Multiple-tube resonance model

Lawrence H. Smith; Douglas J. Nelson

doi:10.1117/12.456494

6 December 2002 Multiple-tube resonance model

Lawrence H. Smith, Douglas J. Nelson

Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII; (2002) https://doi.org/10.1117/12.456494
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

In speech analysis, a recurring acoustical problem is the estimation of resonant structure of a tube of non-uniform cross-sectional area. We model such tubes as a finite sequence of cylindrical tubes of arbitrary, non-uniform length. From this model, we derive a closed form expression of the resonant structure of the model and analytically derive the boundary conditions for the case of a constant group delay. Since it has been noted in the literature that the group delay of the vocal tract is constant, these boundary conditions hold for the vocal tract. In the limiting case, the non-uniform tube model reduces the well studied uniform tube model. For this limiting case, we derive an expression of the tube resonant structure in terms of a Fourier transform. Finally, we derive wave equations from the model, which are consistent with the wave equations for the telegraph wire problem.

Citation Download Citation

Lawrence H. Smith and Douglas J. Nelson "Multiple-tube resonance model", Proc. SPIE 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII, (6 December 2002); https://doi.org/10.1117/12.456494

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