽  
pp. 2318-2326 ◽  
Author(s):  
G Janashia ◽  
E Lagvilava ◽  
L Ephremidze
Keyword(s):  
New Method ◽  
Spectral Factorization ◽  
Matrix Spectral Factorization

scholarly journals On explicit Wiener–Hopf factorization of 2 × 2 matrices in a vicinity of a given matrix

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200027 ◽  
Author(s):  
L. Ephremidze ◽  
I. Spitkovsky
Keyword(s):  
Numerical Simulations ◽  
Matrix Function ◽  
Factorization Method ◽  
Spectral Factorization ◽  
Engineering Applications ◽  
Partial Indices ◽  
Matrix Spectral Factorization

As it is known, the existence of the Wiener–Hopf factorization for a given matrix is a well-studied problem. Severe difficulties arise, however, when one needs to compute the factors approximately and obtain the partial indices. This problem is very important in various engineering applications and, therefore, remains to be subject of intensive investigations. In the present paper, we approximate a given matrix function and then explicitly factorize the approximation regardless of whether it has stable partial indices. For this reason, a technique developed in the Janashia–Lagvilava matrix spectral factorization method is applied. Numerical simulations illustrate our ideas in simple situations that demonstrate the potential of the method.

scholarly journals An elementary proof of the polynomial matrix spectral factorization theorem

2014 ◽  
Vol 144 (4) ◽  
pp. 747-751 ◽  
Author(s):  
Lasha Ephremidze
Keyword(s):  
Unit Circle ◽  
Linear Algebra ◽  
Simple Proof ◽  
Real Line ◽  
Complex Analysis ◽  
Elementary Proof ◽  
Polynomial Matrix ◽  
Spectral Factorization ◽  
Factorization Theorem ◽  
Matrix Spectral Factorization

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

Rank-deficient spectral factorization and wavelets completion problem

2015 ◽  
Vol 13 (03) ◽  
pp. 1550013 ◽  
Author(s):  
L. Ephremidze ◽  
I. Spitkovsky ◽  
E. Lagvilava
Keyword(s):  
Polynomial Matrix ◽  
Elementary Solution ◽  
Spectral Factorization ◽  
Factorization Theorem ◽  
Constructive Proof ◽  
Completion Problem ◽  
Matrix Spectral Factorization

A simple constructive proof of polynomial matrix spectral factorization theorem is presented in the rank-deficient case. It is then used to provide an elementary solution to the wavelets completion problem.

scholarly journals Matrix spectral factorization for SA4 multiwavelet

2017 ◽  
Vol 29 (4) ◽  
pp. 1613-1641 ◽  
Author(s):  
Vasil Kolev ◽  
Todor Cooklev ◽  
Fritz Keinert
Keyword(s):  
Spectral Factorization ◽  
Matrix Spectral Factorization
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