Some simple examples of singular detection of continuous signals in noise.
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A discussion of the assumption--concerning the statistical detection of continuous signals in noise--that the boundedness of the expected value of the likelihood ratio is both a necessary and sufficient condition that the detection be nonsingular. The necessity of this condition is shown, but examples are given to demonstrate that the condition is insufficient unless the additional requirement is also imposed that the noise process be regular. In particular, processes with band-limited or exponential spectra are singular and should be avoided as models of background noise.
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