Optimal distortion measures for the high rate vector quantization of LPC parameters

This paper presents a class of quadratically weighted distortion measures which provide optimal performance for the high rate vector quantization (VQ) of linear predictive coding (LPC) parameters. It is shown that the quantization distortion of a high rate VQ converges to a quadratically weighted measure, where the quadratic weighting matrix is a “sensitivity” matrix, which is a generalization of the scalar sensitivity concept to the vector case. The sensitivity matrix is the second order term of the Taylor series expansion of the original distortion measure. Closed form expressions and computationally efficient methods for computing the sensitivity matrices of the different LPC parameterizations are given, which involve no numerical integration and can be implemented in real-time on modern DSP chips. In the general case, the “sum of sensitivity weighted scalar errors” is not equivalent to the original distortion measure. However the sensitivity matrix of the line spectral pair (LSP) frequencies is exactly diagonal, demonstrating that for LSPs only a “sum of sensitivity weighted scalar errors” will result in optimal performance