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 methods able to catch the main features of recorded earthquakes, generating both spectrum compatible fully non-stationary accelerograms and artificial fullynon-stationARY accelerograms compatible with the site intensity of recorded accelerograms, are presented.
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TL;DR: In this article, asymptotic properties of curve-crossing counts of linear processes and nonlinear time series by curves are investigated. And for the long-range dependence case, the distributions are either multiple Wiener-Ito integrals or integrals with respect to stable Levy processes, depending on the heaviness of tails of the underlying processes.
5 citations
TL;DR: In this article, the authors used the combined application of wavelet transform and Fourier transform to demarcate the stratigraphic boundaries and made a comparison with the conventional method.
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01 Jan 2014
TL;DR: In this article, a broad overview of noise characterization related topics is offered to the reader, with different depth levels, including the practical side of noise measurements and the subsequent steps of noise extraction and modeling, as well as some advanced design methodologies.
Abstract: In this chapter, quite a broad overview of noise characterization-related topics is offered to the reader, with different depth levels. Most of the attention, however, is paid to the practical side of noise measurements and the subsequent steps of noise extraction and modeling, as well as to some advanced design methodologies. A major concern is in the procedures that are necessary to effectively de-embed the measurements from the contribution of the test bench and the adopted methodologies. The scope of the discussion cover a well-assessed theory concerning linear devices operated in the frequency range from a few megahertz to some 100 GHz, and at physical temperatures above some tens of kelvins. In these conditions, 1/f noise can be neglected and Johnson (thermal) noise is approximately independent of frequency; as a consequence, thermal and, possibly, shot noise of elemental noise sources add up to yield a white power spectrum, which can be conveniently described in terms of “equivalent” thermal noise.
The second part of the chapter is devoted to the application of the device noise models in the proper design of single- and multistage low noise amplifiers, including a mixed technique that actually employs characterization techniques directly in the amplifier design.
5 citations
TL;DR: In this article, the difference between inputs that are stochastic or fured is made explicit, and expressions for the variance of gain and phase estimators for a fixed input are derived.
Abstract: Summary. A common problem in geophysical research is the setting of confidence intervals on the gain and phase of frequency response functions. Such functions are widely estimated in seismology, oceanography and meteorology. The literature provides a number of different techniques but their applicability and limitations often are not clear. In this paper the distinction between inputs that are stochastic or fured is made explicit. Expressions for the variance of gain and phase estimators for a fixed input are derived, and compared to those from a stochastic input. Confidence intervals on gain and phase may be formulated in terms of the true (unknown) ‘noise parameter’, or the estimated noise parameter. For the former it is shown that two different expressions for the variance of the standardized gain are equivalent provided the noise parameter is less that about 0.3, i.e. the noise level is not too high. Various expressions for confidence intervals on gain and phase are also equivalent under the same restriction. When the confidence intervals are formulated in terms of the estimated noise parameter, it is demonstrated that only the t-distribution method for phase estimators is useful for high noise levels. Further, a derivation in the literature of a confidence interval for the gain (with the same degree of validity as for the phase) is found to be erroneous due to the incorrect specification of a critical parameter.
5 citations