Recursive coding of spectrum parameters

A theoretical analysis of recursive speech spectrum coding, where predictive and finite state schemes are special cases, is presented. We evaluate the spectral distortion (SD) theoretically and design coders that minimize the SD. The analysis rests on three cornerstones: high-rate theory, PDF modeling, and an approximation of SD. A derivation of the mean L₂-norm distortion of a recursive quantizer operating at high rate is provided. Also, the distortion distribution is supplied. The evaluation of the distortion expressions requires a model of the joint PDF of two consecutive spectrum vectors. The LPC spectrum source considered here has outcomes in a bounded region, and this is taken into account in the choice of model and modeling algorithm. It is further shown how to approximate the SD with an L₂-norm measure. Combining the results, we show theoretically that 16 bits are needed to achieve an average SD of 1 dB when quantizing ten-dimensional (10-D) spectrum vectors using a first-order recursive scheme. A gain of six bits per frame is noted compared to memoryless quantization. These results rely on high-rate assumptions which are validated in experiments. There, actual high-rate optimal coders are designed and evaluated