A study on the multi-peak properties of the level-crossing intervals of a random process

Mimaki, Tadashi; Satō, Hiroshi; Tanabe, Masami

doi:10.1016/0165-1684(84)90003-3

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…The tradition with experimental testing of the dependence assumptions, including the Markov assumption, was continued by Mimaki (1973) and co-workers, (Mimaki et al, 1981(Mimaki et al, , 1984(Mimaki et al, , 1985. Munakata (1997) listed solved and unsolved crossing problems, focusing on experimental evidence and practical application of the available traditional methods to noise in signals.…”

Section: The Problem and Some Of Its Early Historymentioning

confidence: 99%

Effective computations of joint excursion times for stationary Gaussian processes

Lindgren,

Podgorski,

Rychlik

2020

Preprint

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This work is to popularize the method of computing the distribution of the excursion times for a Gaussian process that involves extended and multivariate Rice's formula. The approach was used in numerical implementations of the high-dimensional integration routine and in earlier work it was shown that the computations are more effective and thus more precise than those based on Rice expansions.The joint distribution of successive excursion times is clearly related to the distribution of the number of level crossings, a problem that can be attacked via the Rice series expansion, based on the moments of the number of crossings. Another point of attack is the "Independent Interval Approximation" (IIA) intensively studied for the persistency of physical systems. It treats the lengths of successive crossing intervals as statistically independent. Under IIA, a renewal type argument leads to an expression that provides the approximate interval distribution via its Laplace transform.However, the independence is not valid in most typical situations. Even if it leads to acceptable results for the persistency exponent of the long excursion time distribution or some classes of processes, rigorous assessment of the approximation error is not readily available. Moreover, we show that the IIA approach cannot deliver properly defined probability distributions and thus the method is limited only to persistence studies.The ocean science community favours a third approach, in which a class of parametric marginal distributions, either fitted to excursion data or derived from a narrow band approximation, is extended by a copula technique to bivariate and higher order distributions.This paper presents an alternative approach that is both more general, more accurate and relatively unknown. It is based on exact expressions for the probability density for one and for two successive excursion lengths. The numerical routine RIND

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Section: The Problem and Some Of Its Early Historymentioning

confidence: 99%

Effective computations of joint excursion times for stationary Gaussian processes

Lindgren,

Podgorski,

Rychlik

2020

Preprint

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“…[13], and particularly for BAN propagation in, e.g., [8], [9]. It is important to note that in various earlier radio propagation literature, direct statistical characterization of level crossing intervals and fade durations has been performed, in, e.g., [14], [15]. Such an approach has been adopted in some BAN propagation characterization, in, e.g., [2], [12].…”

Section: Introductionmentioning

confidence: 99%

The body area network channel model: A new look at second-order statistics

Smith

Hanlen

2014

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

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We adopt an innovative approach, previously applied to first order statistics of body area networks (BANs), across multiple links and multiple subjects, to important second-order statistics of radio propagation for BANs. Here it is demonstrated that for statistics of fade durations, level crossing intervals and non-fade durations, where direct characterizations are made of these statistics, an absolute measure allows us to compare across a spectrum of possible second-order characterizations; ranging from single-parameter for an entire ensemble, through to peractivity, per-subject and per-link based parameterized models. The deficiency of specifying one value (or a few mean values) for either level-crossing rate, average fade duration, or average nonfade duration, with respect to either a median or mean channel gain, is demonstrated with respect to a very large "open-access" dataset, and particularly 150 hours of "everyday" on-body link data within that dataset. It is also demonstrated that a 2-parameter lognormal fit, to agglomerate empirical second-order data, is generally simple, accurate and sufficient to characterize fade durations, non-fade durations, and level-crossing intervals.

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Channel Modeling for Wireless Body Area Networks

Smith

Hanlen

2015

Integrated Circuits and Systems

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A study on the multi-peak properties of the level-crossing intervals of a random process

Cited by 6 publications

References 13 publications

Effective computations of joint excursion times for stationary Gaussian processes

Effective computations of joint excursion times for stationary Gaussian processes

The body area network channel model: A new look at second-order statistics

Channel Modeling for Wireless Body Area Networks

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