A FAST ALGORITHM FOR FINDING THE ADAPTIVE COMPONENT WEIGHTED CEPSTRUMFOR 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-zer o 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 f ound 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 t o unity. Therefore, the numerator is the sum of all the (p - 1)th-orde r cofactors of A(z). In this correspondence, we show that the numerato r 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 po lynomial coefficients. Root finding is completely eliminated. Since th e denominator is guaranteed to be minimum phase and the numerator can be proven to be minimum phase, two separate recursions involving the p olynomial 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 findin g the LP cepstrum.