Journal Article•
Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: In this paper, the correlation between the real and imaginary parts of the wave function and between their derivatives is found at speckle spot maxima, and these correlations are identically zero when averaged over the whole wave field.
6 citations
TL;DR: A novel analytical method for characterizing single-channel currents from recordings containing many identical, independent channels based on the assumption that the opening and closing of each single channel contributing to the summed current can be represented as a first-order, discrete-time, binary Markov chain.
6 citations
TL;DR: In this article, a direct method of determining the mean diameter of particles executing Brownian motion is presented, where the temporal coherence of the scattered field from submicroscopic particles illuminated by laser light is a function of both the integration time and the particle diameter.
Abstract: A direct method of determining the mean diameter of particles executing Brownian motion is presented. The temporal coherence of the scattered field from submicroscopic particles illuminated by laser light is a function of both the integration time and the particle diameter. The temporal degree of coherence of the time-averaged scattered intensity decreases as the integration time increases. Statistical processing of the scattered photons leads to a method of particle sizing (average diameter), which circumvents the need for digital autocor-relation or power spectral estimation.
6 citations
01 Apr 1949
TL;DR: In this article, a simplified model of an infra-red detector has been used, defined by three parameters: the minimum energy level, the focal length of the collimator, and the angular dispersion of the prism or grating.
Abstract: The performance of the average infra-red spectrometer is conditioned mainly by the characteristics of the detector employed. Assuming a minimum usable energy level at the exit slit, the square of the minimum frequency band embraced by the exit slit is proportional to the minimum energy level and to the focal length of the collimator, and inversely proportional to the angular dispersion of the prism or grating, the area of the collimator mirror, the energy flux at the entrance slit and the slit length. If, however, the time of response of the detector is taken into account, the inter-relation of spectrum scanning speed, signal-to-noise ratio and resolving power must be considered. For this purpose a simplified model of an infra-red detector has been used, defined by three parameters. This allows the relative merits of detectors to be assessed and the performance of any given spectrometer with a specified detector to be estimated. The inter-relation of resolving power and spectral scanning speed has been examined for "chopped-beam" and "video" presentation.
6 citations
TL;DR: In this article, Rice's theory for the statistical properties of random noise currents has been extended to calculate the distribution of excursion times above a small threshold for arbitrary spacings between an up-crossing and the successive down-crossings.
Abstract: Rice’s theory for the statistical properties of random noise currents has been employed in the context of concentration fluctuations in dispersing plumes. Within this context, the theory has been extended to calculate the distribution of excursion times above a small threshold for arbitrary spacings between an up-crossing and the successive down-crossing. This approach has then been applied to a second-order stochastic model for the evolution of odour concentrations and their time derivative (simple model), and to the superstatistics extension of this model [Reynolds (2007) Phys. Fluids]. In agreement with the measurements of Yee and coworkers [Yee et al. (1993) Boundary-Layer Meteorol. 65, Yee et al. (1994) J. Appl. Meteorol. 33 ], both formulations predict a distribution of excursion times that can be well approximated by a power-law profile with exponent close to −3/2. For the superstatistical model the power-law profile extends over approximately three or more decades, for the simple model this range is smaller. Compared to the simple model, predictions for the superstatistical model are in a better agreement with the measurements.
6 citations