ABSTRACT
Target-directed state equation for hidden speech dynamics (discrete-time):
x(k + 1) = 4'(k)x(k) + [I — 4(k)]t(k) + *d(k), (10.39) where x(k) t if k -4 oo.
control two different temporal regions of the Tongue-Body task variable are distinct, one for each distinct vowel in the utterance. This results in two different target positions, for the same Tongue-Body task variable, at two different temporal regions. In contrast, all three Tongue-Blade features (and the associated target positions of the corresponding task-variable component) in the utterance are identical, and so are the two Velum features and the two Glottal features. An interesting phenomenon shown in this example is a "hiding" of the feature or articulatory gesture of Tongue-Blade of [n] in word ten (drawn as the shaded box in Fig. 10.2). The "hiding" is a result of the complete temporal feature overlapping with the Lips feature in [p]. However, according to the task-dynamic model, the Tongue-Blade task variable exhibits its dynamics preceding the feature onset of complete closure (target position) of the Lip-constriction component of the task variable. The Lip-constriction variable also follows a dynamic path towards the complete closure after the feature onset. Therefore, the predicted acoustics from this model will be very different from that predicted simply by assimilation of [n] to [m] (a complete change of phones in pronunciation) according to the conventional linear phonology. The task dynamics is responsible for this "phonological" change.
