Adaptive mel cepstral analysis based on UELS method

This paper proposes an adaptive mel cepstral analysis technique based on the UELS (unbiased estimation of log spectrum) method. In the UELS method, we utilize a spectral evaluation function derived from the unbiasedness condition for log spectral estimates. The log spectral estimates are obtained by minimizing the spectral evaluation function. In the mel cepstral analysis technique, the model spectrum is represented by the log squared magnitude of the frequency response of the MLSA (mel log spectrum approximation) filter having the filter coefficients of the mel cepstrum. With this mel cepstral analysis technique, we can extract an efficient and precise spectral envelope represented by the mel log spectrum of a trigonometric polynomial with the coefficients of mel cepstrum. The minimization of the spectral evaluation function can be performed iteratively. If the iterative minimization process is mainly performed in frequency domain, block processing is suitable. Since the iterative equation for the minimization can be converted into a time domain iterative equation by the Fourier transform, we obtain an adaptive algorithm for the mel cepstral analysis. At each iteration in the adaptation process, the filter coefficients are updated using only the output vector, whereas the input vector and the output vector are needed to update the filter coefficients in the LMS algorithm. To implement the M-th order mel cepstral analysis, the algorithm requires O(M) operations per sample. It is shown the algorithm has fast convergence properties in comparison with the LMS algorithm