Harmonic Retrieval Using Cumulant-Based Estimator for ARMA Systems

In this paper, we propose a cumulant-based estimator for ARMA systems. The polyspectra, cumulants, and various other related statistics, such as bicepstra and bicoherence are all used to develop cumulant-based algorithms for estimating the parameters of linear (e.g. ARMA) or nonlinear processes. The use of cumulant-based estimator is useful: (1) if the additive noise is Gaussian and the signal is non-Gaussian, (2) the linear system is non-minimum phase (that is, mixed-phase), or (3) the process is nonlinear. The singular value plot shows several significant singular values corresponding to one quadratically coupled triplet; as in the case of the power spectrum (harmonics in noise), overestimating the number of harmonics usually leads to better results.