On estimating the frequency of a sinusoid in autoregressive multiplicative noise

Abstract In classical spectral or frequency estimation, generally, the case of sinusoids embedded in additive noise is studied. Since this model is not relevant in some cases, this paper considers a new multiplicative model denoted ARCOS: a sinusoid amplitude modulated by a random autoregressive process. The spectral properties of such a model are derived and used to define a new frequency estimator. Modified versions of the corresponding algorithm are proposed and a theoretical formula for the asymptotic variance of the estimator is derived. Numerical simulations are presented to illustrate the specific nature of the model and the respective performances of the algorithms. An extension to AR( p ). AR( q ) processes, which generalizes the spectral properties of ARCOS, is also proposed.

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