Adaptive cepstral analysis of speech

This paper proposes an algorithm for adaptive cepstral analysis based on the UELS (unbiased estimation of log spectrum). In the UELS, the model spectrum is represented by cepstral coefficients and the mean square of the inverse filter output is minimized with respect to the cepstral coefficients. By introducing an instantaneous gradient estimate of the criterion in a similar manner of the LMS algorithm, we develop an adaptive cepstral analysis algorithm. In the analysis system, an IIR adaptive filter whose coefficients are given by cepstral coefficients is realized using the log magnitude approximation (LMA) filter. The filter approximates an exponential transfer function and its stability is guaranteed for approximation of speech spectra. To implement the M th order cepstral analysis, the algorithm requires O(M) operations per sample. It is shown that the algorithm has fast convergence properties in comparison with the LMS algorithm. Several examples of the adaptive cepstral analysis for synthetic signal and natural speech are shown to demonstrate the effectiveness of the algorithm.