In Analog systems, the chief objective is the fidelity of reproduction of waveforms, hence, the suitable performance criterion is the output signal to noise ratio. The choice of this criterion stems from the fact that the signal to noise is related to ability of the listener to interpret a message. Matched filter is the optimum linear filter that maximizes the output signal to noise ratio. The Matched filter is optimum in the sense that it maximizes the signal amplitude to rms noise ratio at the decision-making instant. Although it is reasonable to assume that maximization of this signal to noise ratio will minimize the detection error probability, we have not proved that threshold detection is the optimum method from the detection error point of view. It will be shown that when the channel noise is white Gaussian, the matched filter receiver is indeed the optimum receiver that minimizes the detection error probability.-　　　In Analog systems, the chief objective is the fidelity of reproduction of waveforms, hence, the suitable performance criterion is the output signal to noise ratio. The choice of this criterion stems from the fact that the signal to noise is related to ability of the listener to interpret a message. Matched filter is the optimum linear filter that maximizes the output signal to noise ratio. The Matched filter is optimum in the sense that it maximizes the signal amplitude to rms noise ratio at the decision-making instant. Although it is reasonable to assume that maximization of this signal to noise ratio will minimize the detection error probability, we have not proved that threshold detection is the optimum method from the detection error point of view. It will be shown that when the channel noise is white Gaussian, the matched filter receiver is indeed the optimum receiver that minimizes the detection error probability.