Linear Prediction Order Selection

For computing spectral envelopes via linear prediction, the order $M$ of the predictor should be chosen large enough that the envelope can follow the contour of the spectrum, but not so large that it follows the spectral ``fine structure'' on a scale not considered to belong in the envelope. In particular, for voice, $M$ should be twice the number of spectral formants, and perhaps a little larger to allow more detailed modeling of spectral shape away from the formants. For a sum of quasi sinusoids, the order $M$ should be significantly less than twice the number of sinusoids to inhibit modeling the sinusoids as spectral-envelope peaks. For filtered-white-noise, $M$ should be close to the order of the filter applied to the white noise, and so on.