  Like the ordinary power spectrum, higher-order spectra (HOS) describe signal
properties that are invariant under translations in time. Unlike the power
spectrum, HOS retain phase information from which details of the signal
waveform can be recovered. Here we consider the problem of identifying multiple
unknown transient waveforms which recur within an ensemble of records at
mutually random delays. We develop a new technique for recovering filters from
HOS whose performance in waveform detection approaches that of an optimal
matched filter, requiring no prior information about the waveforms. Unlike
previous techniques of signal identification through HOS, the method applies
equally well to signals with deterministic and non-deterministic HOS. In the
non-deterministic case, it yields an additive decomposition, introducing a new
approach to the separation of component processes within non-Gaussian signals
having non-deterministic higher moments. We show a close relationship to
minimum-entropy blind deconvolution (MED), which the present technique improves
upon by avoiding the need for numerical optimization, while requiring only
numerically stable operations of time shift, element-wise multiplication and
averaging, making it particularly suited for real-time applications. The
application of HOS decomposition to real-world signals is demonstrated with
blind denoising, detection and classification of normal and abnormal heartbeats
in electrocardiograms.
