Improved noise stability multiresolution filters based on a class of wavelets

Signal detection in the presence of additive noise is a central problem in signal processing. Multiresolution filters based on wavelets are introduced. An analytic solution for the scale parameter "a" in a way that guarantees high stability relative to the level of additive noise is presented. The filter performance is examined in detection of monochromatic signals in white noise. Our results are shown to be competitive with matched filters.