Related papers: Matrix Spectral Factorization for SA4 Multiwavelet

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,…

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…

A new method of matrix spectral factorization is proposed which reliably computes an approximate spectral factor of any matrix spectral density that admits spectral factorization

In this paper we propose a procedure which allows the construction of a large family of FIR d x d matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts…

In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…

We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…

Spectral and factorization properties of oscillatory matrices leads to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in terms of sequences of mixed multiple orthogonal polynomials…

We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization. We prove there is a Schur factorization for commuting…

Matrix spectral factorization is traditionally described as finding spectral factors having a fixed analytic pole configuration. The classification of spectral factors then involves studying the solutions of a certain algebraic Riccati…

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…

Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal…

We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an…

Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of…

This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…

Polarization is a unique characteristic of transverse wave and is represented by Stokes parameters. Analysis of polarization states can reveal valuable information about the sources. In this paper, we propose a separable low-rank quaternion…

Full-wave simulations are indispensable for nanophotonics and electromagnetics but are severely constrained on large systems, especially multi-channel ones such as disordered media, aperiodic metasurfaces, and densely packed photonic…

Though there have been hundreds of methods on solving rational spectral factorization, most of them are based on a positive definite density matrix assumption. In this work, we propose a novel approach on the spectral factorization of a…

The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…