确定人体声道形状的逆问题
An inverse problem to determine the shape of a human vocal tract
摘要：
逆问题确定的横截面积的人类声道在一个元音的发音被认为是。唇缘处的频率相关边界条件用无限大平面挡板上振动活塞的声阻抗表示。嘴唇处的相应压力用归一化阻抗和与相关薛定谔方程的所谓Jost函数相关的关键量表示。各种输入数据集被认为是解决反问题，包括在嘴唇的压力，在嘴唇的绝对压强，或在嘴唇的压力的极点。利用Gel'fand-Levitan方法求解相应的薛定谔方程，得到了反问题的解。
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. The frequency-dependent boundary condition at the lips is expressed in terms of the acoustic impedance of a vibrating piston on an infinite plane baffle. The corresponding pressure at the lips is expressed in terms of the normalized impedance and a key quantity related to the so-called Jost function of an associated Schrödinger equation. Various input data sets are considered to solve the inverse problem, including the pressure at the lips, the absolute pressure at the lips, or the poles of the pressure at the lips. The solution to the inverse problem is obtained with the help of the Gel'fand-Levitan method for the associated Schrödinger equation.
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