Integrated spectral kurtosis analysis

Spectral kurtosis (SK) analysis is a popular signal processing technique to locate harmonics, transients and repetitive impulses in the frequency domain. As a fourth-order frequency-domain technique the SK belongs to the wide range of higher-order spectral analysis and commonly finds application for the pre-processing of band-limited envelope analyses. We propose a novel definition of the SK, whereby SK estimates are fully resolved in time using the technique of filtering-averaging. Hereby, SK estimates are defined as the average of the full time resolution of trispectral estimates, while the latter can be processed to carry out envelope analyses directly on these estimates. Conjoining SK and envelope analysis specifies an integrated SK analysis, providing insight into the generating mechanisms of its estimates. It further differentiates from the popular short-time Fourier transform (STFT) estimator in a facilitated handling,
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requiring less parameters,
$(\boldsymbol{b})$
circumventing the quasi-stationary assumption of the STFT, and
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providing the frequency bandwidth with a clear meaning.