On Parametrization of Compact Wavelet Matrices

TL;DR

This paper introduces an efficient parametrization method for wavelet matrices using Wiener-Hopf factorization, enabling real-time construction of wavelet matrix coefficients for applications in signal processing.

Contribution

It provides a complete parametrization of wavelet matrices based on polynomial paraunitary matrix-functions, facilitating real-time coefficient computation.

Findings

Complete parametrization of wavelet matrices achieved

Real-time construction of wavelet matrix coefficients demonstrated

Utilizes Wiener-Hopf factorization for efficient computation

Abstract

It is given an efficient complete parametrization of wavelet matrices of rank $m$, genus $g+1$, and degree $g$, which are naturally identified with corresponding polynomial paraunitary matrix-functions. The parametrization depends on Wiener-Hopf factorization of unitary matrix-functions with constant determinant given in the unit circle. This method allows us to construct in real time the coefficients of wavelet matrices from the above class.