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We investigate the interactions of front-end feature extraction and back-end classification techniques in HMM based speech recognizer. This work concentrates on finding the optimal linear transformation of Mel-warped short-time DFT information according to the minimum classification error criterion. These transformations, along with the HMM parameters, are automatically trained using the gradient descent method to minimize a measure of overall empirical error count. The discriminatively derived state-dependent transformations on the DFT data are then combined with their first time derivatives to produce a basic feature set. Experimental results show that Mel-warped DFT features, subject to appropriate transformation in a state-dependent manner, are more effective than the Mel-frequency cepstral coefficients that have dominated current speech recognition technology. The best error rate reduction of 9% is obtained using the new model, tested on a TIMIT phone classification task, relative to conventional HMM.