Some properties of autoregressive model related cepstrum

Abstract

Autoregressive model related cepstrum, or, briefly, LPC cepstrum, recently gained renewed attention because it was shown to be an effective representation in speech recognizer designs [B. H. Juang, J. G. Wilpon, and L. R. Rabiner, Proc. IEEE ICASSP‐86, 765–768 (1986); B. Hanson and H. Wakita, Proc. IEEE ICASSP‐86, 757–760 (1986); Y. Tohkura, Proc. IEEE, ICASSP‐86, 761–764 (1986)]. In this paper, some properties of the LPC cepstrum are investigated that are of important consideration when the recognizer is to be deployed in situations where mismatch between the training conditions and the testing conditions may potentially occur. More specifically, the effects of LPC analysis order, additive noise, and pole movements upon some key characteristics of the LPC cepstrum are considered, such as the average and the norm of the cepstral vector. A simple relationship among the cepstral coefficients, the predictor coefficients, and the reflection coefficients is established, and unlike the Itakura‐Saito distortions, it is shown that the L2 distortion between two cepstra obtained from different‐order LPC models of the same speech data may contain an inherent nonzero bias. Also considered are the effects of additive noise, using an additive power spectrum model and a constrained ARMA model (sum of an all‐pole model and a constant). It is shown that the norm of the LPC‐cepstral vector shrinks as a results of noise contamination, compared to that of the clean speech. Further, moving the poles of an LPC‐model spectrum is shown to be equivalent to multiplying a power series to the cepstrum and thus LPC‐model bandwidth broadening and pole enhancement can be easily accomplished in the cepstral domain. Consequently, evaluation of some frequency‐weighted distortion measures that are believed to be desirable under certain conditions becomes straightforward via cepstral processing.