The ability of the human auditory system to localize the direction of a sound source in a reverberant environment extends from simple clicks to complex speech signals. The perceived location of the auditory event is dominated by the direct sound, for small enough time intervals between the direct sound and reflection-a phenomenon known as the precedence effect. In this paper we present a computer simulation of the precedence effect for speech, implemented using Matlab and tested with speech signals from the TIMIT database. The model is based on the biological assumption that the rate of change of a signal (onset) is critical in triggering the precedence effect. The model demonstrates the precedence effect on speech signals, as opposed to prior models that have only been tested on clicks. In addition, a novel onset enhancement method is described and implemented using the gamma filter, a new class of linear systems for adaptive signal processing. This method can either use fixed coefficients and obtain similar results to prior methods of onset enhancement, or use an adaptive framework. The adaptive framework is promising in its ability to enhance onsets and to reduce the steady state portions of the signal.