Improving the kelly-lochbaum vocal tract model using conical tube sections and fractional delay filtering techniques

An articulatory model of speech production is usually con- structed by approximating the profile of the vocal tract using cylindrical tube sections. This is implemented by a digital ladder filter that is called the Kelly-Lochbaum model. In this paper we propose an extended approach, where the tube sections approximating the profile of the tract are conical instead of cylindrical. Furthermore, the length of each tube section in our model can be accurately controlled using a novel fractional delay filtering scheme. These refinements result in an accurate and intuitively con- trollable vocal tract model that is well suited for articula- tory speech synthesis. that the second restriction is not solved, i.e., the length of each tube section cannot be independently controlled in the discrete-time model. In Strube's method, only one section is continuously controllable while the change of the sampling rate scales the length of all tube sections by the same factor. This restriction mainly gives rise to difficulties in the control of the model. Namely, the mapping of the physi- cal parameters to the model parameters (reflection coeffi- cients in the scattering junctions) is not simple. The artic- ulators move in the front-back dimension and the diameter of the tract also varies whereas in the model only the diameter of the tube can be adjusted at the fixed points. Control would be more intuitive if the junctions could be moved. Recently, we have proposed a method for changing the position of the scattering junctions of the KL model con- tinuously (6), (7). Consequently, the length of every tube section can be continuously varied. This model employs interpolation together with a new technique that we call deinterpolation. In this paper we propose a further improvement to the KL model. Instead of cylindrical tube sections we use truncated cones. The resulting model is computationally only slightly more expensive than the basic KL model. Namely, the reflection coefficient at the joint of two coni- cal tubes of different taper is not a real number as in the case of cylindrical tubes, but a first-order filter. The coni- cal-tube approximation of the tract profile is, however, better than that obtained with the same number of cylin- drical tube sections. This is quickly understood noticing that conical tubes perform a first-order polynomial approx- imation of the vocal tract profile as opposed to the zeroth- order approximation performed by cylindrical tubes. The main contribution of the present work is the intro- duction of digital filters and structures for modeling coni- cal tube systems. Furthermore, we combine the fractional delay junctions and conical tube sections. This results in a novel vocal tract model which is easily controllable and more accurate than the traditional KL model and thus is particularly well suited for articulatory speech synthesis.