In an exploration of the spectral modelling of speech, this thesis presents theory and applications of constrained linear predictive (LP) models. Spectral models are essential in many applications of speech technology, such as speech coding, synthesis and recognition. At present, the prevailing approach in speech spectral modelling is linear prediction. In speech coding, spectral models obtained by LP are typically quantised using a polynomial transform called the Line Spectrum Pair (LSP) decomposition. An inherent drawback of conventional LP is its inability to include speech specific a priori information in the modelling process.
This thesis, in contrast, presents different constraints applied to LP models, which are then shown to have relevant properties with respect to root loci of the model in its all-pole form. Namely, we show that LSP polynomials correspond to time domain constraints that force the roots of the model to the unit circle. Furthermore, this result is used in the development of advanced spectral models of speech that are represented by stable all-pole filters.
Moreover, the theoretical results also include a generic framework for constrained linear predictive models in matrix notation. For these models, we derive sufficient criteria for stability of their all-pole form. Such models can be used to include a priori information in the generation of any application specific, linear predictive model. As a side result, we present a matrix decomposition rule for Toeplitz and Hankel matrices.reviewe
