Weighted maximum likelihood autoregressive and moving average spectrum modeling

We propose new algorithms for estimating autoregressive (AR), moving average (MA), and ARMA models in the spectral domain. These algorithms are derived from a maximum likelihood approach, where spectral weights are introduced in order to selectively enhance the accuracy on a predefined set of frequencies, while ignoring the other ones. This is of particular interest for modeling the spectral envelope of harmonic signals, whose spectrum only contains a discrete set of relevant coefficients. In the context of speech processing, our simulation results show that the proposed method provides a more accurate ARMA modeling of nasal vowels than the Durbin method.