Whiteness of the measurement noise as a criterion for ARMA modelization of speech

One pitch period of voiced speech is considered as the response of an all pole system to initial conditions (these initial conditions give the zeros of the model) to which is added a white measurement noise. According to these assumptions, the AR part of the model is obtained by computing the eigenvector associated to the the smallest eigenvalue of the covariance matrix of the signal (it is a generalization of the method of Pisarenko). Then, the MA part is deduced by the minimization of the error between the measured signal and the output of the model with respect to the parameters representing the initial conditions. Comparisons are done and show that both the spectrum and the impulse response obtained by the present method are much more similar to the original speech signal than the ones deduced by the usual covariance method.