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.

JO - Metrology and Measurement Systems L1 - http://sd.czasopisma.pan.pl/Content/90006/PDF/Journal10178-VolumeXIXIssue4_03.pdf L2 - http://sd.czasopisma.pan.pl/Content/90006 IS - No 4 EP - 658 KW - fluctuation-enhanced sensing KW - correlation detectors KW - indoor and environmental air quality sensing. ER - A1 - Kish, Laszlo Bela A1 - Mingesz, Robert A1 - Gingl, Zoltan A1 - Granqvist, Claes-GĂ¶ran PB - Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation JF - Metrology and Measurement Systems SP - 653 T1 - Spectra for the Product of Gaussian Noises UR - http://sd.czasopisma.pan.pl/dlibra/docmetadata?id=90006 DOI - 10.2478/v10178-012-0057-0