The theory of fractal antenna arrays

Author

Kravchenko, Victor F.

Author_Institution

Inst. of Radio En. & Electron., Russian Acad. of Sci., Moscow, Russia

Volume

1

fYear

2003

fDate

9-12 Sept. 2003

Firstpage

183

Abstract

Foundations of measure theory, the Hausdorff-Besicovitch measure, fractal nowhere differentiable Boltzano, Weierstrass, Cantor, Riemann, Darboux, Van-der-Waerden, Koch, Sierpinski, Besicovitch, and Weierstrass-Mandelbrot functions, and also some atomic functions possessing fractal properties are considered. For the first time, the atomic-fractal functions are constructed. The theory proposed and justified is illustrated on problems of synthesis of radiating structures by means of modeling the corresponding physical processes.

Keywords

Fourier transforms; antenna arrays; antenna radiation patterns; antenna theory; array signal processing; fractals; Besicovitch functions; Cantor functions; Darboux functions; Fourier transform; Hausdorff-Besicovitch measure; Koch functions; Riemann functions; Sierpinski functions; Van-der-Waerden functions; Weierstrass functions; Weierstrass-Mandelbrot functions; antenna theory; atomic functions; atomic-fractal functions; differentiable Boltzano; fractal antenna arrays; fractal nowhere differentiable functions; fractal properties; measure theory; radiating structure synthesis; Antenna arrays; Antenna measurements; Antenna theory; Atomic measurements; Density measurement; Fractal antennas; Gaskets; Geometry; Mathematics; Signal synthesis;

fLanguage

English

Publisher

ieee

Conference_Titel

Antenna Theory and Techniques, 2003. 4th International Conference on

Print_ISBN

0-7803-7881-4

Type

conf

DOI

10.1109/ICATT.2003.1239181

Filename

1239181