The distance measure is of great importance in both the design and coding stage of a vector quantizer. Due to its complexity, however, the spectral distance which best correlates with the perceptual quality is seldom used. On the other hand, various weighted squared Euclidean distance measures give close or even accurate estimation of the meaningful spectral distance. Since they are in general mathematically more tractable, these weighted squared Euclidean distance measures are more commonly used. Significant differences can be found in the performance of different distance measures suggested in previous literatures. In this paper, a complete study and comparison of weighted squared Euclidean distance measures is given. This paper also proposes a new weighted squared Euclidean distance measure for vector quantization of Line Spectrum Pairs (LSP) or Cosine of LSP (CLSP) parameters. It also presents an efficient adaptation apparatus for using the proposed distance measure in the case of split or multi-stage vector quantizers.
Kövesi, B., Saoudi, S., Boucher, J. M., & Horváth, G. (1999). Real time vector quantization of LSP parameters. Speech Communication, 29(1), 39–47. https://doi.org/10.1016/S0167-6393(99)00026-6