Recovering of autoregressive spectral estimates of signals buried in noise

Abstract

In this paper, we propose a noise modeling that does not destroy AR structure of buried signals in noise independently of its nature (white or colored, Gaussian or not) and its variance. Expression of perturbed AR coefficients is derived and proposed restoration does not use any a-priori information on the nature of noise and its variance. It is shown that AR coefficients are closer to nominal ones (noise-free) in the presence of noise for lower frequency contents with respect to the sampling frequency of corresponding continuous-time processes from which samples are taken for AR estimation. For unknown frequency contents, denoising of AR coefficients is obtained by decreasing the time interval separating samples used by AR estimation. A model order selection adapted to degraded signal-to-noise ratios is proposed. Performances of the proposed recovering of original AR spectra are demonstrated via signals buried in white and colored noise. Observed results are in accordance with the developed theory.