Empirical tests have been developed for evaluating the numerical properties of multirate M -band filter banks represented as N ×M matrices of filter coefficients. Each test returns a numerically observed estimate of a 1 × M vector parameter in which the m element corresponds to the m filter band. These vector valued parameters can be readily converted to scalar valued parameters for comparison ...

In this paper we construct IR n-valued biorthogonal, compactly supported multiwavelet families such that one of the biorthogo-nal pairs consists of divergence-free vector wavelets. The construction is based largely on Lemari e's idea of multiresolution analyses intertwined by diierentiation. We show that this technique extends nontrivially to multiwavelets via Strela's two-scale transform. An e...

Surface multiresolution processing is an important subject in CAGD. It also poses many challenging problems including the design of multiresolution algorithms. Unlike images which are in general sampled on a regular square or hexagonal lattice, the meshes in surfaces processing could have an arbitrary topology, namely, they consist of not only regular vertices but also extraordinary vertices, w...

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

The efficient solution of operator equations using wavelets requires that they generate a Riesz basis for the underlying Sobolev space, and that they have cancellation properties of a sufficiently high order. Suitable biorthogonal wavelets were constructed on reference domains as the n-cube, which bases have been used, via a domain decomposition approach, as building blocks to construct biortho...

We consider the generalized eigenvalue problem Aψ = λBψ for two operators A,B. Self-similar closure of this problem under a simplest Darboux transformation gives rise to two possible types of regular algebras of dimension 2 with generators A,B. Realization of the operators A,B by tri-diagonal operators leads to a theory of biorthogonal rational functions. We find the general solution of this pr...

Wavelet methods with polynomial filters are usually favored in applications for their fast wavelet transforms and compact support. However, wavelet methods with rational filters have more freedom to achieve smaller condition numbers, more regularity and better efficiency. Such methods can be attractive if they also possess fast algorithms and have fast decay (as if the corresponding wavelets ha...

The theory of frames is fundamental to timefrequency (TF or time-scale signal expansions like Gabor ysis of frames via two “TF frame representations” called the Weyl symbol and Wigner distribution of a frame. The T F analysis shows how a frame’s properties depend on the signal’s T F location and on certain frame parameters. 1 I N T R O D U C T I O N Linear time-frequency (TF) or time-scale sign...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross-references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...

This paper is intended to present wavelet Galerkin schemes for the boundary element method. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasisparse system matrices which can be compressed to O(NJ ) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(NJ ) denotes th...