Wrapped Gaussian Mixture Models for Modeling and High-Rate Quantization of Phase Data of Speech

The harmonic representation of speech signals has found many applications in speech processing. This paper presents a novel statistical approach to model the behavior of harmonic phases. Phase information is decomposed into three parts: a minimum phase part, a translation term, and a residual term referred to as dispersion phase. Dispersion phases are modeled by wrapped Gaussian mixture models (WGMMs) using an expectation-maximization algorithm suitable for circular vector data. A multivariate WGMM-based phase quantizer is then proposed and constructed using novel scalar quantizers for circular random variables. The proposed phase modeling and quantization scheme is evaluated in the context of a narrowband harmonic representation of speech. Results indicate that it is possible to construct a variable-rate harmonic codec that is equivalent to iLBC at approximately 13 kbps.