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

Fourier transforms

Analytical research

Circuit switching

Defense and security

Matrices

Resistance

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