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Suppose we have a finite time series of real-world events measured at $(t_k), k \in \mathbb{N}$ with $(t_{k-1} < t_k)$. The content of the actual events is irrelevant.

I would like an automated process to analyse the series to see whether the events of this time series occur as the approximate result of a number of periodic processes. Approximate meaning within some bound of such periodic processes for some definition of bound.

Some events may also occur independently of any one periodic process, and the algorithm should cater to this possibility. The result should give me the phase and period of each periodic process found.

I get the feeling that the answer lies in either Fourier transforms or wavelet transforms, but I am not really sure how to proceed.

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