Adaptive cepstral analysis—adaptive filtering based on cepstral representation

AbstractThe unbiased estimation of the log spectrum is a method which is a stricter formulation of the cepstral method from the viewpoint of the spectral estimation. In the unbiased estimation of the log spectrum, the model spectrum is represented by cepstral coefficients and a spectral criterion is minimized with respect to the cepstral coefficients. By introducing an instantaneous gradient estimate of the criterion in a manner similar to the LMS algorithm, we develop an adaptive cepstral analysis algorithm. The properties and the features of the algorithm are discussed. In the analysis system, an IIR adaptive filter whose coefficients are given by the cepstral coefficients is realized by the LMA (log amplitude approximation) filter. The filter has an exponential transfer function and its stability is guaranteed.In contrast to the conventional LMS algorithm, where the coefficients are updated based on the input vector and the output of the filter, the feature of the proposed filter is that the coefficients are updated based only on the output vector. The computational complexity in the update of coefficients and LMA filtering is of the order of0(M), whereMis the order of the analysis. The convergence property of the proposed algorithm is shown through the analysis of synthesized signals, and the usefulness of the method is demonstrated through an application example to the analysis of the natural speech.