GTM Grup de recerca en Tecnologies Mèdia, La Salle, Universitat Ramon Llull, C/Quatre Camins 2, Barcelona 08022, Catalonia, Spain.
J Acoust Soc Am. 2013 Jun;133(6):4197-209. doi: 10.1121/1.4803889.
A two-microphone transfer function (TMTF) method is adapted to a numerical framework to compute the radiation and input impedances of three-dimensional vocal tracts of elliptical cross-section. In its simplest version, the TMTF method only requires measuring the acoustic pressure at two points in an impedance duct and the postprocessing of the corresponding transfer function. However, some considerations are to be taken into account when using the TMTF method in the numerical context, which constitute the main objective of this paper. In particular, the importance of including absorption at the impedance duct walls to avoid lengthy numerical simulations is discussed and analytical complex axial wave numbers for elliptical ducts are derived for this purpose. It is also shown how the direct impedance of plane wave propagation can be computed beyond the TMTF maximum threshold frequency by appropriate location of the virtual microphones. Virtual microphone spacing is also discussed on the basis of the so-called singularity factor. Numerical examples include the computation of the radiation impedance of vowels /a/, /i/, and /u/ and the input impedance of vowel /a/, for simplified vocal tracts of circular and elliptical cross-sections.
采用双传声器传递函数（TMTF）方法建立数值分析框架，计算具有椭圆形截面的三维声道的辐射阻抗和输入阻抗。在最简单的形式中，TMTF 方法仅需要测量阻抗管中两点的声压和相应传递函数的后处理。然而，在数值环境中使用 TMTF 方法时需要考虑一些因素，这构成了本文的主要目的。特别是，讨论了在阻抗管壁上包含吸收以避免冗长的数值模拟的重要性，并为此目的推导出了用于椭圆管的解析复轴向波数。还展示了如何通过适当放置虚拟传声器来计算 TMTF 最大截止频率之外的平面波传播的直接阻抗。还基于所谓的奇异因子讨论了虚拟传声器间距。数值示例包括元音/a/、/i/和/u/的辐射阻抗以及简化圆形和椭圆形截面声道的元音/a/的输入阻抗的计算。
