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In this paper, we present a method of extracting the time-delay between speech signals collected at two microphone locations. Time-delay estimation from microphone outputs is the first step for many sound localization algorithms, and also for enhancement of speech. For time-delay estimation, speech signals are normally processed using short-time spectral information (either magnitude or phase or both). The spectral features are affected by degradations in speech caused by noise and reverberation. Features corresponding to the excitation source of the speech production mechanism are robust to such degradations. We show that these source features can be extracted reliably from the speech signal. The time-delay estimate can be obtained using the features extracted even from short segments (50-100 ms) of speech from a pair of microphones. The proposed method for time-delay estimation is found to perform better than the generalized cross-correlation (GCC) approach. A method for enhancement of speech is also proposed using the knowledge of the time-delay and the information of the excitation source.