The past 20 years witnessed an expansion of power spectrum estimation techniques, which have proved essential in many applications, such as communications, sonar, radar, speech/image processing, geophysics, and biomedical signal processing [13, 11, 7]. In power spectrum estimation the process under consideration is treated as a superposition of statistically uncorrelated harmonic components. The distribution of power among these frequency components is the power spectrum. As such, phase relations between frequency components are suppressed | Athina P. Petropulu. Higher-Order Spectral Analysis. 2000 CRC Press LLC. http . Higher-Order Spectral Analysis Athina P. Petropulu Drexel University Introduction Definitions and Properties of HOS HOS Computation from Real Data Linear Processes Nonparametric Methods Parametric Methods Nonlinear Processes Applications Software Available Acknowledgments References Introduction The past 20 years witnessed an expansion of power spectrum estimation techniques which have proved essential in many applications such as communications sonar radar speech image processing geophysics and biomedical signal processing 13 11 7 . In power spectrum estimation the process under consideration is treated as a superposition of statistically uncorrelated harmonic components. The distribution of power among these frequency components is the power spectrum. As such phase relations between frequency components are suppressed. The information in the power spectrum is essentially present in the autocorrelation sequence which would suffice for the complete statistical description of a Gaussian process of known mean. However there are applications where one would need to obtain information regarding deviations from the Gaussianity assumption and presence of nonlinearities. In these cases power spectrum is of little help and one would have to look beyond the power spectrum or autocorrelation domain. Higher-Order Spectra HOS of order greater than 2 which are defined in terms of higher-order cumulants of the data do contain such information 16 . The third-order spectrum is commonly referred to as bispectrum the fourth-order one as trispectrum and in fact the power spectrum is also a member of the higher-order spectral class it is the second-order spectrum. HOS consist of higher-order moment spectra which are defined for deterministic signals and cumulant spectra which are defined for random processes. In general there are three motivations .
