基于嘴唇处的声压数据确定人体声道半径

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1227-1237.

基于嘴唇处的声压数据确定人体声道半径

高展鹏,徐小川*()

南京信息工程大学数学与统计学院南京 210044

收稿日期:2021-08-27 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 徐小川 E-mail:xcxu@nuist.edu.cn
基金资助:
国家自然科学基金(11901304);南京信息工程大学大学生创新创业训练计划项目(XJDC202110300403)

Determination of Radius of a Human Vocal Tract from the Data of Sound Pressure at the Lips

Zhanpeng Gao,Xiaochuan Xu*()

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044

Received:2021-08-27 Online:2022-08-26 Published:2022-08-08
Contact: Xiaochuan Xu E-mail:xcxu@nuist.edu.cn
Supported by:
the NSFC(11901304);the NUIST Students' Platform for Innovation and Entrepreneurship Training Program(XJDC202110300403)

摘要/Abstract

摘要：

该文研究关于人体声道形状确定的反问题, 旨在由嘴唇处所有正频率的绝对声压或嘴唇处声压函数在复平面内的极点分布, 来重构人体声道半径, 证明两个唯一性定理, 并给出相应的重构算法.

关键词: 反问题, 言语声学, Sturm-Liouville算子, 声道散射

Abstract:

In this paper, we study the inverse problems for the determination of the shape of a human vocal tract, which consist in recovering the radius of a human vocal tract from either the absolute sound pressure at the lips at all positive frequencies or the poles of the sound pressure at the lips in the complex plane. Two uniqueness theorems are proved, and the corresponding reconstruction algorithms are provided.

Key words: Inverse problem, Speech acoustics, Sturm-Liouville operator, Scattering of vocal tract

中图分类号:

O175.8

高展鹏,徐小川. 基于嘴唇处的声压数据确定人体声道半径[J]. 数学物理学报, 2022, 42(4): 1227-1237.

Zhanpeng Gao,Xiaochuan Xu. Determination of Radius of a Human Vocal Tract from the Data of Sound Pressure at the Lips[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1227-1237.

参考文献

1	Aktosun T . Inverse scattering for vowel articulation with frequency-domain data. Inverse Problems, 2005, 21 (3): 899- 914
2	Aktosun T , Machuca A , Sacks P . Determining the shape of a human vocal tract from pressure measurements at the lips. Inverse Problems, 2017, 33 (11): 5002
3	Aktosun T , Sacks P , Xu X C . An inverse problem to determine the shape of a human vocal tract. Journal of Computational and Applied Mathematics, 2021, 393: 113477
4	Fant G . Acoustic Theory of Speech Production. The Hague: Mouton, 1970
5	Flanagan J L . Speech Analysis Synthesis and Perception. New York: Springer, 1972
6	Freiling G , Yurko V A . Inverse Sturm-Liouville Problems and their Applications. New York: NOVA Science Publishers, 2001
7	Gakhov F D . Boundary Value Problems. Oxford: Pergamon Press, 1966
8	Levin B Ja . Distribution of Zeros of Entire Functions. Providence, RI: Amer Math Soc, 1964
9	M?ller M , Pivovarchik V . Direct and inverse Robin-Regge problems. Electronic Journal of Differential Equations, 2017, 2017: 1- 18
10	Portnoff M R. A Quasi-One-Dimensional Digital Simulation for the Time-Varying Vocal Tract[D]. Cambridge: MIT, 1973
11	Rabiner L R , Schafer R W . Digital Processing of Speech Signals. Englewood Cliffs: Prentice-Hall Inc, 1978
12	Rundell W , Sacks P E . Reconstruction techniques for classical inverse Sturm-Liouville problems. Math Comp, 1992, 58 (197): 161- 184
13	Schroeter J , Sondhi M M . Techniques for estimating vocal-tract shapes from the speech signal. IEEE Trans Speech Audio Process, 1994, 2 (1): 133- 149
14	Sondhi M M. A Survey of the Vocal Tract Inverse Problem: Theory, Computations and Experiments//Santosa F, Pao Y H, Symes W W, Holland C. Inverse Problems of Acoustic and Elastic Waves. Philadelphia: SIAM, 1984: 1–19
15	Stevens K N . Acoustic Phonetics. Cambridge: MIT Press, 1998
16	Xu X C . Inverse spectral problems for the generalized Robin-Regge problem with complex coefficients. Journal of Geometry and Physics, 2021, 159: 103936
17	钟玉泉. 复变函数论(第二版). 北京: 高等教育出版社, 1988
17	Zhong Yuquan . Theory of Functions of Complex Varibles. Beijing: Higher Education Press, 1988

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