A fast convergence two-step procedure for AR modeling of power spectral densities

A new technique for the minimization of customary cost functions for all-pole modeling of power spectral densities is presented. In the literature, optimizations are usually based on unnormalized autoregressive (AR) coefficients. In contrast, the proposed method is centered on a two-step descent using normalized AR coefficients on the one hand and the residual power on the other hand. For each cost function, efficient ways to obtain gradients are derived and a descent-based optimization is formulated. The resulting procedure converges significantly faster than the corresponding gradient descents on un-normalized coefficients, while still being computationally efficient. In addition to the traditional Yule-Walker distance, the Itakura-Saito distance, the COSH distance, the RMS log-spectral ratio distance, and a mean-squared error cost function are treated. Convergence results and curves are presented accordingly for different situations.