Evaluation of likelihood functions for Gaussian signals
IEEE Transactions on Information Theory
On the best finite set of linear observables for discriminating two Gaussian signals
IEEE Transactions on Information Theory
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The use of a set of digital matched filters is presented as an alternative to direct computation of the likelihood-ratio, for the problem of detecting a random signal in random noise. It is assumed that a random process composed of Gaussian background noise and (with probability P) a zero-mean Gaussian signal is sampled at N instants, the samples being corrupted by additive Gaussian measurement noise. The samples are processed by K @? N digital correlation filters which are structured so that the signal can be detected with minimum Bayes risk. The optimum filters are shown to be matched to the most relevant components of the simultaneously orthogonal expansion of the set of sampled data. State variable techniques are used to find a very practical method for determining the optimum filter structures.