A fast algorithm for finding the adaptive component weighted cepstrum for speaker recognition

In speaker recognition systems, the adaptive component weighted (ACW) cepstrum has been shown to be more robust than the conventional linear predictive (LP) cepstrum. The ACW cepstrum is derived from a pole-zero transfer function whose denominator is the pth-order LP polynomial A(z). The numerator is a (p-1)th-order polynomial that is up to now found as follows. The roots of A(z) are computed, and the corresponding residues obtained by a partial fraction expansion of 1/A(z) are set to unity. Therefore, the numerator is the sum of all the (p-1)th-order cofactors of A(z). We show that the numerator polynomial is merely the derivative of the denominator polynomial A(z). This greatly speeds up the computation of the numerator polynomial coefficients since it involves a simple scaling of the denominator polynomial coefficients. Root finding is completely eliminated. Since the denominator is guaranteed to be minimum phase and the numerator can be proven to be minimum phase, two separate recursions involving the polynomial coefficients establishes the ACW cepstrum. This new method, which avoids root finding, reduces the computer time significantly and imposes negligible overhead when compared with the approach of finding the LP cepstrum.