  We obtain analytical approximations for the expectation and variance of the
Spectral Kurtosis estimator in the case of Gaussian and coherent transient time
domain signals mixed with a quasi-stationary Gaussian background, which are
suitable for practical estimations of their signal-to-noise ratio and
duty-cycle relative to the instrumental integration time. We validate these
analytical approximations by means of numerical simulations and demonstrate
that such estimates are affected by statistical uncertainties that, for a
suitable choice of the integration time, may not exceed a few percent. Based on
these analytical results, we suggest a multiscale Spectral Kurtosis
spectrometer design optimized for real-time detection of transient signals,
automatic discrimination based on their statistical signature, and measurement
of their properties.
