Decomposition of rotational distortion caused by VTL difference using eigenvalues of its transformation matrix
Daisuke Saito, Nobuaki Minematsu, Keikichi Hirose · 2008
In speech recognition studies, vocal tract length normalization (VTLN) techniques are widely used to cancel age- and gender-difference. In VTLN, the distortion is often modeled as a lin-ear transform in a cepstrum space; ĉ=Ac. In our previous study, the geometrical properties ofA were discussed and it was shown that the matrix can be approximated as rotation matrix. In this study, a new method of better approximating A is pro-posed. Using eigenvalues ofA, its quasi-rotational distortion is factorized into multiple rotation operations and multiple magni-fication operations. Using this method, the intrinsic ambiguity of the rotation angle used in our previous study is resolved. In-stead, multiple rotation angles are introduced to understand bet-ter what kind of geometrical distortionsA induces to cepstrum vectors. Experiments show the validity of the new method and a new speech feature is also derived by the new method. Index Terms: frequency warping, rotation matrix, vocal tract length, eigenvalue, rotational plane