Energy optimized orthonormal wavelet filter bank with prescribed sharpness

Optimization with respect to some energy measure such as compaction energy is a widely used criterion for designing wavelet filter banks. The filter bank can be adapted to the signal that it is analyzing to achieve good performance. The frequency selectivity property of a traditional low-pass filter is however not ensured using this criterion. Frequency selectivity is important to ensure the effects on aliasing is minimized in the subband and to give a regular equivalent wavelet function. In this work the design of energy optimized filters with a prescribed sharpness in the frequency response is presented. The sharpness, which determines the degree of selectivity, is achieved by the zero-pinning technique on the Bernstein polynomial. The design technique can be cast as a Semidefinite Programming (SDP) problem which can be solved with efficient interior point algorithms.