Recent developments in observation techniques such as magnetic resonance imaging allow us to obtain an accurate description of the vocal-tract shape. It is thus possible to perform analyses of the acoustic characteristics of three-dimensional vocal-tracts at higher frequencies where the assumption of plane wave propagation does not hold. Historical and conventional one-dimensional models of vocal-tracts are briefly described followed by recent knowledge of the acoustic characteristics of three-dimensional vocal-tracts.

IntroductionMRI data on the vocal tract during the production of Japanese vowels indicate coupling between the oral cavity and the nasal cavity. A large number of studies have been carried out on the nasalized vowels on the basis of a onedimensional speech production model. Acoustic analysis of the three-dimensional nasal tract has also been performed by the finite element method (FEM) [1,2]. Moreover, acoustic coupling between the oral and nasal cavities in the radiation space has been studied using simplified finite element models [3]. However, as for the case with three-dimensional radiation from the lips and nostrils, the acoustic characteristics of vocaltract shape based on MRI data are not clear. Simulations based on a detailed vocal-tract shape with proper boundary conditions are important for studying the acoustic characteristics of speech, especially at high frequencies where individual information possibly exists.In this paper, using vowel MRI data of the vocal tract with the nasal cavity during phonation of the Japanese /a/, we examine the effects of the nasal cavity on the acoustic characteristics of the speech production system. The acoustic analysis of three-dimensional geometrical vocal-tract models is performed by the FEM. Two types of models are composed on the basis of MRI data. One is a model with a threedimensional nasal cavity, and the other, for the purpose of comparison, is without a nasal cavity. The nasal cavity is also coupled to the oral cavity through a space between the lips and the nostrils in a three-dimensional volume of radiation. The effects of the wall impedance of the vocal tract are also examined.

The spatial distributions of sound pressure in artificial oral cavities were measured to examine the characteristics of wave propagation in the vocal tract. The measurement was performed with plaster replicas of the oral cavity, and pure tones were used as the driving signals to obtain both amplitude and phase distributions at varied frequencies. Plane-wave propagation, which has been widely assumed for speech production models, was examined from the measured spatial distributions of sound pressure. Trajectories of media particles and vectorial maps of acoustic intensity, which can be computed from the measured pressure distributions, were also presented to visualize the acoustic field in the oral cavity. The results showed that at certain frequencies there existed points where sound pressure was absolutely zero, with the phase spatially circulating around them. Up to about 4 kHz, except at these certain frequencies, the wave front was almost one-dimensional, though an amplitude gradient was seen in the vertical direction.

A method of computing the acoustic characteristics of a simplified three-dimensional vocal-tract model with wall impedance is presented. The acoustic field is represented in terms of both plane waves and higher order modes in tubes. This model is constructed using an asymmetrically connected structure of rectangular acoustic tubes, and can parametrically represent acoustic characteristics at higher frequencies where the assumption of plane wave propagation does not hold. The propagation constants of the higher order modes are calculated taking account of wall impedance. The resonance characteristics of the vocal-tract model are evaluated using the radiated acoustic power. Computational results show an increase in bandwidth and a small upward shift of peaks, particularly at lower frequencies, as already suggested by the one-dimensional model. It is also shown that the sharp peaks at higher frequencies are less sensitive to the values of wall impedance even though the attenuation of the higher order modes is larger than that of plane waves.

In this paper, we describe a comparison of the acoustic characteristics of one-dimensional and three-dimensional models of vocal tracts with nasal coupling. One-dimensional acoustic propagation is computed using an electric analog model. A finite element method is used for threedimensional acoustic simulation. The comparison of these two approaches involves the vocal-tract shape of two subjects, one Japanese male and one French male pronouncing the vowel /a/ in their native language. Results show that the pole/zero pairs ascribed to the nasal coupling for both simulations appeared at almost the same frequency, at least below 2 kHz. Little difference between the one-dimensional and three-dimensional simulations in the transfer functions for the French subject is observed, since the three-dimensional mesh for the French subject is smoother. An extra pole exists in the transfer function of the three-dimensional model for the Japanese subject, possibly caused by the asymmetric structure of the laryngeal cavity. In the three-dimensional distribution of the active sound intensity vectors for the French subject, sound energy fluxes circulate between oral and nasal cavities coupled in the vicinity of the lips and nostrils.