Harmonic retrieval is an important issue in the the field of statistical signal processing. However, in the case of harmonic retrieval in mixed colored Gaussian and Non-Gaussian Autoregressive movingaverage (ARMA) noises, the corresponding existing approaches can not retrieve a harmonic signal either with quadratic phase coupling components, or with cubic phase coupling components, or when the colored non-Gaussian ARMA noise is symmetrically distributed. In this paper, a new general approach is proposed to retrieve a one-dimensional real harmonic signal in the above mixed ARMA noises. A suitable filter is first used to remove all the sharp power spectrum peaks of the noisy observed process, then some kind of fourth-order cumulant is employed to identify the Autoregressive (AR) parameter values of the colored non-Gaussian ARMA noise model. After the real noisy observed data are filtered with the identified AR parameter values again, cumulant based methods can be made use of to retrieve the harmonics. The proposed new approach can be applied to retrieve a one-dimensional real harmonic signal in the above mixed colored Gaussian and non-Gaussian ARMA noises with no restrictions on the phase coupling of the harmonics and the distribution of the colored non-Gaussian ARMA noise. Simulation examples are presented to demonstrate its effectiveness.
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