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 authors proposed a turbulent layer model to explain the aspect sensitivity of the echoes, where anisotropic turbulence is confined to a very thin (few meters) region at the boundary of turbulent layer.
Abstract: A new technique, using beam broadening effects, has been developed to measure the aspect sensitivity of atmospheric clear air VHF radar echoes. It uses the relatively broad antenna beam of the vertical-pointing antenna of the new Chung-Li stratospheric-tropospheric radar (25°N, 120°E). The aspect sensitivity measurement using this method is straightforward and free from convolution effects introduced by the finite width of the antenna beam pattern. The observed results agree very well with other measurements. The authors propose a turbulent layer model to explain the aspect sensitivity of the echoes. In this model, anisotropic turbulence is confined to a very thin (few meters) region at the boundary of a turbulent layer. This region is responsible for the aspect sensitivity of the echoes obtained from the vertical direction. The isotropic echoes obtained from the oblique beam arise from the isotropic turbulence embedded in the center of the layer, with 30–300 m in vertical extent. We show in an appendix that the magnitude of the partial reflection coefficient is much more sensitive to the shape, length scale, and smoothness, than to the slope of the refractive index profile. Therefore the functional shape of the refractive index profile is very important for estimating the reflection coefficient. Large errors can be made when assuming, for simplicity, nonphysical profiles. For partial reflecting mechanisms to be important, steplike discontinuities, confined within length scales of the order of a meter, would be required.
95 citations
TL;DR: In this paper, a review of recent developments in structural reliability that are relevant to earthquake engineering problems are reviewed, and the topics of reliability sensitivity, updating of reliability, and treatment of uncertainties in the estimation of reliability are discussed.
94 citations
TL;DR: In this article, the authors used the Cartwright and Longuet-Higgins probability density function to describe the distribution of swash maxima in a nearshore environment, and found that the model is satisfactory for describing various distribution statistics including the average maxima, the proportion of negative maxima and the elevation at which one third of the swash minima are exceeded.
Abstract: Cartwright and Longuet-Higgins (1956) describe the statistical distribution of maxima that would result from the linear superposition of random, Gaussian waves. The distribution function depends solely upon the relative width of the power spectrum and root-mean-square value of the process time series. Runup field data from three experiments are presented to determine the extent to which the distribution of swash maxima can be approximated using the Cartwright and Longuet-Higgins probability density function. The model is found to be satisfactory for describing various distribution statistics including the average maxima, the proportion of negative maxima, and the elevation at which one third of the swash maxima are exceeded. However, systematic discrepancies that scale as a function of time series skewness are observed in the statistics describing the upper tail of the distributions. Although we conclude that the linear model is incapable of delineating these apparent nonlinearities in the swash time series, the extent of the deviation can be estimated empirically for the purpose of constraining nonlinear models and nearshore engineering design.
94 citations
TL;DR: Of the five different methods of signal-to-noise ratio measurement for partially parallel imaging (PPI) acquisitions, the image subtraction method is recommended to be used for SNR calculations due to its relative accuracy and ease of implementation.
Abstract: Purpose: To assess five different methods of signal-to-noise ratio (SNR) measurement for partially parallel imaging (PPI) acquisitions.
Methods: Measurements were performed on a spherical phantom and three volunteers using a multichannel head coil a clinical 3T MRI system to produce echo planar, fast spin echo, gradient echo, and balanced steady state free precession image acquisitions. Two different PPI acquisitions, generalized autocalibrating partially parallel acquisition algorithm and modified sensitivity encoding with acceleration factors (R) of 2–4, were evaluated and compared to nonaccelerated acquisitions. Five standard SNR measurement techniques were investigated and Bland–Altman analysis was used to determine agreement between the various SNR methods. The estimated g-factor values, associated with each method of SNR calculation and PPI reconstruction method, were also subjected to assessments that considered the effects on SNR due to reconstruction method, phase encoding direction, and R-value.
Results: Only two SNR measurement methods produced g-factors in agreement with theoretical expectations (g ≥ 1). Bland–Altman tests demonstrated that these two methods also gave the most similar results relative to the other three measurements. R-value was the only factor of the three we considered that showed significant influence on SNR changes.
Conclusions: Non-signal methods used in SNR evaluation do not produce results consistent with expectations in the investigated PPI protocols. Two of the methods studied provided the most accurate and useful results. Of these two methods, it is recommended, when evaluating PPI protocols, the image subtraction method be used for SNR calculations due to its relative accuracy and ease of implementation.
91 citations
TL;DR: Application of the linearising properties of auxiliary signals added to the sinusoidal stimulus resulted in the determination of a functional sequence of the events in the retina and also of the characteristics of some of these processes.
90 citations