Speech analysis homomorphic prediction

Linear prediction is a generally accepted method for obtaining all-pole speech representations. However, in many situations (e.g., nasalization studies) spectral zeros are important and a more general modeling procedure is required. Unfortunately, the need for pitch synchronization has limited the success of available techniques. This paper explores a novel approach to pole-zero analysis, called homomorphic prediction, which seems to avoid the synchronization problem. A minimum-phase estimate of the vocal-tract impluse response is obtained by homomorphic filtering of the speech waveform. Such a signal, by definition, has a known time registration. Linear prediction is applied to this waveform to identify its poles. The LPC "residual" (error signal) is computed by inverse filtering. This signal contains the information about the zeros. Its z transform is then approximated by a polynomial either through a weighted least squares procedure (homomorphic prediction, using Shanks\´ method of finding zeros), or by spectral inversion followed by a second pass of LPC (homomorphic prediction involving "inverse LPC"). Results of a preliminary evaluation on real and synthetic speech are presented.