Optimal free parameters in orthonormal approximations

Author

Den Brinker, Albertus C. ; Belt, Harm J W

Author_Institution

Fac. der Elektrotech., Eindhoven Univ., Netherlands

Volume

46

Issue

8

fYear

1998

fDate

8/1/1998 12:00:00 AM

Firstpage

2081

Lastpage

2087

Abstract

We consider orthonormal expansions where the basis functions are governed by some free parameters. If the basis functions adhere to a certain differential or difference equation, then an expression can be given for a specific enforced convergence rate criterion as well as an upper bound for the quadratic truncation error. This expression is a function of the free parameters and some simple signal measurements. Restrictions on the differential or difference equation that make this possible are given. Minimization of either the upper bound or the enforced convergence criterion as a function of the free parameters yields the same optimal parameters, which are of a simple form. This method is applied to several continuous-time and discrete-time orthonormal expansions that are all related to classical orthogonal polynomials

Keywords

approximation theory; convergence of numerical methods; difference equations; differential equations; error analysis; parameter estimation; polynomials; signal processing; basis functions; continuous-time orthonormal expansion; difference equation; differential equation; discrete-time orthonormal expansion; enforced convergence rate criterion; optimal free parameters; orthonormal approximations; quadratic truncation error; signal measurements; upper bound minimisation; Belts; Convergence; Difference equations; Discrete transforms; Finite wordlength effects; Parameter estimation; Polynomials; Signal processing; System identification; Upper bound;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.705414

Filename

705414