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: There is a need to examine the feasibility of improving the frequency stability of radio stations, which will allow a greater compactness in `ether'.
Abstract: increasing the transmission capacity of `ether' by means of directional antennas, both receiving and transmitting antennas. (6) The operating frequency range in `ether' should be broadened by employing, where possible, ultrashort waves and by studying this frequency range. (7) There is a need to examine the feasibility of improving the frequency stability of radio stations, which will allow a greater compactness in `ether'.
2 citations
TL;DR: It is shown that the amplitude information of ultrasound echoes is carried mainly by the envelope peaks (EPs), and it is demonstrated that the entire envelope could be approximately reconstructed from the EPs.
2 citations
TL;DR: It is demonstrated that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure and promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.
Abstract: Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.
2 citations
TL;DR: A system that exhibits nonlinear oscillations in the presence of low friction and weak fluctuations is considered and an expression for the mean density of level crossings whose duration exceeds a certain value is derived under the assumption of the high Q factor of the oscillations.
Abstract: A system that exhibits nonlinear oscillations in the presence of low friction and weak fluctuations is considered. An expression for the mean density of level crossings whose duration exceeds a certain value is derived under the assumption of the high $Q$ factor of the oscillations.
2 citations
TL;DR: In this paper, the bearing errors in direction finding of transient sources caused by unfavourable surrounding conditions can considerably be reduced through the use of a broadband evaluation, in order to obtain the direction of incidence the time-averaged energy flow density is determined and evaluated.
Abstract: In real cases of direction finding sites the direct wave, which propagates undisturbed between the source of interest and the direction finder, is superposed by a lot of coherent waves. This causes stationary fields of interference and often results in large bearing errors. This report shows by means of mathematical statistics that the bearing errors in direction finding of transient sources caused by unfavourable surrounding conditions can considerably be reduced through the use of a broadband evaluation. In order to obtain the direction of incidence the time-averaged energy-flow density is determined and evaluated.
2 citations