A fast algorithm for computing the vocal-tract impulse response from the transfer function

This paper describes a fast algorithm that computes the impulse response of the vocal tract from its transfer function. First, numerical methods for computing the transfer function of a given vocal-tract configuration are briefly outlined. These methods include techniques (1) to decompose the numerator and denominator of the transfer function and (2) to efficiently determine the resonance modes of the vocal tract. Next, is a description of how to calculate residues at the poles and how to express the vocal-tract transfer function as a partial fraction expansion series. Each term in the expansion corresponds to an elementary formant generator, and the additive terms correspond to a parallel formant architecture. A second-order digital filter is derived for each formant generator. The impulse response of the vocal tract can therefore be specified compactly by a set of such filters. Good agreement is observed between the directly calculated transfer function and the one synthesized by the proposed algorithm. The algorithm is being used in the articulatory speech synthesizer under development both at Rutgers University and at the Royal Institute of Technology, Sweden. An ambitious goal is to incorporate the method into a text-to-speech synthesizer and/or an adaptive voice mimic system.