The Mean Value of the Envelope of a Sine and Coherent Wave Superimposed on the Narrow-band Gaussian Noise†

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Abstract
The mean value of the envelope of a sine and coherent wave superimposod on the narrow-band Gaussian noise for additive coherent detection of electrical signals is analysed. The mean value is calculated and plotted as a function of both the sine wave-to-noise and coherent wave-to-noise ratios of the coherent detector input wave. Attention is paid to the mean value of the envelope for various phase angles between the coherent wave and the sine wave plus narrow-band Gaussian noise. The normalized form of the mean value's computed curves suitable for direct application on an additive type of coherent detector is given.

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