Spectra for the product of Gaussian noises

Laszlo Bela Kish, Robert Mingesz, Z. Gingl, Claes Goran Granqvist

Research output: Article

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)653-658
Number of pages6
JournalMetrology and Measurement Systems
Volume19
Issue number4
Publication statusPublished - 2012

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White noise
random noise
Bandwidth
Monitoring
Computer simulation
products
Air
environmental quality
air quality
noise spectra
rice
white noise
radiant flux density
computerized simulation
oscillators
formalism
bandwidth

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Instrumentation

Cite this

Kish, L. B., Mingesz, R., Gingl, Z., & Granqvist, C. G. (2012). Spectra for the product of Gaussian noises. 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.

In: Metrology and Measurement Systems, Vol. 19, No. 4, 2012, p. 653-658.

Research output: Article

Kish, LB, Mingesz, R, Gingl, Z & Granqvist, CG 2012, 'Spectra for the product of Gaussian noises', Metrology and Measurement Systems, vol. 19, no. 4, pp. 653-658.
Kish LB, Mingesz R, Gingl Z, Granqvist CG. Spectra for the product of Gaussian noises. Metrology and Measurement Systems. 2012;19(4):653-658.
Kish, Laszlo Bela ; Mingesz, Robert ; Gingl, Z. ; Granqvist, Claes Goran. / Spectra for the product of Gaussian noises. In: Metrology and Measurement Systems. 2012 ; Vol. 19, No. 4. pp. 653-658.
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