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

Robert V. Foutz and Hoonja Lee

Journal of Time Series Analysis, 2000, vol. 21, issue 6, 649-662

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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:21:y:2000:i:6:p:649-662

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