Regularization techniques for discrete cepstrum estimation

Abstract

Traditional spectral envelope estimation methods suffer from significant drawbacks in (high-pitched) voiced segments: spectral peaks tend to be biased toward pitch harmonics. To alleviate this drawback, discrete modeling techniques have been proposed. 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. The article 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.