Statistical properties of an LPC distance measure

A wide variety of distance measures for comparing sets of LPC coefficients have been proposed. The most popular one has been the log likelihood ratio test as proposed by Itakura [1]. Although this measure is both computationally efficient, and theoretically sound, de Souza, in a recent paper [2], found that the measured distribution of LPC distances was significantly different from the one predicted by theory. De Souza then proposed alternative statistical tests for measuring LPC distances. In this paper we present both theoretical and experimental results which show that there is, in general, excellent agreement between theory and practice when using the log likelihood ratio to measure LPC distance. Included in the paper are discussions of the effects of LPC analysis method (covariance or auto-correlation), the use of fixed pre-emphasis, and the effects of additive, uncorrelated noise on the distributions.