Fourth‐order statistics can be useful in many signal processing applications, offering advantages over or supplementing second‐order statistical techniques. One reason is that fourth‐order statistics can discriminate between non‐Gaussian signals and Gaussian noise. Another is that fourth‐order statistics contain phase information, whereas second‐order statistics do not. In the continuing development of the mathematical properties of fourth‐order statistics, several researchers have derived existence conditions and definitions for the unaliased and aliased principal domains of the discrete trispectrum, which is significantly more complex than the power or energy spectrum. The consistencies and inconsistencies of these results are presented and resolved in this paper. The most flexible definitions give four individual principal domains for the discrete trispectrum: two unaliased and two aliased. The most useful combinations are those that combine the two unaliased domains together and the two aliased domains together, which can be done easily from the four individual domains. The relationship between the individual trispectral domains and signal bandwidth is important when using the fourth‐order statistic for applications because they have particular properties that can be detrimental to some deconvolution algorithms. The reasons for this, as well as the validity of proposed solutions to this problem, are explained by the trispectral structure and its origins.
Signal parameter estimation of complex exponentials using fourth order statistics: additive Gaussian noise environment