Identification of mixed-phase systems from frequency slices of the bispectrum

Abstract

The identification of the parameters of a linear, time-invariant system is an important problem in signal processing and control. Power spectral methods cannot be used in the identification of mixed-phase systems, or when the output is corrupted by Gaussian noise of unknown power spectral density. Bispectral methods are effective in those cases. In this paper we present a new procedure to identify mixed-phase systems using frequency slices of the bispectral phase to obtain the group delay of the system from which we then find the system parameters. For mixed-phase moving average (MA) or minimum-phase autoregressive moving average (ARMA) systems, we show that a single slice of the bispectral phase is sufficient to identify the parameters and the order of the system, while two slices of the bispectrum are needed for mixed-phase ARMA systems. The basis of our procedure is to obtain an equivalent minimum-phase system which has the same phase as the original one. Using the modified least squares (MLS) rational approximation for the equivalent system we find the parameters of the original system. In the mixed-phase ARMA case, additional separation of the minimum- and the maximum-phase components is necessary. Examples illustrating our procedure are given.