This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The work funded by this grant addresses theoretical issues pertaining to potential applications of higher-order spectra (polyspectra) for communications and measurement. Although the sensitivity to additive Gaussian noise provided a motive for our interest in the bispectrum, the research done here focused on the ability of the bispectrum to see outside the Nyquist interval. The main contribution of this work is a new understanding of the everyday phenomenon of aliasing that is described below. The second contribution this work makes is significant, though limited, progress in understanding the joint realizability, conditions for spectra and bispectra. A third contribution, which arose in efforts to broaden our results on joint realizability, is the awareness that a very common inequality, used to normalize the bispectrum, is invalid. This result has considerable significance for the practical use of the bispectrum.
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