### Abstract

Products of Gaussian noises often emerge as the result of non-linear detection techniques or as parasitic effects, and their proper handling is important in many practical applications, including fluctuation-enhanced sensing, indoor air or environmental quality monitoring, etc. We use Rice's random phase oscillator formalism to calculate the power density spectra variance for the product of two Gaussian band-limited white noises with zero-mean and the same bandwidth W. The ensuing noise spectrum is found to decrease linearly from zero frequency to 2W, and it is zero for frequencies greater than 2W. Analogous calculations performed for the square of a single Gaussian noise confirm earlier results. The spectrum at non-zero frequencies, and the variance of the square of a noise, is amplified by a factor two as a consequence of correlation effects between frequency products. Our analytic results are corroborated by computer simulations.

Original language | English |
---|---|

Pages (from-to) | 653-658 |

Number of pages | 6 |

Journal | Metrology and Measurement Systems |

Volume | 19 |

Issue number | 4 |

Publication status | Published - 2012 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Instrumentation

### Cite this

*Metrology and Measurement Systems*,

*19*(4), 653-658.

**Spectra for the product of Gaussian noises.** / Kish, Laszlo Bela; Mingesz, Robert; Gingl, Z.; Granqvist, Claes Goran.

Research output: Article

*Metrology and Measurement Systems*, vol. 19, no. 4, pp. 653-658.

}

TY - JOUR

T1 - Spectra for the product of Gaussian noises

AU - Kish, Laszlo Bela

AU - Mingesz, Robert

AU - Gingl, Z.

AU - Granqvist, Claes Goran

PY - 2012

Y1 - 2012

N2 - Products of Gaussian noises often emerge as the result of non-linear detection techniques or as parasitic effects, and their proper handling is important in many practical applications, including fluctuation-enhanced sensing, indoor air or environmental quality monitoring, etc. We use Rice's random phase oscillator formalism to calculate the power density spectra variance for the product of two Gaussian band-limited white noises with zero-mean and the same bandwidth W. The ensuing noise spectrum is found to decrease linearly from zero frequency to 2W, and it is zero for frequencies greater than 2W. Analogous calculations performed for the square of a single Gaussian noise confirm earlier results. The spectrum at non-zero frequencies, and the variance of the square of a noise, is amplified by a factor two as a consequence of correlation effects between frequency products. Our analytic results are corroborated by computer simulations.

AB - Products of Gaussian noises often emerge as the result of non-linear detection techniques or as parasitic effects, and their proper handling is important in many practical applications, including fluctuation-enhanced sensing, indoor air or environmental quality monitoring, etc. We use Rice's random phase oscillator formalism to calculate the power density spectra variance for the product of two Gaussian band-limited white noises with zero-mean and the same bandwidth W. The ensuing noise spectrum is found to decrease linearly from zero frequency to 2W, and it is zero for frequencies greater than 2W. Analogous calculations performed for the square of a single Gaussian noise confirm earlier results. The spectrum at non-zero frequencies, and the variance of the square of a noise, is amplified by a factor two as a consequence of correlation effects between frequency products. Our analytic results are corroborated by computer simulations.

KW - Correlation detectors

KW - Fluctuation-enhanced sensing

KW - Indoor and environmental air quality sensing

UR - http://www.scopus.com/inward/record.url?scp=84872186739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872186739&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84872186739

VL - 19

SP - 653

EP - 658

JO - Metrology and Measurement Systems

JF - Metrology and Measurement Systems

SN - 0860-8229

IS - 4

ER -