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Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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Related Experiment Video

Updated: May 25, 2026

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
08:25

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

Mean level signal crossing rate for an arbitrary stochastic process: comment.

José Cândido S Santos Filho1, Michel D Yacoub, George K Karagiannidis

  • 1Department of Communications, School of Electrical and Computer Engineering, University of Campinas, Av. Albert Einstein 400, 13083-852 Campinas, SP, Brazil. candido@decom.fee.unicamp.br

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|February 15, 2012
PubMed
Summary

The Yura-Hanson formula for mean level crossing rate is a special case. This study provides a more general solution consistent with the established Rice formula for arbitrary random processes.

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Last Updated: May 25, 2026

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Published on: April 27, 2021

Area of Science:

  • Probability theory
  • Random processes
  • Signal processing

Background:

  • The Yura-Hanson (2010) paper proposed a general expression for the mean level crossing rate (MLCR) of arbitrary random processes.
  • The authors noted discrepancies between their results and existing literature, leaving the reason unexplained.

Discussion:

  • This work clarifies the discrepancy by demonstrating that the Yura-Hanson formula is a specific instance of a broader solution.
  • The analysis highlights the limitations of the Yura-Hanson approach for certain probability distribution functions.

Key Insights:

  • A novel, more general MLCR formula is presented, applicable to a wider range of arbitrary random processes.
  • The derived solution reconciles the Yura-Hanson results with the widely accepted Rice MLCR formula.
  • This provides a unified framework for analyzing level crossing rates in random processes.

Outlook:

  • The generalized formula offers improved accuracy and applicability in fields relying on random process analysis.
  • Further research can explore the application of this generalized formula in complex systems and advanced signal processing techniques.