Recovery of periodicities hidden in heavy-tailed noise

What is it about?

We address a parametric joint detection-estimation problem for discrete signals consisting of a finite number of nonharmonic exponentials, with an additive noise represented by independent centered complex random variables. The distributions are assumed to be unknown, but satisfying various sets of conditions. We prove that in the case of a heavy-tailed noise it is possible to construct asymptotically strongly consistent estimators for the unknown parameters of the signal, i.e., frequencies, their number, and complex coefficients. The construction of estimators is based on detection of singularities of anti-derivatives for Z-transforms and on a two-level selection procedure for special discretized versions of superlevel sets. The consistency proof relies on the convergence theory for random Fourier series.

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