Identification of Autoregressive Systems in Noise Based on a Ramp-Cepstrum Model

In this paper, a new approach for the identification of a minimum-phase autoregressive (AR) system in the presence of a heavy noise is presented. First, a model, valid for both white noise and periodic impulse-train excitations, for the ramp-cepstrum (RC) of the one-sided autocorrelation function of an AR signal is proposed. A residue-based least-squares optimization technique is then employed in conjunction with the RC model to estimate the AR parameters from a noisy output, with a guaranteed system stability. The proposed ramp-cepstral model fitting combines the good features of both the correlation and cepstral domains, and thus provides a more accurate estimate of the parameters in a noisy environment. Extensive simulations are carried on on synthetic AR systems of different orders in the presence of white as well as colored noise. Simulation results demonstrate quite a satisfactory identification performance even for a signal-to-noise ratio of -5 dB, a level at which most of the existing methods fail to provide accurate estimation. To illustrate the suitability of the proposed technique in practical applications, a spectral estimation of a human vocal-tract system is carried out using noise-corrupted natural speech signals.