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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: The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice's sum-of-sinusoids, and it is pointed out that Gudmundson’s correlation model results in an infinite LCR.
Abstract: The focus of this paper is on the higher order statistics of spatial simulation models for shadowing processes. Such processes are generally assumed to follow the lognormal distribution. The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice's sum-of-sinusoids. Both exact and approximate expressions are presented for the level-crossing rate (LCR) and the average duration of fades (ADF) of the simulation model. It is pointed out that Gudmundson's correlation model results in an infinite LCR. To avoid this problem, two alternative spatial correlation models are proposed. Illustrative examples of the dynamic behavior of shadow fading processes are presented for all three types of correlation models. Emphasis will be placed on two realistic propagation scenarios capturing the shadowing effects in suburban and urban areas.
29 citations
TL;DR: The results of a theoretical and experimental investigation into the non-linear, planar propagation of sinusoidal and band-limited noise signals in air are presented in this paper, where the extension to spherical waves and the possible role played by nonlinearity in the propagation of aircraft noise are discussed.
29 citations
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TL;DR: In this article, a model for the scattering of ultrasound by well-oriented planar defects is combined with noise theory to produce a calculated capability of detection, based on the likelihood that the defect signal exceeds the specified threshold.
Abstract: This paper describes a mathematical model for predicting the theoretical probability of detection (POD) of planar buried defects, for conventional ultrasonic pulse-echo inspection. A model for the scattering of ultrasound by well-oriented planar defects is combined with noise theory to produce a calculated capability of detection, based on the likelihood that the defect signal exceeds the specified threshold. The problem of false indications, the recording of a defect when none is present, is also addressed by the model, showing how any improvement in POD predictions must be considered in parallel with the associated change in the probability of false indication. We use examples to illustrate how the model may be used to check on proposed inspections, showing how factors such as reporting threshold, probe scan pattern and the criterion for the number of probe positions at which an indication must be seen before a defect is recorded, all affect the probability of detection and of false indication. The effects of defect roughness on detection probabilities are studied. We also use the model to quantify the uncertainties that result in POD predictions, when defect properties such as orientation, roughness, aspect ratio and depth within the specimen are themselves uncertain. The problems of equipment and human error are not addressed, although we discuss how, if these can be quantified, they may be incorporated into the model.
28 citations
TL;DR: In this article, a stable step-by-step procedure is proposed to evaluate the mean square response of a linear system with several degrees of freedom, subjected to earthquake ground motion.
28 citations
TL;DR: The present model attempts to relate statistical characteristics of evoked responses, recorded by gross electrodes, to the statistical activity of the neural elements that contribute to the responses.
Abstract: Neuroelectric activity recorded after presentation of a controlled stimulus is called an “evoked response.” Evoked responses are random, in that repeated presentations of a stimulus do not produce identical responses despite all effort to maintain identical conditions for all stimulus presentations. Responses may then be described statistically. The present model attempts to relate statistical characteristics of evoked responses, recorded by gross electrodes, to the statistical activity of the neural elements that contribute to the responses. The model postulates one or more populations of elements which, when they fire, contribute elemental waveforms to a gross response in which these waveforms are linearly summed. The statistical behavior of the elements in a population is described by their instantaneous firing rate, which is a function of time. In terms of the model, the statistical properties of the gross response (such as the mean and variance, both of which are functions of time) are shown to be related in a simple way to the instantaneous firing rates and elemental waveforms of the populations that contribute to the response. The model is an extension of the shot-noise model to time-variant phenomena; but some of the assumptions of the shot-noise model (specifically, statistical independence of firings) are relaxed.
28 citations
Cites methods from "Mathematical Analysis of Random Noi..."
...In its formal mathematical structure the present model is a generalization of a model discussed by N. Campbell (1909), J. M. Whit taker ~1937), and, most completely by S. O. Rice (1944, 1945)....
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