Statistical properties of an LPC distance measure

Several distance measures have been proposed for comparing sets of LPC coefficients. The most popular one has been the "log likelihood ratio" proposed by Itakura [1]. In this paper we discuss this measure (strictly speaking, a somewhat generalized version of it) from both a theoretical and a practical point of view. We derive its statistical properties both when the reference vector is known and when it is estimated from the data. We also show how these properties are affected by windowing, additive noise, and preemphasis. We present results of extensive simulations in support of the theoretical predictions. Finally, we argue that de Souza's [2] recent criticism of this measure is unjustified.