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Spectral Analysis of Time-Limited Observations of Infinitely Long Processes

  • Burkhard Buttkus
Chapter

Abstract

Due to experimental constraints, geophysical observations take place within a finite time interval. In this chapter, therefore, we will investigate the effects of such limitations on the analysis of deterministic nonperiodic processes of infinite length. The limitation to a finite time interval T can be simulated by multiplication of an infinitely long signal s(t) by a window or weighting function that is equal to 1 within the interval T and zero outside this interval. This rectangular function, also called the boxcar function, is defined as follows:
$$ w\left( t \right) = \left\{ {\begin{array}{*{20}{c}} 1 & {for} \\ 0 & {for} \\ \end{array} } \right.\begin{array}{*{20}{c}} {\left| t \right|} \\ {\left| t \right|} \\ \end{array} \begin{array}{*{20}{c}} \leqslant \\ > \\ \end{array} \begin{array}{*{20}{c}} {\frac{T}{2}} \\ {\frac{T}{2}} \\ \end{array} . $$
(4.1)

Keywords

Weighting Function Window Function Side Lobe Cosine Function Finite Time Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Burkhard Buttkus
    • 1
  1. 1.Federal Institute for Geosciences and Natural ResourcesHannoverGermany

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