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Principal components analysis and cyclostationarity

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  • Boudou, Alain
  • Viguier-Pla, Sylvie

Abstract

In this paper, we give a definition of a cyclostationary function, which specifies and extends usual definitions of cyclostationary processes. We transform such a cyclostationary function into a series. The property of stationarity of the series lets us proceed to the Principal Components Analysis in the frequency domain. This technique requires the introduction of new notions as the conjugated of a spectral measure, the association of a set of unitary operators with a family of stationary series, and the ampliation. We illustrate this work by a simulated example, and we end by a particular case of cyclostationary function, where the Principal Components Analysis in the frequency domain is equivalent to the classical Principal Components Analysis.

Suggested Citation

  • Boudou, Alain & Viguier-Pla, Sylvie, 2022. "Principal components analysis and cyclostationarity," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001536
    DOI: 10.1016/j.jmva.2021.104875
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    References listed on IDEAS

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    1. Boudou, A. & Dauxois, J., 1994. "Principal Component Analysis for a Stationary Random Function Defined on a Locally Compact Abelian Group," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 1-16, October.
    2. Boudou, Alain & Romain, Yves, 2002. "On spectral and random measures associated to discrete and continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 145-157, September.
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