True discrete cepstrum: An accurate and smooth spectral envelope estimation for music processing

In the tradition of the spectral envelope estimation of periodic sounds, we propose a new accurate method, called True Discrete Cepstrum. Solving a constrained optimization problem, it provides a smooth envelope which fits exactly the given peak values. Moreover, based on the auditory masking, we propose a release of the constraint which improves the smoothness, without perceptual change. Contrarily to some other methods, the parametrization of this method is easy, and it gives a complete control of the maximal deviation of the spectral envelope from the peak values. The benefit of this new method is illustrated and an evaluation procedure validates it with a comparison with some other methods.