Higher‐Order Statistics

AbstractIn the past 15 years, we have witnessed an expansion of higher‐order statistics (spectra) (HOS)‐based techniques, which have been applied to a wide range of signal processing and system theory problems. This expansion is a direct result of the advantageous properties of HOS, which make them favorable in problems where nonGaussianity, nonminimum phase, colored noise, or nonlinearities are important and must be accounted for. To this end, HOS have been applied to the design of advanced communications, sonar, radar, speech, biomedical, geophysical, and imaging systems. The purpose of the present study is to review the main aspects of the application of HOS in the biomedical engineering field by presenting biomedical application problems that can directly benefit from the use of HOS, in order to aid the reader in grasping the utility of HOS‐based techniques within the biomedical signal processing framework. Fundamental definitions and properties of HOS are initially presented, pointing out the general reasons that are behind the use of HOS in signal processing (i.e., extraction of information because of deviations from normality, estimation of the phase of parametric signals, and detection and characterization of the properties of nonlinear mechanisms that generate time series). Next, a variety of HOS‐based biomedical applications are described, referring to detection of nonlinearities (e.g., quadratic phase‐coupling), denoising‐signal estimation, system identification, classification, and compression issues, and involving analysis of electroencephalogram, electrocardiogram, surface electromyogram, electroneurogram, bioacoustic signals (lung, heart, bowel sounds), tremor, and tissue signatures. Finally, an extensive list of references in the area is provided as a companion aid to the reader for further exploitation of HOS.