La quantification vectorielle des signaux: approche algébrique

AnalyseLa quantification vectorielle sphérique (qvs)consiste à quantifier séparément la norme d’un vecteur d’une part et son orientationd’autre part. La mise en œuvre d’un tel quantificateur nécessite la spécification d’un ensemble de vecteurs normés (points sur la sphère unité) qui sont les valeurs arrondies possibles pour l’orientation du vecteur. Une façon efficace de construire un quantificateur consiste à considérer le sousensemble sphérique d’un réseau régulier de points. En particulier un algorithme très rapide est donné pour laqvsutilisant les points du réseau de Gosset en 8 dimensions. Un second algorithme (optimal également) est donné pour le réseau de Leech en 24 dimensions. Les performances de tels quantificateurs pour le bruit blanc gaussien sont comparées aux limites prédites par la théorie de l’information. Enfin l’application de ces techniques au codage du résidu de parole est discutée.AbstractSpherical vector quantization (svq)consists of quantizing separately on the one hand the norm of a vector and, on the other hand, its orientation.Implementing such quantizer requires a set of normalized vectors (points on the unit sphere) which are the possible rounded-off values for the vector’s orientation. A clever way to design such a quantizer consists of taking a spherical subset from a regular point lattice. In particular a fast algorithm is given for the Gosset lattice in 8 dimensions. A second algorithm, equally optimal, is given for the Leech lattice in 24 dimensions. The performances of such quantizers for white Gaussian noise is compared to information theory limits. Finally, the application of these techniques for encoding speech residual is discussed.

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