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Detection of transient signals by wavelet packet transform and stochastic resonance

The problem of detecting an unknown transient signal in noise is considered. The observed data is first, quantized by a symmetric quantizer. By an optimum matching of the quantizer thresholds to the noise probability density function, the signal-to-noise ratio in the data is enhanced by the phenomenon of stochastic resonance. The output of the stochastic resonator (optimal quantizer) is then transformed using a translation-invariant wavelet packet transform (TIWPT). The magnitude of the maximum magnitude coefficient, in the entire TI-WPT decomposition is used as the test-statistic. Simulation results are presented to show that, at very low SNRs, the TIWPT detector preceded by the stochastic resonator gives a much better detection performance than a detector based on the TIWPT alone.