On the best finite set of linear observables for discriminating two Gaussian signals

1 April 1967

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory

Vol. 13 (2) , 278-284
https://doi.org/10.1109/tit.1967.1054013

Abstract

Consider the problem of discriminating two Gaussian signals by using only a finite number of linear observables. How to choose the set of n observables to minimize the error probabilityP_{e}, is a difficult problem. BecauseH, the Hellinger integral, andH^{2}form an upper and a lower bound forP_{e}, we minimizeHinstead. We find that the set of observables that minimizesHis a set of coefficients of the simultaneously orthogonal expansions of the two signals. The same set of observables maximizes the HájekJ-divergence as well.

Keywords

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