Abstract
Here we employ discrete wavelet transforms (DWTs) to develop test statistics for the detection of transients, i.e., signals with a short duration and unknown shape, embedded in Gaussian white noise. Distributions of the test statistics under both the null and alternative hypotheses can be easily derived. We test performance on a set of 78 templates provided by theoretical studies on gravitational waves emitted in a supernova explosion where we seek the maximal detection distance of the source generating the signal at which the tests correctly reject the null hypothesis. We discuss practical implementation issues and performance assessment methods. We compare results with both matched filtering, an optimal method that requires the prior knowledge of the signal shape, and with the slope filtering, that uses limited prior knowledge on the signal. The wavelet statistics show a good behavior for each of the considered waveforms, unlike other detection methods.
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