Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 71. Fitting All-Pole Models to Deterministic Signals: Covariance Method

This note describes the covariance method for finding the parameters needed to fit an all-pole model to a finite sequence of samples obtained from a deterministic signal.

The covariance method is a technique for fitting an all-pole model to a deterministic signal that is assumed to be auto regressive, but where knowledge about the signal is limited to a sequence of N samples, x[0] through x[N –1]. This method is an alternative to the autocorrelation method described in Note 70. Rather than optimizing the total error over all non-negative n and assuming that x[n] = 0 for n outside the interval [0, n –1], as the autocorrelation method does, the covariance method is based ...