Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization

TL;DR

This paper presents a method for designing orthogonal multiwavelets using matrix spectral factorization, demonstrating a simple filter construction, algebraic derivation of the wavelet, and numerical experiments to analyze its properties.

Contribution

It introduces a straightforward approach to construct orthogonal multiwavelets via matrix spectral factorization with algebraic techniques considering symmetry.

Findings

Constructed a simple matrix filter with desirable properties

Derived the orthogonal multiwavelet SA1 explicitly

Performed numerical experiments analyzing the influence of calculation precision

Abstract

We consider the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization (MSF). As a test problem, we construct a simple matrix product filter with desirable properties, and factor it using Bauer's method, which in this case can be done in closed form. The corresponding orthogonal multiwavelet function is derived using algebraic techniques which allow symmetry to be considered. This leads to the known orthogonal multiwavelet SA1, which can also be derived directly. We also give a lifting scheme for SA1, investigate the influence of the number of significant digits in the calculations, and show some numerical experiments.