Summary
2007 International Symposium on Nonlinear Theory and its Applications
2007
Session Number:19AM1-C
Session:
Number:19AM1-C-3
SOUND-MORPHING METHOD USING CONSTRUCTIVE MORSE THEORY
Yoshinao SHIRAKI,
pp.385-388
Publication Date:2007/9/16
Online ISSN:2188-5079
DOI:10.34385/proc.41.19AM1-C-3
Summary:
We investigate the relation between a speaker adaptation method such as VFS (Vector Field Smoothing [5]) and a sound-morphing method from a geometrical point of view. It is shown that topological field theory yields the systematic treatment of these two methods by the fact that the chain complex (Witten’s complex) plays a central role in their deformations of spectra. Witten’s complex combines the local and the global information of a manifold (or spectrum) algebraically. Consequently, it gives us numerical and algebraic invariants of the manifold. Some of the examples and the application to speech-spectra of classical mathematical ideas ? for example, Morse theory and generalized Poincar`e’s conjecture in higher dimensions ?for topological field theory are discussed.