Detecting a transient signal by bispectral analysis

Abstract

A method for detecting a transient waveform of unknown shape in additive stationary noise is presented. The method uses a statistic computed from the sample bispectrum of a sampled record of the signal-plus-noise of length T=N tau , where 1/ tau is the sampling rate. The key result underlying the method is that the bispectrum of the noise is zero in a triangle that is a proper subset of the principal domain triangle. It is shown that the probability of detecting the signal is high if (3/16)/sup 1/2/N/sup 5/6/ is larger than rho /sup -1/, where rho is the energy signal-to-noise ratio. The result implies that the bispectrum-based test may detect a weak signal of unknown form which evades detection by other methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>