从唇压测量确定人声道的形状
Determining the shape of a human vocal tract from pressure measurements at the lips
摘要：
在元音发音过程中确定人声道横截面积的逆问题被认为是由嘴唇处的声压的绝对值组成的数据。如果上唇是弯曲的话语过程中向下，它表明，可能有高达$M$倍的非唯一性的确定，其中$M$是最大数量的合格的共振与相关的薛定谔算子。对应于相同绝对压强的声道区域的每个$M$这样的不同候选者被唯一地确定。数学理论的恢复，每个候选人的声道面积，和容许标准的每个$M$候选人是一个声道半径指定。另一方面，如果上唇是水平的或在说话期间向上弯曲，则逆问题具有唯一解。发展的理论与一些例子说明。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
