Optimal duration-bandwidth localized antisymmetric biorthogonal wavelet filters

Abstract

We present a design of a new class of compactly supported antisymmetric biorthogonal wavelet filter banks which have the analysis as well as the synthesis filters of even-length. Here, the analysis and the synthesis filters are designed to have minimum joint duration-bandwidth localization (JDBL). The design of filters has been formulated as a direct time-domain linearly constrained eigenvalue problem that does not involve any parametrization and iterations. The optimal analysis and synthesis filters have been obtained as the eigenvectors of the positive definite matrices. The closed form analytic expression for the objective function has been presented. The perfect reconstruction and regularity conditions have been incorporated in the design by employing time-domain matrix characterization. The method can control duration and bandwidth localizations of the analysis and synthesis filters, independently. A few design examples have been presented and compared with previous works. The performance of the optimal filter banks designed by employing the proposed method has been evaluated in image coding and signal denoising applications.