THEORY OF EVOLVING NORMAL MODES AND THE VOCAL TRACT. PART II: EVOLVING FREQUENCY AND AMPLITUDE.
Paul Jospa · Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) · 1985
The solution is sought of the two equations, the wave equation and adiabatic invariance equation, which govern an evolving normal mode in a time-varying acoustic pipe. It is assumed that the temporal deformations of the pipe are sufficiently slow to satisfy the adiabatic approximation condition. The time evolution of the frequency and the spatio-temporal behavior of the amplitude function (i. e. the instantaneous mean-amplitude), are expressed as functionals of the pipe-area function. The results hold for the vocal tract, because articulatory movements largely satisfy the condition of the adiabatic approximation. This explains why the various existent speech synthesis systems based on the quasi-stationary vocal tract model are able to produce high quality synthetic speech.