Lasha Ephremidze

Lasha Ephremidze, Edem Lagvilava

A new parametrization (one-to-one onto map) of compact wavelet matrices of rank $m$ and of order and degree $N$ is proposed in terms of coordinates in the Euclidian space $R^{(m-1)N}$. The developed method depends on Wiener-Hopf factorization of corresponding unitary matrix functions and allows to construct compact wavelet matrices efficiently. Some applications of the proposed method are discussed.

Nika Salia, Alexander Gamkrelidze, Lasha Ephremidze

Factorization of compact wavelet matrices into primitive ones has been known for more than 20 years. This method makes it possible to generate wavelet matrix coefficients and also to specify them by their first row. Recently, a new parametrization of compact wavelet matrices of the same order and degree has been introduced by the last author. This method also enables us to fulfill the above mentioned tasks of matrix constructions. In the present paper, we briefly describe the corresponding algorithms based on two different methods, and numerically compare their performance

Lasha Ephremidze, Aleksander Gamkrelidze, Edem Lagvilava

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