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A digital computer has been used to simulate the passage of white, Gaussian noise through a narrow-band filter, followed by a detector and a post-detection filter. The amplitude distribution of the output of the post-detection filter has been obtained for several different detectors. In addition, the variation of false alarm rates with detector law, post-detection filtering, time constants, and threshold setting has been investigated. Not only the numerical results but also the approach, and the new detectors described are believed of interest.