On the Design of Arbitrary Shape Two-Channel Filter Bank Using Eigenfilter Approach
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In our paper, we have extended an eigenfilter-based approach for the design of arbitrary shape two-channel filter bank. The method is based on designing arbitrary shape analysis filter, followed by the design of complementary arbitrary shape synthesis filter. In eigenfilter designing, eigenvector is computed corresponding to the minimum eigenvalue of a real, symmetric and positive-definite matrix. In our case, this matrix is formulated using the combination of pass-band and stop-band errors between frequency response of desired and designed arbitrary shape filters. After designing the arbitrary shape analysis filter, same is used in perfect-reconstruction constraint, for the design of complementary arbitrary shape synthesis filter. The length of this arbitrary shape synthesis filter should satisfy certain condition depending on the length of the pre-designed arbitrary shape analysis filter. This ensures the existence of the solution for the complementary arbitrary shape synthesis filter. We have demonstrated the usefulness of this method in designing the arbitrary shapes such as, differentiator, integrator and comb shape.
KeywordsArbitrary shape filter bank Eigenfilter Perfect reconstruction Pass-band error Stop-band error
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