Spectral Kurtosis Statistics of Transient Signals

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.