2016/10/05 by Tuncay Aktosun, Alicia Machuca, Paul Sacks
Mathematics · Medicine · Physics and Astronomy · Psychology · #Human voice #Inverse #Inverse problem #Mathematical Analysis and Transform Methods #Phonation #Phonetics and Phonology Research #Pressure measurement #Vocal tract #Voice and Speech Disorders #Vowel #math-ph #math.MP #msc:34A55 #msc:35R30 #msc:76Q05
paper · pdf · doi:10.1088/1361-6420/aa882d
published as Inverse Problems, vol. 33, (2017), 115002, 33 pages · 47 pages, 4 figures
arxiv created 2016/10/05 · openalex created_date 2016/10/14 · openalex publication_date 2017/08/24 · arxiv updated 2018/05/08 · openalex updated_date 2026/08/08
Abstract The inverse problem of determining the cross-sectional area of a human vocal tract during the utterance of a vowel is considered in terms of the data consisting of the absolute value of sound pressure at the lips. If the upper lip is curved downward during the utterance, it is shown that there may be up to an M -fold nonuniqueness in the determination, where M is the maximal number of eligible resonances associated with a related Schrödinger operator. Each of the M such distinct candidates for the vocal-tract area corresponding to the same absolute pressure is uniquely determined. The mathematical theory is presented for the recovery of each candidate for the vocal-tract area, and the admissibility criterion for each of the M candidates to be a vocal-tract radius is specified. On the other hand, if the upper lip is horizontal or curved upward during the utterance, then the inverse problem has a unique solution. The theory developed is illustrated with some examples.