Transient Detection With Cross Wavelet Transforms and Wavelet Coherence

Effective detection of unknown, transient oscillations in strong, colored, time varying noise and clutter has remained a signal processing challenge. Recently we presented a self-normalized wavelet detector for this purpose. Here, we revisit this detection problem for the case of a tapered, complex, transient oscillation observed coherently in two time series. We develop and compare three detectors based on the following: 1) the self-normalized Morlet cross wavelet spectrum (NCM); 2) the normalized cross discrete wavelet transforms (DWT), extended from Wang and Willet's DWT power law detector (NCDWT3); and 3) wavelet coherence (WCOH). Each detector normalizes the cross wavelet spectrum to perform a binary hypothesis test for noise only. Simulated receiver operating curves for complex tapered transient oscillations in colored, slowly time varying, Gaussian noise and 60dB low frequency clutter are included for the three detector types and for one based on the fast Fourier transform (FFT) (NCFFT3) for comparison. Without clutter, detection rates at 0.1% false alarm rates for a (signal on) signal to noise ratio of 0.5 are: 99.4%, 99.1%, 97.0% and 96.3% for the NCFFT3, NCM, WCOH, and NCDWT3 detectors, respectively. When 60 dB clutter is present, the NCM and WCOH detection rates were unchanged, but the NCFFT3 and NCDWT3 detectors became ineffective