B-Spline Model Order Selection With Optimal MDL Criterion Applied to Speech Fundamental Frequency Stylization

Abstract

In the speech processing field, stylization of fundamental frequency <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> has been subjected to numerous works. Models proposed in the literature rely on knowledge stemming from phonology and linguistics. We propose an approach that deals with the issue of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> curve stylization requiring as few linguistic assumptions as possible and in the framework of B-spline models. A B-spline model, characterized by a sequence of knots with which control points are associated, enables the formalization of discontinuities in the derivatives of the observed values sequence. Beyond the implementation of a B-spline model to stylize an open curve sampled using a constant step, we address the problem of the optimal model order choice. We propose to use a parsimony criterion based on a minimum description length (MDL) approach, in order to optimize the number of knots. We derive several criteria relying on bounds estimated from parameter values. We demonstrate the optimality of these choices in the theoretical MDL framework. We introduce a notion of variable precision of parameters which enables a good compromise between the modeling precision and degrees of freedom of the estimated models. Experiments are performed on a French speech corpus and compare three MDL criteria. The use of both B-spline model and MDL methodology enables an efficient modeling of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> curves and provides an RMS error around 1 Hz while allowing a relatively high compression rate about 40%.