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On $1/f$ noise. (English) Zbl 1264.94060
Summary: Due to the fact that $1/f$ noise gains the increasing interests in the field of biomedical signal processing and living systems, we present this introductive survey that may suffice to exhibit the elementary and the particularities of $1/f$ noise in comparison with conventional random functions. Three theorems are given for highlighting the particularities of $1/f$ noise. The first says that a random function with long-range dependence (LRD) is a $1/f$ noise. The secondindicates that a heavy-tailed random function is in the class of $1/f$ noise. The third provides a type of stochastic differential equations that produce $1/f$ noise.

MSC:
94A12Signal theory (characterization, reconstruction, filtering, etc.)
62M10Time series, auto-correlation, regression, etc. (statistics)
62M15Spectral analysis of processes
60G22Fractional processes, including fractional Brownian motion
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