具有类似分形概率转换率的随机电报信号

Symmetry Pub Date : 2024-09-08 DOI:10.3390/sym16091175
Sergio Elaskar, Pascal Bruel, Luis Gutiérrez Marcantoni
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引用次数: 0

摘要

许多物理过程都具有随机电报信号的特征,例如,时间信号 c(t) 随时间在两个值之间随机切换。本研究的重点是一类电报过程,其转换率是用分形表达式来表述的。通过考虑有关等待时间统计的各种限制性假设,本分析提供了无条件和条件概率、平均等待时间、平均相位持续时间、自相关函数和相关积分时间尺度、频谱密度和平均切换频率的相应表达式。为了评估各种假设的相关性,我们构建了合成信号,并将其作为参考来评估理论推导表达式的预测质量。如果认为等待时间概率密度函数是以相应平均值为中心的狄拉克峰,则可获得最佳预测结果。
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Random Telegraphic Signals with Fractal-like Probability Transition Rates
Many physical processes feature random telegraph signals, e.g., a time signal c(t) that randomly switches between two values over time. The present study focuses on the class of telegraphic processes for which the transition rates are formulated by using fractal-like expressions. By considering various restrictive hypotheses regarding the statistics of the waiting times, the present analysis provides the corresponding expressions of the unconditional and conditional probabilities, the mean waiting times, the mean phase duration, the autocorrelation function and the associated integral time scale, the spectral density, and the mean switching frequency. To assess the relevance of the various hypotheses, synthetically generated signals were constructed and used as references to evaluate the predictive quality of the theoretically derived expressions. The best predictions were obtained by considering that the waiting times probability density functions were Dirac peaks centered on the corresponding mean values.
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