Estimation of the spectral envelope of voiced sounds using a penalized likelihood approach

Estimation of the spectral envelope (magnitude of the transfer function) of a filter driven by a periodic signal is a long-standing problem in speech and audio processing. Recently, there has been a renewed interest in this issue in connection with the rapid developments of processing techniques based on sinusoidal modeling. In this paper, we introduce a new performance criterion for spectral envelope fitting which is based on the statistical analysis of the behavior of the empirical sinusoidal magnitude estimates. We further show that penalization is an efficient approach to control the smoothness of the estimation envelope. In low-noise situations, the proposed method can be approximated by a two-step weighted least-squares procedure which also provides an interesting insight into the limitations of the previously proposed "discrete cepstrum" approach. A systematic simulation study confirms that the proposed methods perform significantly better than existing ones for high pitched and noisy signals.