Edem Lagvilava

A New Method of Matrix Spectral Factorization

A new algorithm of matrix spectral factorization is proposed which can be applied to compute an approximate spectral factor of any positive definite matrix function which satisfies the Paley-Wiener condition.

A new efficient matrix spectral factorization algorithm

An absolutely new method of matrix spectral factorization is proposed which leads to the most simple computational algorithm. A demo version of the software implementation is located at www.ncst.org.ge/MSF-algorithm.

An approximation of Daubechies wavelet matrices by perfect reconstruction filter banks with rational coefficients

It is described how the coefficients of Daubechies wavelet matrices can be approximated by rational numbers in such a way that the perfect reconstruction property of the filter bank be preserved exactly.

Rank-deficient spectral factorization and wavelets completion problem

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.