All-Pole Modeling of Discrete Spectral Powers: A Unified Approach

In this correspondence, a unified approach to the autoregressive (AR) modeling of power spectral densities is described. We show that by introducing auxiliary sequences, the minimization of several customary spectral distances can be performed with the exact same convenient approach, whether a gradient-descent or a Newton/quasi-Newton descent is chosen. Moreover, we extend the usual optimization of unnormalized AR coefficients to a two-step optimization of normalized AR coefficients, and provide evidence that this alternative approach can accelerate convergence and provide robustness to erroneous initializations. Convergence and modeling results are also given.