Balanced-uncertainty optimized wavelet filters with prescribed vanishing moments

In this paper, a localization measure that represents a balance between time and frequency localizations, called the Heisenberg balanced-uncertainty metric, is used for designing a class of wavelet filters. The filter banks belong to the class of halfband pair filter banks and are defined by two kernels. The parametric Bernstein polynomial is used to construct the kernels. The optimization problem is shown to be the minimization of a ratio of quadratic functions, and an efficient technique for finding the solution is presented. Filters with different degrees of balance between time and frequency localizations can be designed with ease. Some interesting aspects of the localization measure of filters are also discussed.