Inverse filtering of tube models with frequency dependent tube terminations

The tube model, realized by lattice filters in discrete time, can be used to describe the propagation of plane sound waves through the vocal tract. The tube model which is treated in this contribution contains two prescribed terminations. One for the lip opening and one for the constriction at the glottis. These two terminations are frequency dependent and the lip termination must be adapted to the specific speech sound. To estimate the parameters of this tube model, standard algorithms like the Burg-method and related methods are not applicable. Therefore a procedure is proposed to estimate the parameters of these tube models in an adequate way. The procedure is based on inverse filtering, which is carried out iteratively. The analysis of test signals, which are generated from prescribed systems, shows almost perfect results by the proposed algorithm. The analysis of consonants shows, that the corresponding constrictions in the vocal tract area functions can be observed. Using these estimated constrictions it is possible to synthesize VCV transitions too, which implies the typical formant movements.