False Alarm Probability of a DWT-Based Estimation Algorithm

Abstract

Noonan, J. P., and Marquis, D. A., False Alarm Probability of a DWT-Based Estimation Algorithm,Digital Signal Processing6 (1996), 155–159.Recently, the wavelet transform has been applied to the problem of detecting and estimating transient signals in additive white noise. The general procedure of these algorithms is to take a discrete wavelet transform (DWT) of the data, eliminate some of the DWT coefficients based on some criteria, and then inverse DWT the remaining coefficients to obtain the transient signal estimate. Most of the research has focused on the estimation performance of these algorithms. This research computes the false alarm probability on each DWT scale level for the algorithm described in (Noonanet al.,Digital Signal Processing 3, 1993, 89–96). The false alarm probability is the probability that one or more DWT coefficients on a difference level is nonzero.