On the rms bandwidth of nonlinearly envelope detected narrow-band Gaussian noise

This paper determines the relationship between the rms bandwidth of the envelope of a narrow-band Gaussian process and the rms bandwidth of the process itself for a general nonlinear (no-memory) envelope detector. The interesting result is shown that the output rms bandwidth depends only on the input rms bandwidth and the nonlinear device and not on the shape of the input spectrum. As an illustrative example, it is shown that the rms bandwidth of the output of a th-law envelope detector is times the rms bandwidth of the input process. Some attention is given to the determination of higher moments of the output spectrum in terms of moments of the input spectrum.