The spectral kurtosis of nonstationary signals: Formalisation, some properties, and application

The spectral kurtosis is a statistical tool heuristically introduced in the 80's to detect the presence of transients in a signal and their location in the frequency domain. In spite of its pleasant properties, it has been rarely used thus far, probably because of its lack of formalism. This paper provides an attempt of formalisation by means of the Wold-Cramér decomposition of nonstationary processes. This leads to a simple definition, and enables the deduction of numerous properties. An estimator of the spectral kurtosis is also proposed, based on the short-time Fourier transform. Its scope of validity and statistical performance are investigated in detail. Finally, the value of the spectral kurtosis is illustrated on an industrial application.