Description:
<jats:p>The problem of choosing an “optimal” number of poles in fitting an all-pole model can be formulated as an estimation problem with an associated measure of fit. One measure of fit is the information theoretic criterion proposed by Akaike as an estimate of the mean log likelihood. Under the assumption that the signal is Gaussian, the criterion can be given as I(p) = logVp + 2p/N, where Vp is the normalized linear prediction error, p is the number of poles, and N is the “effective length” of the signal I(p) is computed as a function of p up to the maximum value of p that is of interest. That value of p for which I(p) is minimum is taken as optimal and the resulting model is said to characterize the given signal adequately. This criterion can be used in a speech compression system to determine an adequate predictor order for each frame of the analysis. Only that number of parameters need be transmitted, resulting in a lower transmission rate. Another possible application is in speech recognition, where the “optimal” predictor order can be used as a measure of formant structure.</jats:p>