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 i ssue in connection with the rapid developments of processing techniques bas ed on sinusoidal modeling. In this paper, we introduce a new performance cr iterion for spectral envelope fitting which is based on the statistical ana lysis of the behavior of the empirical sinusoidal magnitude estimates. We F urther show that penalization is an efficient approach to control the smoot hness of the estimation envelope, In low-noise situations, the proposed met hod can be approximated by a two steps weighted least-squares procedure whi ch also provides an interesting insight into the limitations of the previou sly proposed "discrete cepstrum" approach. A systematic simulation study co nfirms that the proposed methods perform significantly better than existing ones for high pitched and noisy signals.