Optical EngineeringM-band wavepacket-based transient signal detector using a translation-invariant wavelet transform
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A transient signal detector based on M-band wavepackets, using an M-band, translation-invariant wavelet transform is presented. The detection statistic consists of the maximum energy value in the best basis, derived from the full M-band wavepacket decomposition. The full wavepacket decomposition uses the M-band translation-invariant wavelet transform (MTI), recently developed by Weiss. Use of the MTI provides two advantages over the use of traditional wavepacket methods. One advantage is that the MTI detector pertormance is independent of sample shifts of the input signal. The second advantage is that use of the MTI provides superior energy concentration; more energy is concentrated in fewer coefficients. This results in higher peak energy values. We present receiver operating characteristic curves generated by Monte-Carlo simulation, illustrating detector performance on exponentially damped sinusoids. Performance is compared to similar detectors based on the nominal wavepacket decomposition and the Mallat wavelet decomposition.