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Adaptive Fourier Series and the Analysis of Periodicities in Time Series Data

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  • Robert V. Foutz
  • Hoonja Lee

Abstract

A Fourier series decomposes a function x(t) into a sum of periodic components that have sinusoidal shapes. This paper describes an adaptive Fourier series where the periodic components of x(t) may have a variety of differing shapes. The periodic shapes are adaptive since they depend on the function x(t) and the period. The results, which extend both Fourier analysis and Walsh–Fourier analysis, are applied to investigate the shapes of periodic components in time series data sets.

Suggested Citation

  • Robert V. Foutz & Hoonja Lee, 2000. "Adaptive Fourier Series and the Analysis of Periodicities in Time Series Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(6), pages 649-662, November.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:6:p:649-662
    DOI: 10.1111/1467-9892.00202
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