All-Pole Estimation in Spectral Domain

Autoregressive (AR) modeling is a popular spectral analysis method commonly resolved in the time domain. This paper presents a novel AR analysis framework dealing with the estimation of poles directly from spectral samples. The basis of the method lies on a minimizing functional built with a certain mapping of the spectral residue. The optimization mechanism is based on the multivariate Newton-Raphson algorithm. Two different mappings are considered, namely, linear and logarithmic. The linear case results in a nonquadratic convex functional, whose global minimum is equivalent to that of the time-domain autocorrelation method. The logarithmic case under the Maximum Likelihood criterion turns out equivalent to the Whittle likelihood, proven here to be suitable for frequency selective estimation. The statistical and convergence performance of the method is demonstrated with simulations on stochastic and deterministic harmonic signals.