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Algorithms for Spectral Analysis of Irregularly Sampled Time Series

Author

Listed:
  • Mathias, Adolf
  • Grond, Florian
  • Guardans, Ramon
  • Seese, Detlef
  • Canela, Miguel
  • Diebner, Hans H.

Abstract

In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.

Suggested Citation

  • Mathias, Adolf & Grond, Florian & Guardans, Ramon & Seese, Detlef & Canela, Miguel & Diebner, Hans H., 2004. "Algorithms for Spectral Analysis of Irregularly Sampled Time Series," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i02).
    • Handle: RePEc:jss:jstsof:v:011:i02
    DOI: http://hdl.handle.net/10.18637/jss.v011.i02
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    Cited by:

    1. Gabriel Desrosiers-Grégoire & Gabriel A. Devenyi & Joanes Grandjean & M. Mallar Chakravarty, 2024. "A standardized image processing and data quality platform for rodent fMRI," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    2. Josué M. Polanco-Martínez, 2014. "Estimación espectral de datos ambientales no equiespaciados vía el periodograma suavizado de Lomb-Scargle. Una breve revisión," Analítika, Analítika - Revista de Análisis Estadístico/Journal of Statistical Analysis, vol. 8(2), pages 7-23, Diciembre.

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