Balanced-uncertainty optimized wavelet filters with prescribed regularity

The Heisenberg Uncertainty Principle dictates that a filter cannot have simultaneous localization in the spatial domain and the frequency domain: there is a trade-off between spatial and frequency localizations. In this paper the author considers a localization measure metric that has a balance between spatial and frequency localizations. The metric is called the Heisenberg Balanced-Uncertainty metric and was proposed by Monro et al. (1997). The author presents an efficient technique for designing a class of biorthogonal wavelet filters which have a prescribed regularity (number of zeros at z=-1) and are optimized with respect to the Balanced-Uncertainty metric