Comput Math Methods Med - A robust algorithm for optimisation and customisation of fractal dimensions of time series modified by nonlinearly scaling their time derivatives: mathematical theory and practical applications.

Tópicos

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{ method(2212) result(1239) propos(1039) }
{ framework(1458) process(801) describ(734) }
{ error(1145) method(1030) estim(1020) }
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Resumo

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

Resumo Limpo

standard method comput fractal dimens time seri usual test continu nowher differenti function benchmark actual signal therefor can produc opposit result extrem signal method also use differ scale method differ amplitud multipli make difficult compar fractal dimens obtain differ method purpos research develop optimis method comput fractal dimens normalis dimensionless modifi time seri signal robust algorithm run averag method maximis differ two fractal dimens exampl minimum maximum one signal modifi transform amplitud multipli nonlinear effect signal time deriv optimis method identifi optim multipli normalis amplitud target decis make base fractal dimens optimis method provid addit filter effect make fractal dimens less noisi method exemplifi explain differ signal human movement eeg acoust signal

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