Fractal system as represented by singularity function

Author

Charef, A. ; Sun, H.H. ; Tsao, Y.Y. ; Onaral, B.

Author_Institution

Dept. of Electr. & Comput. Eng., Drexel Univ., Philadelphia, PA, USA

Volume

37

Issue

9

fYear

1992

fDate

9/1/1992 12:00:00 AM

Firstpage

1465

Lastpage

1470

Abstract

A fractional slope on the log log Bode plot has been observed in characterizing a certain type of physical phenomenon and has been called the fractal system or the fractional power pole. In order to represent and study its dynamical behavior, a singularity function method is presented which consists of cascaded branches of a number of pole-zero (negative real) pairs or simple RC section. The distribution spectrum of the system can also be easily calculated, and its accuracy depends on a prescribed error specified in the beginning. The method is then extended to a multiple-fractal system which consists of a number of fractional power poles. The result can be simulated by a combination of singularity functions, each representing a single-fractal system

Keywords

fractals; poles and zeros; random processes; transfer functions; RC section; distribution spectrum; dynamical behavior; fractional power pole; fractional slope; log log Bode plot; multiple-fractal system; pole-zero pairs; random processes; single-fractal system; singularity function; 1f noise; Accuracy; Fractals; Frequency; Function approximation; Impedance; Polarization; Power system modeling; Sun; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.159595

Filename

159595