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 article, the average fading characteristics of 42 MHz auroral backscatter and compares them to the general spectral (Doppler) features of the echoes are presented. And the present fading analysis supports the existence of at least two radio auroral scattering processes, in agreement with previously reported Doppler spectral results.
3 citations
3 citations
TL;DR: In this article, a theoretical analysis has been made which, on the basis of reasonable arguments, predicts that when fatigue tests are conducted using narrow band random loading, truncation of stress peaks may lead to significant differences in the test data collected compared with the data obtained in the absence of truncation.
3 citations
TL;DR: In this article, it was shown that the point process defined by random variables converges to a non-Poissonian limit on the scale of $n \to \infty.
Abstract: Let $f_n(z) = \sum_{k = 0}^n \varepsilon_k z^k$ be a random polynomial where $\varepsilon_0,\ldots,\varepsilon_n$ are i.i.d. random variables with $\mathbb{E} \varepsilon_1 = 0$ and $\mathbb{E} \varepsilon_1^2 = 1$. Letting $r_1, r_2,\ldots, r_k$ denote the real roots of $f_n$, we show that the point process defined by $\{|r_1| - 1,\ldots, |r_k| - 1 \}$ converges to a non-Poissonian limit on the scale of $n^{-1}$ as $n \to \infty$. Further, we show that for each $\delta > 0$, $f_n$ has a real root within $\Theta_{\delta}(1/n)$ of the unit circle with probability at least $1 - \delta$. This resolves a conjecture of Shepp and Vanderbei from 1995 by confirming its weakest form and refuting its strongest form.
3 citations
TL;DR: In this article, a generator is described which is capable of producing pulses occuring randomly in time, and the mean pulse rate may be set between 10 c/s and 100 kc/s.
3 citations