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The Fourier-Chebychev approximation for time series with a great many terms

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Abstract

A new type of approximation is proposed to evaluate Fourier series with a great many terms. It combines Fourier series and Chebychev polynomials to represent time series over a finite time interval. On one side, the high frequencies are approximate multiples of a basic frequency to represent short periodic terms; on the other side, the slowly variable functions of the time, on a given interval, which contain terms with long periods, are approximated by Chebychev polynomials. Application is made in case of the Lunar Theory ELP which contains about 30 000 trigonometric terms. The computing time necessary to evaluate coordinates is very much reduced when we give to series the intermediary representation inF-T form, as compared to a direct substitution of the time in the arguments.

One shows also on a numerical example, that the Fourier-Chebychev approximation smoothly degrades outside its range of representation.

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Authors
  1. Jean Chapront
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Bureau des Longitudes. Equipe de Recherche Associée au CNRS

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Chapront, J. The Fourier-Chebychev approximation for time series with a great many terms. Celestial Mechanics 28, 415–430 (1982). https://doi.org/10.1007/BF01372123

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  • DOI: https://doi.org/10.1007/BF01372123

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