Retrieving sinusoids in colored Rayleigh noise by a cumulant-based FBLP approach

It is known that sinusoids generate lines in their spectra but false lines may appear due to additive colored noise. Employing the fourth-order cumulant of the noisy sinusoids for retrieving the sinusoids has become an approach to handling Gaussian noise either white or colored. But the assumption that the noise is Gaussian does not exist in some applications. This paper presents a new investigation of employing cumulants for retrieving sinusoids in colored non-Gaussian noise. It is concerned with estimating the frequencies and spectrum of the sinusoids and no attention is given to the amplitudes. It is shown theoretically and experimentally that employing cumulants is an attractive approach to handling colored Rayleigh noise. Results of a presented cumulant-based forward-backward linear prediction (CBFBLP) approach are compared with that of a correlation-based counterpart.