Regularization techniques for discrete cepstrum estimation

The discrete cepstrum method consists in fitting a spectral envelope parameterized by cepstrum coefficients to a discrete set of spectral points using a log-spectral distortion criterion. Unfortunately, this estimation problem is ill conditioned in many cases of interest. This letter introduces a simple regularization technique that guarantees that the spectral envelope is well behaved. A modification of the basic regularization criterion is proposed in order to take into account a possible prior knowledge of the spectral tilt of the envelope.