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Medical and biological engineering

, Volume 13, Issue 5, pp 731–741 | Cite as

On the variance of linearly summated identical waveforms

  • M. ten Hoopen
  • P. A. Zandt
Article

Abstract

The variance of linearly summated identical waveforms is formulated as a function of the degree of overlap of the individual waves, the irregularity in their temporal spacing, and the sequential dependency of their occurrence. In addition, the variance of the sum of a number of such wave sequences is considered, when the coupling between the sequences ranges from complete synchronism to total asynchronism. In numerical computations, the shape of the wave packets is taken as a negative exponential function.

Keywords

Variance Time series Point processes 

Sommaire

La variation de formes d'onde identiques à sommation linéaire est formulée en fonction du degré de cheveuchement des diverses ondes, de l'irrégularité de leur espacement dans le temps et de la dépendance séquentielle de leur apparition. En outre, la variation de la somme de plusieurs de ces séquences d'onde est examinée lorsque l'accouplement entre les séquences varie du synchronisme complet à l'asynchronisme total. Dans les calculs numériques, la forme des groupes d'ondes est considérée comme fonction exponentielle négative.

Zusammenfassung

Die Varianz von linearsummierten identischen Wellenformen wird als Funktion dei Überlappungsstärke der einzelnen Wellen, der Unregelmäßigkeit in ihrem zeitlichen Abstand und der Reihenfolgenabhängigkeit ihres Auftretens formuliert. Ferner wird die Varianz der Summe mehrerer solcher Wellenfolgen in Betracht gezogen, wenn die Kopplung zwischen den Reihenfolgen von völliger Synchronisierung zu totaler Asynchronisierung reicht. In numerischen Berechnungen wird die Form der Wellengruppen als negative Exponentialfunktion angenommen.

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Copyright information

© International Federation for Medical & Biological Engineering 1975

Authors and Affiliations

  • M. ten Hoopen
    • 1
  • P. A. Zandt
    • 1
  1. 1.Institute of Medical Physics TNOUtrechtThe Netherlands

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