Line spectral frequencies modeling by a mixture of von Mises–Fisher distributions

• A new representation of LSF parameters, the square-root ΔLSFΔLSF (SRΔLSFSRΔLSF), is presented.
• Based on the directional property, we model the SRΔLSFSRΔLSF by a von Mises-Fisher mixture model (VMM).
• A VMM-based vector quantization (VVQ) scheme is proposed.
• The proposed VVQ outperforms Gaussian mixture model- and Dirichlet mixture model-based VQ.

Efficient quantization of the linear predictive coding (LPC) parameters plays a key role in parametric speech coding. The line spectral frequency (LSF) representation of the LPC parameters has found its applications in speech model quantization. In practical implementations of vector quantization (VQ), probability density function optimized VQ has been shown to be more efficient than the VQ based on training data. In this paper, we present the LSF parameters by a unit vector form, which has directional characteristics. The underlying distribution of this unit vector variable is modeled by a von Mises–Fisher mixture model (VMM). An optimal inter-component bit allocation strategy is proposed based on high rate theory and a distortion-rate (D-R) relation is derived for the VMM based-VQ (VVQ). Experimental results show that the VVQ outperforms the recently introduced Dirichlet mixture model-based VQ and the conventional Gaussian mixture model-based VQ, in terms of modeling performance and D-R relation.