Detecting a transient signal by bispectral analysis

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=Nτ, where 1/τ 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)^1/2N^5/6 is larger than ρ^-1, where ρ 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