Contents

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

Stephen Del Marco
Aware, Inc.
Bedford, Ma. 01730-1413
and
John Weiss
Applied Mathematics Group
Arlington, MA 02174-7523

Abstract:

This paper presents the theory of M-band, extended translation- invariant wavelet transforms (ETI). The ETI generalizes the translation-invariant wavelet transform of Weiss. 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 performance over previously defined wavepacket-based detectors. A performance analysis is conducted. ROC curves, generated by Monte-Carlo simulation are presented indicating detector performance. Detector performance is demonstrated to be independent of the signal translation.