Directional dependency of cepstrum on vocal tract length

In this paper, we prove that the direction of cepstrum vectors strongly depends on vocal tract length and that this dependency is represented as rotation in the n dimensional cepstrum space. In speech recognition studies, vocal tract length normalization (VTLN) techniques are widely used to cancel age- and gender-differences. In VTLN, a frequency warping is often carried out and it can be implemented as a linear transformation in a cepstrum space; (c) over cap = Ac. However, the geometric properties of this transformation matrix A have not been well discussed. In this study, its properties are made clear using n dimensional geometry and it is shown that the matrix rotates any cepstrum vector similarly and apparently. Experimental results using resynthesized speech demonstrate that cepstrum vectors extracted from a speaker of 180 [cm] in height and those from another speaker of 120 [cm] in height are reasonably orthogonal. This result makes clear one of the reasons why children's speech is very difficult for conventional speech recognizers to deal with adequately.