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, a three-dimensional stochastic model of the pulsed ultrasonic Doppler velocimeter for the case of a highly focused and damped transducer and isotropic turbulence is presented.
Abstract: The pulsed ultrasonic Doppler velocimeter has been used extensively in transcutaneous measurement of the velocity of blood in the human body. It would be useful to evaluate turbulent flow with this device in both medical and non-medical applications. However, the complex behaviour and limitations of the pulsed Doppler velocimeter when applied to random flow have not yet been fully investigated.In this study a three-dimensional stochastic model of the pulsed ultrasonic Doppler velocimeter for the case of a highly focused and damped transducer and isotropic turbulence is presented. The analysis predicts the correlation and spectral functions of the Doppler signal and the detected velocity signal. The analysis addresses specifically the considerations and limitations of measuring turbulent intensities and one-dimensional velocity spectra.Results show that the turbulent intensity can be deduced from the broadening of the spectrum of the Doppler signal and a mathematical description of the effective sample-volume directivity.In the measurement of one-dimensional velocity spectra at least two major complicacations are identified and quantified. First, the presence of a time-varying, broad-band random process (the Doppler ambiguity process) obscures the spectrum of the random velocity. This phenomenon is similar to that occurring in laser anemometry, but the ratio of the level of the ambiguity spectrum to the largest detected velocity spectral component can be typically two to three orders of magnitude greater for ultrasonic technique owing to the much greater wavelength.Secondly, the spatial averaging of the velocity field in the sample volume causes attenuation in the measured velocity spectrum. For the ultrasonic velocimeter, this effect is very significant.The influence of the Doppler ambiguity process can be reduced by the use of two sample volumes on the same acoustic beam. The signals from the two sample volumes are cross-correlated, removing the Doppler ambiguity process, while retaining the random velocity. The effects of this technique on the detected velocity spectrum are quantified explicitly in the analysis for the case of a three-dimensional Gaussianshaped sample-volume directivity.
73 citations
73 citations
TL;DR: It is shown experimentally on the biceps, extensor digitorum and first dorsal interosseus muscles that an excellent agreement exists between the time averages of Fm and ZCR in normal muscles under a variety of muscle length tension and fatigue conditions.
Abstract: A system is described which monitors spectral changes of the surface EMG. It is shown analytically that a relationship exists between the zero crossing rate (ZCR) and the mean, Fa, and median, Fm, frequencies of the surface EMG. Under the existing conditions of this relationship a system can be built which can estimate and monitor the Fa or Fm of the surface EMG from the measured ZCR. It is shown experimentally on the biceps, extensor digitorum and first dorsal interosseus muscles that an excellent agreement exists between the time averages of Fm and ZCR in normal muscles under a variety of muscle length tension and fatigue conditions. A simple portable microcomputer unit which performs the ZCR calculations and which can be used as a muscle fatigue monitor is described.
72 citations
TL;DR: In this paper, a three-dimensional model of a tungsten-silver composite is statistically constructed from an experimental two-dimensional image, and the effective Young's modulus (E) of the model is computed in the temperature range 25-1060 degrees C using a finite element method.
Abstract: A three-dimensional model of a tungsten-silver composite is statistically constructed from an experimental two-dimensional image. The effective Young's modulus (E) of the model is computed in the temperature range 25-1060 degrees C using a finite element method. The results are in good agreement with experimental data. The reconstructed and overlapping sphere models are examples of bi-continuous (non-particulate) media. The computed moduli of the models are not generally in good agreement with the predictions of the self-consistent method. It has also been possible to evaluate the three-point variational bounds on the Young's moduli of the models using the results of Beran, Molyneux, Milton and Phan-Thien. The measured data were close to the upper bound if the properties of the two phases were similar (1/6 < E-1/E-2 < 6). (C) 1999 Elsevier Science Ltd. All rights reserved.
72 citations
TL;DR: The field of wind-generated ocean surface gravity waves is reviewed in this article for the period covering the last fifteen years and theories and observations relevant to understanding the physics of wind waves are discussed, as well as techniques for measuring and forecasting waves.
Abstract: The field of wind-generated ocean surface gravity waves is reviewed for the period covering the last fifteen years. Theories and observations relevant to understanding the physics of wind waves are discussed, as well as techniques for measuring and forecasting waves.
70 citations