Coherent harmonic detection using non-stationary higher order spectra

Abstract

Consider the detection of coherently related narrowband signals in the presence of noise. In this paper we define non-stationary higher order spectra (HOS) and develop nonparametric estimators of the first two non-stationary HOS, the non-stationary power spectrum and non-stationary bispectrum. The finite sample and asymptotic statistics of these estimators are presented and used to compare their detection performance to the stationary power spectrum for the case just mentioned. Detection performance is quantified in terms of probability of detection as a function of signalto-noise ratio at a fixed false alarm rate. Both theoretical and experimentally measured detection performance are presented. Normalization of the HOS is shown to have an adverse effect on their detection performance, while no normalization results in detection performance that is superior to the detection performance of the periodogram estimator of the power spectrum.