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Heavy-tailed prediction error: a difficulty in predicting biomedical signals of \(1/f\) noise type. (English) Zbl 1261.92029

Summary: A fractal signal \(x(t)\) in biomedical engineering may be characterized by \(1/f\) noise, that is, the power spectrum density (PSD) divergences at \(f = 0\). According to Taqqu’s law, \(1/f\) noise has the properties of long-range dependence and heavy-tailed probability density functions (PDFs). The contribution of this paper is to exhibit that the prediction error of a biomedical signal of \(1/f\) noise type is long-range dependent (LRD). Thus, it is heavy-tailed and of \(1/f\) noise. Consequently, the variance of the prediction error is usually large or may not exist, making predicting biomedical signals of \(1/f\) noise type difficult.

MSC:

92C55 Biomedical imaging and signal processing
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