The TD model represents articulatory gestures in speech as coordination of multiple articulators to accomplish a linguistic task (Saltzman & Munhall, 1989). TD has been implemented as a MATLAB application called Task Dynamic Application (TADA) for simulating inter-articulator speech coordination (Nam et al., 2015). Based on the current form of TD as a stable second-order critically damped system, we have simplified it so that its transfer function is
The time domain version of TD is quite similar to PENTA but has only static gesture targets and at the second-order:
where x denotes the F0 gestural target and τ denotes the time constant of the system. c1 and c2 are solved from the initial conditions, including F0 level and velocity. At the end of each interval, these dynamic states are also transferred to the next interval as initial conditions, similar to PENTA.
Nam, H., V. Mitra, M. Tiede, M. Hasegawa-Johnson, C. Espy-Wilson, E. Saltzman and L. Goldstein, “A procedure for estimating gestural scores from speech acoustics,” The Journal of the Acoustical Society of America, vol. 132, pp. 3980-3989, 2012.