A cyclostationary function specifies and extends the usual definition of a periodically correlated process. In this paper, we show that with any cyclostationary random function, a unique spectral measure can be associated. With a supplementary continuity hypothesis, we can also associate a unique stationary series. This is a way to consider for such a function the Principal Components Analysis in the frequency domain.

cyclostationarity, random measures, spectral measures, stationary processes, unitary operators.

Received: July 27, 2022; Accepted: September 25, 2022; Published: October 21, 2022

How to cite this article: Emmanuel Nicolas Cabral and Alain Boudou, Spectral elements associated to a cyclostationary function, Far East Journal of Theoretical Statistics 66 (2022), 105-133. http://dx.doi.org/10.17654/0972086322015

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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