Empirical Determination of the Frequencies of an
Almost Periodic Time Series
Harry Hurd
This paper is concerned with the problem of determination of the finite or countable set L of frequencies belonging to an almost periodic signal {x_k}. We seek a simple finite computational method in which a finite set Ln of estimators of frequencies is produced at each stage n from the finite observation x_0, . . . ,x_2n of the sequence. We also want Ln converges to L but yet each Ln is not too big.
We provide a method based on the local maxima of
weighted discrete Fourier transform of the finite observation of the almost periodic sequence. The produced estimators are taken from a finite grid of [0,2pi). They converge to the true frequencies with rate O(1/n). We first consider that the signal is observed without noise, and secondly with an additive noise. Then this method is adapted to an almost periodically correlated signal also
called almost cyclostationnary signal.