# Bauer's Spectral Factorization Method for Low Order Multiwavelet Filter Design

arXiv: https://arxiv.org/abs/2312.05418 · HTML: https://mlsanity.com/paper/2312.05418/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 51 references that are in the map.
- First posted on arXiv 9 Dec 2023.

## Builds on (most cited first, 2 of 2)

- [Matrix Spectral Factorization for SA4 Multiwavelet](https://mlsanity.com/paper/1910.06468/) (2019)
- [Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization](https://mlsanity.com/paper/1910.07133/) (2019)

## Built on by (most cited first, 1 of 1)

- [New Orthogonal Multiwavelet Filters Derived by Matrix Spectral Factorization](https://mlsanity.com/paper/2608.11518/) (2026)

## Abstract (arXiv)

Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to functions useful in control theory systems, basis functions in numerical methods or multiscaling functions used in signal processing. We introduce a fast algorithm for matrix spectral factorization based on Bauer's method. We convert Bauer' method into a nonlinear matrix equation (NME). The NME is solved by two different numerical algorithms (Fixed Point Iteration and Newton's Method) which produce approximate scalar or matrix factors, as well as a symbolic algorithm which produces exact factors in closed form for some low-order scalar or matrix polynomial matrices, respectively. Convergence rates of the two numerical algorithms are investigated for a number of singular and nonsingular scalar and matrix polynomials taken from different areas. In particular, one of the singular examples leads to new orthogonal multiscaling and multiwavelet filters. Since the NME can also be solved as a Generalized Discrete Time Algebraic Riccati Equation (GDARE), numerical results using built-in routines in Maple 17.0 and 6 Matlab versions are presented.