Improved transient signal detection using a wavepacket-based detector with an extended translation-invariant wavelet transform

This paper presents the theory of M-band, extended translation-invariant (ETI) wavelet transforms. The ETI generalizes the translation-invariant wavelet transform of Weiss (1933). It is shown that iteration of the ETI, in a tree structure, provides a signal decomposition into an orthonormal wavepacket basis. Other properties such as translation invariance and invertibility of the transform are proven. The theory is then applied to transient signal detection through development of a family of translation-invariant wavepacket-based detectors. This family of detectors provides improved the performance over previously defined wavepacket-based detectors. A performance analysis is conducted. ROC curves generated by Monte-Carlo simulation are presented, indicating the detector performance. The detector performance is demonstrated to be independent of the signal translation.