Nonstationary higher order spectral analysis

This report discusses the detection performance of a variety of higher order spectra for a variety of signals. Of particular significance is the introduction of a new type of higher order spectra called nonstationary higher order spectra. Nonstationary higher order spectra are not the stationary higher order spectral representations of nonstationary process, but are in fact different spectra which contain the stationary higher order spectra as a subset of their domain. It is shown quantitatively through theoretical predictions and simulations that these type of spectra perform better at detecting nonstationary signals than do the traditional stationary spectra. For the first time, small sample statistics have been derived and applied to the detection performance rather than asymptotic statistics, resulting in a more accurate performance prediction for typical sample sizes for nonstationary signals.