Estimating the parameters of a noisy all-pole process using pole-zero modeling

Linear predictive coding (LPC) has been successfully applied to the encoding of speech and other time series. It has been widely observed, however, that the performance of an LPC algorithm deteriorates rapidly in the presence of background noise. In this paper, we describe and discuss one approach to the identification of a time series corrupted by additive white noise. A common approach to this problem is to prefilter the noisy time series, and then to apply an estimation algorithm which treats the time series as if it were noise-free. We describe an alternative approach which involves modifying the time-series model at the outset to account for the presence of noise. An estimation algorithm is then developed for this modified model. We discuss the development of the model, the estimation algorithm, and some representative experimental results.