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2000•Journal of Time Series AnalysisRequires access

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

Robert V. Foutz, Hoonja Lee

Open publisher page 3 citations

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.

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What this paper is about

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.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Fourier series, Discrete Fourier series, Mathematics, Fourier analysis, Series (stratigraphy), Fourier sine and cosine series, Fourier transform, Periodic function

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