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A general likelihood ratio formula of the author's for the detection of signals in independent white Gaussian noise is extended to allow a "one-sided" dependence in which only the future white noise is required to be independent of past signal and noise. The assumption of Gaussian additive noise is also somewhat relaxed. The proof is based on some recent martingale theorems and on the concept of the innovations process.
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T. Kailath (1970) studied this question.
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