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The amplitude response of a receiver to off-tuned pulses is shown to approximately consist of a sin x impulse followed by a steady state portion with a second sin x impulse concluding the response. The probability of detecting the sin x impulse is determined and some typical results presented. These results can also be used to predict the probability of detecting optimum design pulses whose response is a sin x function. The detection curves of the sin x pulse are compared to those of the ideal square pulse and it is shown that a 1/(square root of 2) reduction of the peak pulse amplitude approximates the correct probability of detection curves. The total probability of detection is obtained by using a peak factor (F factor) to calculate the probability of detecting the impulse responses and applying conservation of energy to calculate the probability of detecting the steady state portion. (Author)