Optimal duration-bandwidth localized antisymmetric biorthogonal wavelet filters

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. HighlightsA design of a new class of even-length antisymmetric biorthogonal filer banks is proposed.The optimality criterion chosen is joint duration-bandwidth localization (JDBL) of the filters.The method presents a direct time-domain approach that does not involve any integrations, iterations and parameterization.The closed form expressions for the objective function and constraints are provided.The method provides globally optimal filters that are obtained as eigenvectors of a positive definite matrix.The performance of the designed filter banks has been evaluated in image compression and signal denoising applications.

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