Abstract
Estimation of vocal tract area function (VTAF) from speech signals is an inverse scattering problem. The medical application of VTAF includes clinical analysis of aphasia and dysarthria, language training, and phoniatrics for the hearing-impaired. The estimation results of VTAF provide a visual feedback on auditory sense. According to Wakita's method, the filtering processes of the inverse digital filter in signal analysis and the acoustic tube model in physics are identical. It could be confirmed by the relationship between linear prediction coding and analysis lattice structure. The efficiency of calculation could be improved with the Levinson-Durbin recursive algorithm. Due to the restriction of all-pole transfer functions, the speech production was modeled by Wakita as follows: sound waves produced by the glottis pass from the throat to the oral cavity and then radiate at lips. One could notice that the procedure does not take the nasal resonance effect into consideration. In this thesis, we use an iterative procedure proposed by Schnell and Lacroix to obtain pole-zero type transfer functions. After that, we set up initial conditions and boundary conditions based on the typical size and shape of the human vocal tract. Last, with the assistance of factorization and exhaustive search, the vocal tract is described as a three-branched model which could be divided into the main tract, the oral cavity and the nasal cavity. Thus, we could estimate VTAF by considering the nasal resonance effect. We use nasalized vowels and non-nasalized vowels to verify the validity of the acoustic tube model and the solution of the inverse scattering problem.