On compact wavelet matrices of rank m and of order and degree N

TL;DR

The paper introduces a new parametrization method for compact wavelet matrices of specific rank, order, and degree, enabling efficient construction through Wiener-Hopf factorization with practical applications.

Contribution

It presents a novel one-to-one parametrization of wavelet matrices using Euclidean space coordinates, improving construction efficiency via Wiener-Hopf factorization.

Findings

New parametrization of wavelet matrices in Euclidean space

Efficient construction method using Wiener-Hopf factorization

Discussion of practical applications of the method

Abstract

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.