Study of Jacobian Normalization for VTLN

The divergence of the theory and practice of vocal tract length normalization (VTLN) is addressed, with particular emphasis on the role of the Jacobian determinant. VTLN is placed in a Bayesian setting, which brings in the concept of a prior on the warping factor. The form of the prior, together with acoustic scaling and numerical conditioning are then discussed and evaluated. It is concluded that the Jacobian determinant is important in VTLN, especially for the high dimensional features used in HMM based speech synthesis, and difficulties normally associated with the Jacobian determinant can be attributed to prior and scaling.