On \(1/f\) noise.

*(English)*Zbl 1264.94060Summary: 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:

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62M15 | Inference from stochastic processes and spectral analysis |

60G22 | Fractional processes, including fractional Brownian motion |

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\textit{M. Li} and \textit{W. Zhao}, Math. Probl. Eng. 2012, Article ID 673648, 23 p. (2012; Zbl 1264.94060)

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