Cumulant-based approach to the harmonic retrieval (Q2783683)

The authors argue that in the sinusoidal regression with dependent noise the assumption that the initial phases of the harmonics are uniformly distributed on \([-\pi,\pi)\) is unrealistic and does not work well in practice. Hence, they assume that the phases are nonrandom and introduce, using a combination of expected values and time averages, the concept of mixed cumulants as an adaption of the usual cumulants to this case. They obtain several properties of the mixed cumulants and apply them to harmonic retrieval, putting the emphasis on the case of several sinusoids. They also show that their method works well for data with wide dynamic range.