### Abstract

An interesting experimental fact concerning Gaussian 1/f noise was reported a few years ago: when the noise amplitude is truncated at two levels under rather general conditions, the power spectral density remains the same. In this Letter, we present a theoretical derivation of this invariant property of 1/f noise, together with a generalization for Gaussian 1/f(α) noises with 0 <α <2. More specifically, it is proved that when 0 <α ≤ 1, a transformation of keeping only the sign of 1/f(α) noise, i.e. y(t) = sgn[x(t)], leads to the same 1/f(α) spectrum. When 1 <α <2, the transformation yields 1/f((α + 1)/2) noise. Our theoretical results are confirmed by numerical simulations. (C) 2000 Elsevier Science B.V.

Original language | English |
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Pages (from-to) | 7-12 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 269 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 24 2000 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*269*(1), 7-12. https://doi.org/10.1016/S0375-9601(00)00182-1

**Amplitude truncation of Gaussian 1/f(α) noises.** / Ishioka, Shunya; Gingl, Z.; Choi, Donghak; Fuchikami, Nobuko.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 269, no. 1, pp. 7-12. https://doi.org/10.1016/S0375-9601(00)00182-1

}

TY - JOUR

T1 - Amplitude truncation of Gaussian 1/f(α) noises

AU - Ishioka, Shunya

AU - Gingl, Z.

AU - Choi, Donghak

AU - Fuchikami, Nobuko

PY - 2000/4/24

Y1 - 2000/4/24

N2 - An interesting experimental fact concerning Gaussian 1/f noise was reported a few years ago: when the noise amplitude is truncated at two levels under rather general conditions, the power spectral density remains the same. In this Letter, we present a theoretical derivation of this invariant property of 1/f noise, together with a generalization for Gaussian 1/f(α) noises with 0 <α <2. More specifically, it is proved that when 0 <α ≤ 1, a transformation of keeping only the sign of 1/f(α) noise, i.e. y(t) = sgn[x(t)], leads to the same 1/f(α) spectrum. When 1 <α <2, the transformation yields 1/f((α + 1)/2) noise. Our theoretical results are confirmed by numerical simulations. (C) 2000 Elsevier Science B.V.

AB - An interesting experimental fact concerning Gaussian 1/f noise was reported a few years ago: when the noise amplitude is truncated at two levels under rather general conditions, the power spectral density remains the same. In this Letter, we present a theoretical derivation of this invariant property of 1/f noise, together with a generalization for Gaussian 1/f(α) noises with 0 <α <2. More specifically, it is proved that when 0 <α ≤ 1, a transformation of keeping only the sign of 1/f(α) noise, i.e. y(t) = sgn[x(t)], leads to the same 1/f(α) spectrum. When 1 <α <2, the transformation yields 1/f((α + 1)/2) noise. Our theoretical results are confirmed by numerical simulations. (C) 2000 Elsevier Science B.V.

UR - http://www.scopus.com/inward/record.url?scp=0034708924&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034708924&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(00)00182-1

DO - 10.1016/S0375-9601(00)00182-1

M3 - Article

VL - 269

SP - 7

EP - 12

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 1

ER -