This paper presents a general discriminative training method for both the front end feature extractor and back end acoustic model of an automatic speech recognition system. The front end and back end parameters are jointly trained using the Rprop algorithm against a maximum mutual information (MMI) objective function. Results are presented on the Aurora 2 noisy English digit recognition task. It is shown that discriminative training of the front end or back end alone can improve accuracy, but joint training is considerably better.