This paper provides several constructions of compactly supported wavelets generated by interpolatory reenable functions. It was shown in D1] that there is no real compactly supported orthonormal symmetric dyadic reenable function, except the trivial case; and also shown in L] and GM] that there is no compactly supported interpolatory orthonormal dyadic reenable function. Hence, for the dyadic d...

Problems of the system identification using orthonormal functions are discussed and algorithms of computing parameters of the discrete time state-space model of the plant based on the generalized orthonormal functions and the Laguerre functions are derived. The adaptive LQ regulator and the predictive controller based on the Laguerre function model are also presented. The stability and the robu...

Consider the sequence of poles A = {α1, α2, . . .}, and suppose the rational functions φn with poles inA form an orthonormal system with respect to an Hermitian positive-definite inner product. Further, assume the φn satisfy a three-term recurrence relation. Let the rational function φ n\1 with poles in {α2, α3, . . .} represent the associated rational function of φn of order 1; i.e. the φ n\1 ...

Consider the sequence of polesA = {α1, α2, . . .}, and suppose the rational functions φj with poles in A form an orthonormal system with respect to a Hermitian positive-definite inner product. Further, assume the φj satisfy a three-term recurrence relation. Let the rational function φ j\1 with poles in {α2, α3, . . .} represent the associated rational function of φj of order 1; i.e. the φ (1) j...

Nonlinear adaptive ltering has witnessed an explosion of interest in recent years. This progress report describes the achievements to date of the EPSRC funded research program to investigate orthonormal functions for nonlinear signal processing. The report introduces a structure based upon the multi{dimensional Fourier series which can be applied to nonlinear system identi-cation, channel equal...

Glossary 5 Introduction 6 Definition of Wavelets 7 Definition of Filters 8 Multi-Resolution Analysis 9 Wavelet Decomposition and Reconstruction 10 Refinable Functions 11 Compactly Supported Orthonormal Wavelets 12 Parameterization of Orthonormal Wavelets 13 Biorthogonal Wavelets 14 Prewavelets 15 Tight Wavelet Frames 16 Tight Wavelet Frames over Bounded Domain 17 q-Dilated Orthonormal Wavelets ...