Fractal dimension and nonlinear dynamical processes

Robert C. McCarty; John P. Lindley

doi:10.1117/12.162690

18 November 1993 Fractal dimension and nonlinear dynamical processes

Robert C. McCarty, John P. Lindley

Proceedings Volume 2038, Chaos in Communications; (1993) https://doi.org/10.1117/12.162690
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

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Robert C. McCarty and John P. Lindley "Fractal dimension and nonlinear dynamical processes", Proc. SPIE 2038, Chaos in Communications, (18 November 1993); https://doi.org/10.1117/12.162690

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KEYWORDS

Fractal analysis

Signal processing

Chaos

Nonlinear optics

Radar signal processing

Acoustics

Radar

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