Med Biol Eng Comput - Modeling the relationship between Higuchi's fractal dimension and Fourier spectra of physiological signals.

Tópicos

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Resumo

The exact mathematical relationship between FFT spectrum and fractal dimension (FD) of an experimentally recorded signal is not known. In this work, we tried to calculate signal FD directly from its Fourier amplitudes. First, dependence of Higuchi's FD of mathematical sinusoids on their individual frequencies was modeled with a two-parameter exponential function. Next, FD of a finite sum of sinusoids was found to be a weighted average of their FDs, weighting factors being their Fourier amplitudes raised to a fractal degree. Exponent dependence on frequency was modeled with exponential, power and logarithmic functions. A set of 280 EEG signals and Weierstrass functions were analyzed. Cross-validation was done within EEG signals and between them and Weierstrass functions. Exponential dependence of fractal exponents on frequency was found to be the most accurate. In this work, signal FD was for the first time expressed as a fractal weighted average of FD values of its Fourier components, also allowing researchers to perform direct estimation of signal fractal dimension from its FFT spectrum.

Resumo Limpo

exact mathemat relationship fft spectrum fractal dimens fd experiment record signal known work tri calcul signal fd direct fourier amplitud first depend higuchi fd mathemat sinusoid individu frequenc model twoparamet exponenti function next fd finit sum sinusoid found weight averag fds weight factor fourier amplitud rais fractal degre expon depend frequenc model exponenti power logarithm function set eeg signal weierstrass function analyz crossvalid done within eeg signal weierstrass function exponenti depend fractal expon frequenc found accur work signal fd first time express fractal weight averag fd valu fourier compon also allow research perform direct estim signal fractal dimens fft spectrum

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