On the statistical properties of line spectrum pairs

Accurate quantization of the LPC model is of prime importance for the quality of low bitrate speech coders. In the literature, the quantization properties of several representations of the LPC model have been studied. The best results have generally been obtained with the LSP frequencies. In scalar quantization schemes, the immitance spectrum pairs (ISP) perform even slightly better. The good quantization performance of LSP and ISP can be attributed to their theoretical statistical properties: they are uncorrelated when estimated from stationary autoregressive processes, in contrast to the other representations. For small variations in the coefficients of any representation, the spectral distortion can be expressed as a weighted squared distortion measure. The optimal weighting matrix is the inverse of the covariance matrix of the coefficients. For the LSP and ISP this matrix is a diagonal matrix and hence the best weighting factors are the inverses of the theoretical variances. The difference between the LSP and ISP is due to their distributions in speech