LPC distance measures and statistical tests with particular reference to the likelihood ratio

Several LPC distance measures and statistical tests have been proposed for use in speech processing, the most popular of which is Itakura's log likelihood ratio statistic, and some simple variants thereof. In this paper it is shown that these statistics share some undesirable properties. It is argued that there are more tractable and more sensitive measures available including other relevant likelihood ratio statistics. It is also shown that when Itakura's measure is used to compare two estimated LPC vectors, it is not the log likelihood ratio at all, and the true likelihood ratio for these conditions is derived.