An Acoustic-to-Articulatory Transformation for Vowel-Like Sounds in Human Speech
Dean Andrew Chalker, David Mackerras · 1987
In this paper, the joint probability density function of the weight vector in LMS adaptation is studied for Gaussian data models. An exact expression is derived for the characteristic function of the weight vector at time n + 1 conditioned on the weight vector at time n. The conditional characteristic function is expanded in a Taylor se- ries and averaged over the unknown weight density to yield a first or- der partial differential-difference equation in the unconditioned char- acteristic function of the weight vector. The equation is approximately solved for small values of the adap- tation parameter, and the weights are shown to be jointly Gaussian with time-varying mean vector and covariance matrix given as the so- lution to well-known difference equations for the weight vector mean and covariance matrix. The theoretical results are applied to analyzing the use of the weights in detection and time delay estimation. Abstract-The acoustic transfer function of the human vocal tract depends upon several articulator positions defining the vocal tract ar- ticulatory state. The acoustic attributes of voiced speech may be deter- mined by using a transmission line analog of the vocal tract to obtain its acoustic transfer function for a given articulatory state. This for- ward transformation is relatively straightforward compared to the in- verse transformation from acoustic attributes to vocal tract state. We present a database lookup method for achieving the inverse transfor- mation for nonnasalized vowel-like sounds in human speech. Using a six-parameter articulatory model, a database was generated c,ompris- ing 11 385 states with given articulatory settings and corresponding computed acoustic attributes. A method was developed for determin- ing, from a given speech sample, the database entry having the closest match to the acoustic attributes of the sample, thus obtaining the cor- responding articulatory state. The results of three types of test of the method are presented, which show that the method does recover real- istic vocal tract states for most nonnasalized vowel-like sounds.