Effect of Jacobian Compensation in Linear Transformation Based VTLN Under Matched and Mis-Matched Speaker Conditions

In this paper, the authors 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.