  We introduce a new approach for Gaussianity testing using the envelope of a
signal and its coefficient of variation. The envelope of a Gaussian signal
follows the Rayleigh distribution, and given that the coefficient of variation
of the Rayleigh distribution is invariant, the envelope of Gaussian noise's
coefficient of variation is a universal constant and can be exploited as a
discriminating statistic. The main application of this approach is to detect
the Gaussianity of time series. However, the coefficient of variation of the
envelope is also a measure of amplitude modulation patterns that captures the
structure of the Fourier phase profile, making it a useful parameter to
differentiate types of non-Gaussianity and for signal classification.
