Recursive coding of spectrum parameters

Estimates of optimal performance in terms of spectral distortion (SD) for first order time-recursive spectrum coders are presented. Extensions of high rate theory provides us with the formulas to calculate estimates and also tells us how to design coders with optimal VQ point density. For this purpose, the PDF of the current spectrum parameter vector, given the previous, is needed. This conditional PDF is obtained analytically from a model PDF for pairs of consecutive parameter vectors, based on Gaussian mixtures. The theory gives a lower bound of 16 bits to achieve 1 dB SD. Practical coders must base the adaptive codebook design on quantized previous vectors and experiments suggest that another 2-3 bits is needed to achieve 1 dB SD. Informal subjective tests indicate that transparent quality may be maintained at even lower rates.