An extension of the classical LPC model of speech production is proposed, where the LPC spectral trajectories are viewed as the output of linear shift-invariant filters (articulator filters: representing the articulator responses to a brain command), excited by piece-wise constant signals (command signals: representing brain commands). Efficient procedures for the articulator filters estimation and for the command signals computation from the speech signal are outlined. The model is then used to design a very low bit rate, low computational burden vocoder, the Step Decomposition Vocoder, from which comprehensible speech can be obtained with about 650 bps, and with a 250 millisec. algorithmic delay.