Spectral Kurtosis Theory-A Review through Simulations
Kurtosis of a time signal has been a popular tool for detecting nongaussianity. Recently, kurtosis as a function frequency defined in spectral domain has been successfully used in the fault detection of induction motors, machine bearings. A link between the nongaussianity and nonstationaity has been established through Wold-Cramer’s decomposition of a nonstationary signal, and the properties of the so-designated conditional nonstationary (CNS) process have been analytically obtained. As the nonstationary signals are abundantly found in music, the spectral kurtosis could find applications in audio processing e.g. music instrument classification and music-speech classification. In this paper, the theory of spectral kurtosis is briefly reviewed from the first principles and the spectral kurtosis properties of some popular stationary signals, nonstationary signals and mixed processes are analytically obtained. Extensive Monte Carlo simulations are carried out to support the theory.
