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.
This paper presents a portable exhaled breath analyser, developed to detect selected diseases. The set-up
employs resistive gas sensors: commercial MEMS sensors and prototype gas sensors made of WO3 gas
sensing layers doped with various metal ingredients. The set-up can modulate the gas sensors by applying
UV light to induce physical changes of the gas sensing layers. The sensors are placed in a tiny gas
chamber of a volume of about 22 ml. Breath samples can be either injected or blown into the gas chamber
when an additional pump is used to select the last breath phase. DC resistance and resistance fluctuations
of selected sensors using separate channels are recorded by an external data acquisition board. Low-noise
amplifiers with a selected gain were used together with a necessary bias circuit. The set-up monitors other
atmospheric parameters interacting with the responses of resistive gas sensors (humidity, temperature, atmospheric
pressure). The recorded data may be further analysed to determine optimal detection methods.