A level-crossing-based scaling dimensionality transform applied to stationary Gaussian processes

Author

Barbe, A.

Author_Institution

Dept. of Electr. Eng., Katholieke Univ. Leuven, Heverlee, Belgium

Volume

38

Issue

2

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

814

Lastpage

823

Abstract

The scaling dimensionality transform D/sub a/(r, theta ) of stochastic processes is introduced as a generalization of the fractal dimension concept over an infinite range of time scales. It is based on the expected number of crossings of a constant level a, and is a function of two variables: the scaling factor r and the sampling time theta . General properties of this transform are discussed, whereby D/sub a/(1, theta ) emerges as the fundamental transform. Results for stationary Gaussian processes, calculable from Rice´s formula (1945) are applied to signals with asymptotic f/sup - beta / spectra and to the problem of adjusting amplitude quantization to the sampling period in discrete signal representations.<>

Keywords

Brownian motion; fractals; signal processing; stochastic processes; transforms; Rice´s formula; amplitude quantization; discrete signal representations; fractal dimension concept; fractional Brownian motion; level-crossing based transform; sampling time; scaling dimensionality transform; scaling factor; signal analysis; stationary Gaussian processes; stochastic processes; Discrete transforms; Fractals; Gaussian processes; Joining processes; Quantization; Sampling methods; Signal processing; Signal representations; Signal sampling; Stochastic processes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.119738

Filename

119738