Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free. To facilitate joint chaos and fractal analysis of biosignals, we report an adaptive multiscale decomposition algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction schemes; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; (4) offers a new formulation of fractal and multifractal analysis that is better than the popular detrended fluctuation analysis when a biosignal contains a strong oscillatory component. The effectiveness of the approach is demonstrated by applying it to classify EEGs for the purpose of detecting epileptic seizures.

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