Quantization and bit allocation in speech processing

The topic of quantization and bit allocation in speech processing is studied using an L2norm. Closed-form expressions are derived for the root mean square (rms) spectral deviation due to variations in one, two, or multiple parameters. For one-parameter variation, the reflection coefficients, log area ratios, and inverse sine coefficients are studied. It is shown that, depending upon the criterion chosen, either log area ratios or inverse sine quantization can be viewed as optimal. From a practical point of view, it is shown experimentally that very little difference exists among the various quantization methods beyond the second coefficient. Two-parameter variations are studied in terms of formant frequency and bandwidth movement and in terms of a two-pair quantization scheme. A lower bound on the number of quantization levels required to satisfy a given maximum spectral deviation is derived along with the two-pair quantization scheme which approximately satisfies the bound. It is shown theoretically that the two-pair quantization scheme has a 10-bit superiority over other above-mentioned quantization schemes in the sense of theoretically assuring that a maximum overall log spectral deviation will not be exceeded.