This paper investigates the theory and structure of a large subclass of M -channel linear-phase perfect-reconstruction FIR filter banks—systems with analysis and synthesis filters of length Li = KiM + , where is an arbitrary interger, 0 < M , and Ki is any positive interger. For this subclass of systems, we first investigate the necessary conditions for the existence of linear-phase perfect-rec...

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian a...

In this paper, we develop the theory of the wavelet transform over Galois elds. To avoid the limitations inherent in the number theoretic Fourier transform over nite elds, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the in nite dimensional vector spaces for which an orthonormal basis expansion of any sequen...

2-band paraunitary FIR lter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets. The lter design problem is formulated and solved (a) as a constrained L1 optimization problem and (b) as a constrained L2 optimization problem which allows arbitrary compromises between an L2 and an L1 approach with both of them as special cases. Additional at...

This paper presents boundary optimization techniques for the nonexpansive decomposition of arbitrary-length signals with multirate filterbanks. Both biorthogonal and paraunitary filterbanks are considered. The paper shows how matching moments and orthonormality can be imposed as additional conditions during the boundary filter optimization process. It provides direct solutions to the problem of...

A new unified method for designing both paraunitary cosine-modulated FIR filter banks and cosine-modulated wavelets is proposed in this paper. This problem has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constraint matrices are symmetric and positive definite. Furthermore, a specific analog neural network whose energy function is chosen as t...

Laplacian pyramid based Laurent polynomial (LP2) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal algorithms in Signal Processing. In this paper, we investigate when such matrices are scalable, that is when right multiplication by Laurent polynomial diagonal matrices results in paraunitary matrices. The notion of scala...

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...

In this article, we address the problem of singular value decomposition of polynomial matrices and eigenvalue decomposition of para-Hermitian matrices. Discrete Fourier transform enables us to propose a new algorithm based on uniform sampling of polynomial matrices in frequency domain. This formulation of polynomial matrix decomposition allows for controlling spectral properties of the decompos...