| Abstract: | We address a parametric joint detection‐estimation problem for discrete signals of the form  ,  , with an additive noise represented by independent centered complex random variables  . The distributions of  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 N, and complex coefficients  . For example, one of considered classes of noise is the following:  are independent identically distributed random variables with  and  . 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. |
