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15 March 1994 Wavepacket-based transient signal detector using a translation-invariant wavelet transform
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Abstract
This paper presents a wavepacket-based transient signal detector for detecting unknown deterministic signals in Gaussian white noise. The detector consists of the best wavepacket basis algorithm of Coifman and Wickerhauser, together with the recently developed translation invariant wavelet transform (TI) of Weiss. The uniqueness of this approach concerns the use of the TI which provides two advantages over nominal wavepacket methods. One advantage is that the TI detector performance is independent of sample shifts of the input signal. The second advantage concerns energy distribution in the wavepacket domain. The adaptability of wavepackets to the input signal, provides a distinct advantage over wavelet methods. Use of the TI with wavepacket methods provides the further advantage of a sharper energy concentration in the wavepacket domain. That is, more energy is concentrated into a fewer number of coefficients, thereby providing larger peak energy values. We exploit this higher peak energy, by using the maximum energy as a detection statistic. A numerical investigation is conducted by sweeping over frequency, phase and damping constant for an exponentially damped sinusoid. Detector performance is evaluated through ROC curve comparison, generated by Monte-Carlo simulation. TI detector performance is compared to the Mallat wavelet transform detector and the nominal wavepacket based detector. Results show on average, a performance improvement in the TI based detector over the nominal wavepacket and wavelet detectors.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Stephen P. Del Marco, John E. Weiss, and Karl B. Jagler "Wavepacket-based transient signal detector using a translation-invariant wavelet transform", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170077
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