Impulse response recovery of linear systems through weighted cumulant slice

Identifiability of the so-called ω-slice algorithm is proven for ARMA linear systems. Although proofs were developed in the past for the simpler cases of MA and AR models, they were not extendible to general exponential linear systems. The results presented in this paper demonstrate a unique feature of the ω-slice method, which is unbiasedness and consistency when order is overdetermined, regardless of the IIR or FIR nature of the underlying system, and numerical robustness.

Source separation techniques applied to linear prediction

The prediction filters are well known models for signal estimation, in communications, control and many others areas. The classical method for deriving linear prediction coding (LPC) filters is often based on the minimization of a mean square error (MSE). Consequently, second order statistics are only required, but the estimation is only optimal if the residue is independent and identically distributed (iid) Gaussian. In this paper, we derive the ML estimate of the prediction filter. Relationships with robust estimation of auto-regressive (AR) processes, with blind deconvolution and with source separation based on mutual information minimization are then detailed. The algorithm, based on the minimization of a high-order statistics criterion, uses on-line estimation of the residue statistics. Experimental results emphasize on the interest of this approach.