Effect of jacobian compensation in linear transformation based VTLN under matched and mis-matched speaker conditions

In this paper we study the effect of use of jacobian in different linear transformation (LT) based methods of VTLN. In conventional VTLN, the jacobian is highly non-linear and can not be computed and hence is ignored. In the LT based VTLN, since VTLN scaling is expressed as a matrix multiplication of un-warped MFCC features, jacobian is simply turns out as the determinant of the VTLN warp matrices. Hence in this framework of VTLN it is possible to account for jacobian. Two different methods, namely, L-VTLN and T-VTLN, are used for implementing LT based VTLN. By conducting experiments on the RM task and the TIDIGITs databases in matched and mismatched speaker conditions, the performance of using jacobian in warp-factor estimation have been evaluated. It is observed that in almost every matched and mis-matched speaker conditions jacobian improves performance in L-VTLN framework. In T-VTLN, however, jacobian does not improve the performance in any mis-matched speaker conditions. The cases in which jacobian degrades performance in L-VTLN and T-VTLN have been studied in detail.