Stochastic Realization of Non-Minimum Phase Systems

In this paper we present a stochastic realization method for linear, time-invariant, non-minimum phase systems when only output data are available. The input sequence need not be independent and identically distributed. It must be non-Gaussian, with some special properties that are described in the text. Our method proceeds in two stages. First, a minimum phase system is obtained using second-order statistics of the output. Next, an all-pass filter is realized, by exploiting higher-order statistics of the innovations. The cascade of the minimum-phase and all-pass systems yields the desired non-minimum phase system.