Maximum entropy extrapolation of cumulant statistics: linear processes

The authors extrapolate, in the maximum-entropy (ME) sense, one-dimensional (1-D) cumulant statistics of a stationary random process which is the output of a linear, time-invariant (LTI) model excited by a non-Gaussian, independent and identically distributed input. The entropy rate of a linear process, is related with a special 1-D polyspectrum. Based on this relationship they derive 1-D polyspectral estimates that correspond to the most random time series whose cumulant sequence is consistent with the given finite set of 1-D cumulant statistics. The ME extension of the cumulant sequence of linear processes corresponds to that of an AR (autoregressive) process whose coefficients can be computed as the solution of a system of linear equations. The AR filter obtained using the ME cumulant extrapolation is applied to harmonic retrieval, and phase estimation of nonminimum-phase LTI systems