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A theory for the detection of pulsed carriers (of constant amplitude) in narrow-band random noise is described, based on several types of optimum tests of a statistical hypothesis against an alternative (i.e., signal and noise vs noise). Siegert's concept of the betting curve is introduced, whereby, for a finite integration time, the minimum detectable signal is uniquely defined. Three types of observer are next considered: the Neyman-Pearson, the Ideal, and the Sequential observer, whose properties are determined by the manner in which the test is carried out. For each observer it is verified that the best second detector is a logI0-rectifier, which in practice is closely approximated by the usual half-wave linear envelope-tracer. In Part II specific betting curves are calculated and the performance of the three observers is analyzed for both the weak (threshold) and strong-signal cases.
David Middleton (Wed,) studied this question.
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