Optimality conditions for a specific class of truncated Kautz series

Author

Brinker, Albertus C den

Author_Institution

Dept. of Electr. Eng., Eindhoven Univ. of Technol., Netherlands

Volume

43

Issue

8

fYear

1996

fDate

8/1/1996 12:00:00 AM

Firstpage

597

Lastpage

600

Abstract

Kautz functions constitute a basis in L² and can be used for filter synthesis starting from a prescribed transient response. In a practical situation, only truncated series are used and thus the speed of convergence of such series is of importance. This convergence speed is a function of the parameters. The Kautz functions that are considered can be generated by a line of identical Nth-order allpass sections. The optimality conditions for the parameters of this specific class of truncated Kautz series are established solely on the basis of the orthonormality and the polynomial character of the basis functions

Keywords

all-pass filters; convergence; filtering theory; network synthesis; series (mathematics); transient response; Kautz function; L² basis functions; allpass filter; convergence; filter synthesis; optimality conditions; orthonormality; polynomial; transient response; truncated Kautz series; Adaptive filters; Convergence; Filter bank; Frequency synthesizers; Laplace equations; Network synthesis; Polynomials; Signal analysis; Signal synthesis; Transient response;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.532006

Filename

532006