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: An Appendix is provided whose purpose is to call attention to the wide variety of possibilities in the specification of the relevant properties of radiation detectors, and thereby to encourage precision in the statement of these properties in the future periodical literature.
Abstract: In Part I, the need for a suitably defined factor of merit for comparing the sensitivity of different radiation detectors is explained (Section 1). Both the advantages and the very important limitations of such a factor of merit are discussed.In Section 2, separate factors of merit for Type I and Type II detectors are defined. The factor of merit for Type I detectors is defined as the ratio of the noise equivalent power given by the fundamental limit defined in Paper I to the noise equivalent power actually measured in the reference condition. The factor of merit for Type II detectors is similarly defined in terms of the actual noise equivalent power in the reference condition and the empirically determined minimum value for the noise equivalent power proposed by R. J. Havens. Section 3 contains a brief discussion of the significance of the factor of merit for the special case of the bolometer.In Part II, the noise equivalent power in the reference condition, and the factor of merit is determined for about fifty thermocouples and bolometers. The results are presented in Tables I and II, and in Figs. 1 and 2. A description of each detector is given in Section 5, along with a statement of any special calculations which were necessary.All of the results presented are based on measurements made by other persons; no measurements were performed by the writer. The sources of information are described in Section 3.An Appendix is provided whose purpose is to call attention to the wide variety of possibilities in the specification of the relevant properties of radiation detectors, and thereby to encourage precision in the statement of these properties in the future periodical literature.
33 citations
TL;DR: In this paper, the authors investigated detection thresholds in polarized intensity and polarization bias correction for surveys where the polarization information is obtained from rotation measure (RM) synthesis and found that a detection threshold of 8'σQU applied to the Faraday spectrum with a single RM with a false detection rate less than 10−4, but polarized intensity is more strongly biased than Ricean statistics suggest.
Abstract: Detection thresholds in polarized intensity and polarization bias correction are investigated for surveys where the polarization information is obtained from rotation measure (RM) synthesis. Considering unresolved sources with a single RM, a detection threshold of 8 σQU applied to the Faraday spectrum will retrieve the RM with a false detection rate less than 10–4, but polarized intensity is more strongly biased than Ricean statistics suggest. For a detection threshold of 5 σQU, the false detection rate increases to ~4%, depending also on λ2 coverage and the extent of the Faraday spectrum. Non-Gaussian noise in Stokes Q and U due to imperfect imaging and calibration can be represented by a distribution that is the sum of a Gaussian and an exponential. The non-Gaussian wings of the noise distribution increase the false detection rate in polarized intensity by orders of magnitude. Monte Carlo simulations assuming non-Gaussian noise in Q and U give false detection rates at 8 σQU similar to Ricean false detection rates at 4.9 σQU.
33 citations
TL;DR: In this paper, an instantaneous time series distance is defined through the equal time correlation coefficient, which is applied to the Gross Domestic Product (GDP) yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation.
Abstract: An instantaneous time series distance is defined through the equal time correlation coefficient. The idea is applied to the Gross Domestic Product (GDP) yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation. Some data discussion is first presented to decide what (EKS, GK, or derived) GDP series should be studied. Distances are then calculated from the correlation coefficient values between pairs of series. The role of time averaging of the distances over finite size windows is discussed. Three network structures are next constructed based on the hierarchy of distances. It is shown that the mean distance between the most developed countries on several networks actually decreases in time, —which we consider as a proof of globalization. An empirical law is found for the evolution after 1990, similar to that found in flux creep. The optimal observation time window size is found ≃15 years.
33 citations
TL;DR: In this article, the authors established another kind of integral representation for the Neumann series of Bessel functions of the first kind J ν, and derived a closed-form integral expression for J ∆.
Abstract: Recently, Pogany and Suli [Integral representation for Neumann series of Bessel functions, Proc. Amer. Math. Soc. 137(7) (2009), pp. 2363–2368] derived a closed-form integral expression for a Neumann series of Bessel functions. In this note, our aim is to establish another kind of integral representations for the Neumann series of Bessel functions of the first kind J ν.
33 citations