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...

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This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalized orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and ...

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...

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identif...