The Itakura distance measure

Consider the case where a speech, , is passed through the linear predictor, a, corresponding to a template. The residual mean squared error, E, is:

So can define

Or in the autocorrelation case:

Let be the augmented vector of ``template'' or ``reference'' LP coefficients and the augmented vector of ``observed'' or ``unknown'' LP coefficients then:

In the autocorrelation case this can be computed with similar complexity to the Euclidean distance.