The relationship of sequential filter theory to information theory and its application to the detection of signals in noise by Bernoulli trials

In this paper the problem of detecting signals in noise by the method of sequential filtering is formulated. A slicing operator for converting a given random variable into a Bernoulli random variable is defined. A method for choosing an optimum slicing operator in a certain prescribed sense is given. It is also shown that the Bernoulli sequential test is defined by three parameters , and rather than four, as one would normally expect. The significance of these transformations is briefly discussed. Finally, the theory of Bernoulli sequential detection is applied to the detection of a sine-wave carrier in noise when the signal-to-noise ratio is less than one. The efficiency of this detector is calculated and compared with the results of others. Curves of the significant Bernoulli sequential detector characteristics are given for this problem.