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Fractals and the analysis of waveforms.

M J Katz
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Abstract

Waveforms are planar curves--ordered collections of (x, y) point pairs--where the x values increase monotonically. One technique for numerically classifying waveforms assesses their fractal dimensionality, D. For waveforms: D = log(n)/(log(n) + log(d/L], with n = number of steps in the waveform (one less than the number of (x, y) point pairs), d = planar extent (diameter) of the waveform, and L = total length of the waveform. Under this formulation, fractal dimensions range from D = 1.0, for straight lines through approximately D = 1.15 for random-walk waveforms, to D approaching 1.5 for the most convoluted waveforms. The fractal characterization may be especially useful for analyzing and comparing complex waveforms such as electroencephalograms (EEGs).

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Biological EvolutionElectrocardiographyElectroencephalographyMathematicsPattern Recognition, AutomatedJournal ArticleResearch Support, Non-U.S. Gov'tResearch Support, U.S. Gov't, P.H.S.

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M J Katz. 1988. Fractals and the analysis of waveforms.. https://doi.org/10.1016/0010-4825(88)90041-8

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