As the first step in investigating uses of the Wigner distribution function (WD) for pattern recognition applications, we consider its use in a simple binary detection problem. Using the output signal-to-noise ratio as a performance measure, we show that WD based methods provide similar performance to the conventional cross-correlator. We show that, by proper extension of the known reference signal, the computation involved in WD based methods can be reduced. Simulation results are provided to illustrate our theoretical conclusions.