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Journal Article

Mathematical Analysis of Random Noise-Conclusion

01 Jan 1945-Bell System Technical Journal-Vol. 24, pp 46-156
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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Journal ArticleDOI
TL;DR: A stochastic process that may experience random reset events which suddenly bring the system to the starting value is considered and interesting properties emerge, like the existence of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior.
Abstract: In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

121 citations

Journal ArticleDOI
TL;DR: In this paper, a simple method for estimating frequency-dependent attenuation via measurement of the zero crossing density of the signal is presented and validated, both the effects of the frequency dependence of scatter and stochastic variability of the measurement are considered and discussed.

117 citations

Journal ArticleDOI
TL;DR: The capacity of a molecular machine is sharply limited by the dissipation and the thermal noise, but the machine failure rate can be reduced to whatever low level may be required for the organism to survive.

116 citations

Journal ArticleDOI
TL;DR: Results demonstrate the efficacy of all three methods by producing very sparse indications of damage at the correct locations even in the presence of model mismatch and significant noise.
Abstract: Ultrasonic guided waves are gaining acceptance for structural health monitoring and nondestructive evaluation of plate-like structures. One configuration of interest is a spatially distributed array of fixed piezoelectric devices. Typical operation consists of recording signals from all transmit-receive pairs and subtracting pre-recorded baselines to detect changes, possibly due to damage or other effects. While techniques such as delay-and-sum imaging as applied to differential signals are both simple and capable of detecting flaws, their performance is limited, particularly when there are multiple damage sites. Here a very different approach to imaging is considered that exploits the expected sparsity of structural damage; i.e., the structure is mostly damage-free. Differential signals are decomposed into a sparse linear combination of location-based components, which are pre-computed from a simple propagation model. The sparse reconstruction techniques of basis pursuit denoising and orthogonal matching pursuit are applied to achieve this decomposition, and a hybrid reconstruction method is also proposed and evaluated. Noisy simulated data and experimental data recorded on an aluminum plate with artificial damage are considered. Results demonstrate the efficacy of all three methods by producing very sparse indications of damage at the correct locations even in the presence of model mismatch and significant noise.

112 citations

Journal ArticleDOI
01 Mar 2004-Extremes
TL;DR: In this article, a stepwise procedure for estimating quantiles of the hydrological extremes floods and droughts is introduced based on daily streamflow observations, and the authors find that a seasonal variation should be included in the GEV distribution fitting for floods using block sizes less than one year.
Abstract: Estimation of flood and drought frequencies is important for reservoir design and management, river pollution, ecology and drinking water supply. Through an example based on daily streamflow observations, we introduce a stepwise procedure for estimating quantiles of the hydrological extremes floods and droughts. We fit the generalised extreme value (GEV) distribution by the method of block maxima and the generalised Pareto (GP) distribution by applying the peak over threshold method. Maximum likelihood, penalized maximum likelihood and probability weighted moments are used for parameter estimation. We incorporate trends and seasonal variation in the models instead of splitting the data, and investigate how the observed number of extreme events, the chosen statistical model, and the parameter estimation method effect parameter estimates and quantiles. We find that a seasonal variation should be included in the GEV distribution fitting for floods using block sizes less than one year. When modelling droughts, block sizes of one year or less are not recommended as significant model bias becomes visible. We conclude that the different characteristics of floods and droughts influence the choices made in the extreme value modelling within a common inferential strategy.

112 citations