Redundancy in a frame of wavelets-based matched-filter

We propose in this paper a formulation for the matched-filter (MF) based on the frame of wavelets. We precisely compare the performance of the time-domain MF to that of this wavelet-based MF, with respect to the level of redundancy of the sampling of the time-scale plane, or equivalently, of the frame. The main result is that the redundancy of the discrete wavelet transform, instead of improving the detection performance, introduces false alarms which degrades this performance in the sense of the Neyman-Pearson criterion.