A. Acoustic Theory and Modeling of the Vocal Tract
A. Acoustic Theory and Modeling of the Vocal Tract by H.W. Strube, Drittes Physikalisches Institut, Universität Göttingen A.l Introduction This appendix is intended for those readers who want to inform themselves about the mathematical treatment of the vocal-tract acoustics and about its modeling in the time and frequency domains. Apart from providing a funda mental understanding, this is required for all applications and investigations concerned with the relationship between geometric and acoustic properties of the vocal tract, such as articulatory synthesis, determination of the tract shape from acoustic quantities, inverse filtering, etc. Historically, the formants of speech were conjectured to be resonances of cavities in the vocal tract. In the case of a narrow constriction at or near the lips, such as for the vowel [uJ, the volume of the tract can be considered a Helmholtz resonator (the glottis is assumed almost closed). However, this can only explain the first formant. Also, the constriction - if any - is usu ally situated farther back. Then the tract may be roughly approximated as a cascade of two resonators, accounting for two formants. But all these approx imations by discrete cavities proved unrealistic. Thus researchers have have now adopted a more reasonable description of the vocal tract as a nonuni form acoustical transmission line. This can explain an infinite number of res onances, of which, however, only the first 2 to 4 are of phonetic importance. Depending on the kind of sound, the tube system has different topology: • for vowel-like sounds, pharynx and mouth form one tube; • for nasalized vowels, the tube is branched, with transmission from pharynx through mouth and nose; • for nasal consonants, transmission is through pharynx and nose, with the closed mouth tract as a "shunt" line.
[Show full text]