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Products of Gaussian noises often emerge as the result of non-lineardetection techniques or as a parasitic effect, and their proper handling isimportant in many practical applications, including in fluctuation-enhancedsensing, indoor air or environmental quality monitoring, etc. We use Rice'srandom phase oscillator formalism to calculate the power density spectravariance for the product of two Gaussian band-limited white noises withzero-mean and the same bandwidth W. The ensuing noise spectrum is found todecrease linearly from zero frequency to 2W, and it is zero for frequenciesgreater than 2W. Analogous calculations performed for the square of a singleGaussian 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 aconsequence of correlation effects between frequency products. Our analyticresults is corroborated by computer simulations.

Spectra for the product of Gaussian noises