In this disserattion we consider detection of signals in discrete-time observations from three distinct aspects.
In the first part of this dissertation, fuzzy statistical techniques are considered in the optimum signal detection problems. The likelihood ratio for fuzzy detection of known signals is obtained. As a special case of the fuzzy signal detector, a fuzzy set theoretic approach to sign detection of known signals is considered. Specifically, the test statistic of the fuzzy sign detector for known signals is obtained. Some properties of the fuzzy sign nonlinearity, which constitutes the fuzzy sign detector, are also described. Finally the performance characteristics of the fuzzy sign detector are investigated and compared to those of the crisp sign detector.
In the second part, the test statistic of the two-sample locally optimum rank detector is derived for weak random signals in additive noise. It is shown that the two-sample locally optimum rank detector for random signals has interesting similarities to the one-sample locally optimum rank detector for random signals. The detector is also shown to be viewed as a generalization of the two-sample locally optimum rank detector for known signals. Some examples and properties of the score functions constituting the locally optimum rank test statistic are investigated.
In the last part of this dissertation, a new test criterion for binary decision problems is introduced. The integrated power function over a parameter interval is considered as an extension of the power function. The concept of the most integrated powerful (MIP) test based on the integrated power function is introduced. It is shown that the MIP test is the same as the uniformly most powerful (UMP) test for the one-parameter exponential family. As an application of the MIP test, the test statistic of the MIP detector for known and random signals is obtained and discussed, and then approximation to the MIP test statistic are investigated. The performance characteristics for the MIP detector are discussed and compared to those of other well-known detectors through finite sample-size performance comparison.
