The complex cepstrum of higher order cumulants and nonminimum phase system identification

A computationally efficient identification procedure is proposed for a nonGaussian white-noise-driven linear, time-invariant, nonminimum phase system. The method is based on the idea of computing the complex cepstrum of higher order cumulants of the system output. In particular, the differential cepstrum parameters of the nonminimum phase impulse response are estimated directly from higher-order cumulants by least-squares solution or two-dimensional FFT operations. The method reconstructs the minimum-phase and maximum-phase impulse response components separately. It is flexible enough to be applied on autoregressive (AR), moving average (MA), or ARMA system without a priori knowledge of the type of the system. Benchmark simulation examples demonstrate the effectiveness of the method even with short length data records