Detection and estimation of multiplicative jumps using the continuous wavelet transform

This paper addresses the problem of multiplicative jump detection and estimation in the time-scale plane. The signature is derived for a multiplicative jump in the time-scale plane. The signature allows the study of two wavelet based detectors. The first detector computes the continuous wavelet transform (CWT) correlation with 2D signature. The second detector sums fixed scale slices of the CWT. For comparison purpose, the optimal Neyman-Pearson detector (NPD) is then derived. The NPD requires a priori knowledge of the jump and signal parameters. A sub-optimal detector is presented which replaces these parameters by appropriate estimates. The performance of this detector is studied.