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A Signal-to-Noise Property of Binary Decisions

Naturevolume 193pages604605 (1962) | Download Citation



THE statistical theory of Neyman and Pearson1, which uses the likelihood ratio in making binary decisions, has proved very valuable when applied to the physical problem of detecting a signal in noise2. This theory uses error probabilities as the basic criterion of performance in detection and tends to suggest that the attention given to the signal-to-noise ratio in older approaches is now outmoded. The purpose of this communication is to point out that, while a maximum signal-to-noise property is not any longer to be considered necessary in an optimum receiver for detection, a suitably formulated signal-to-noise requirement is sufficient to lead to a likelihood ratio receiver. This conclusion rests on a fully general property of the Neyman–Pearson binary decision theory which seems to have escaped previous notice.

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  1. 1

    Neyman, J., and Pearson, E. S., Phil. Trans. Roy. Soc., A, 231, 289 (1933).

  2. 2

    For exposition and bibliography, see Peterson, W. W., Birdsall, T. G., and Fox, W. C., Trans. Inst. Radio Eng., PGIT-4, 171 (Sept. 1954), also Middleton, D., An Introduction to Statistical Communication Theory, Chap. 19 (McGraw-Hill, New York, 1960).

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  1. University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, San Diego, 52, California



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