THE EFFECT OF A RANDOM NOISE BACKGROUND UPON THE DETECTION OF A RANDOM SIGNAL

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Abstract
A noise distributed in phase and power according to a Rayleigh law is studied in terms of its effect upon the detectability of a signal of similar phase and amplitude distribution. An expression is derived for the probability distribution of the ratio of the power of the signal plus noise to that of the noise in the absence of the signal. The corresponding result is given for the ratio of the averages over several observations. Also derived is the probability distribution of the fractional change in noise plus signal power due to a given fractional change in signal power.

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