The most widely used technique to estimate the time-frequency representation of a discrete speech signal is the spectrogram. A technique based upon Cohen's class of generalized time frequency representations (TFR) is proposed herein and a technique for using this representation in a speech recognition system is described. The kernel design considerations used for analyzing speech signals and their rationale are detailed. Several well-known kernel functions as well as several novel kernel functions are studied. The TFR based coefficients are used to train and test the Apple Computer PlainTalk (TM) speech recognition system. A significant reduction in both the sentence and word error rates are shown.