A novel system for speech recognition uses differential cepstra over time frames as acoustic features, together with the traditional static cepstral features, for hidden trajectory modeling, and provides greater accuracy and performance in automatic speech recognition. According to one illustrative embodiment, an automatic speech recognition method includes receiving a speech input, generating an interpretation of the speech, and providing an output based at least in part on the interpretation of the speech input. The interpretation of the speech uses hidden trajectory modeling with observation vectors that are based on cepstra and on differential cepstra derived from the cepstra. A method is developed that can automatically train the hidden trajectory model's parameters that are corresponding to the components of the differential cepstra in the full acoustic feature vectors.