Efficient Design of Oversampled NPR GDFT Filterbanks

We propose a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized discrete Fourier transform (GDFT) filterbank. Such filterbanks have several desirable properties for subband processing systems that are sensitive to aliasing, such as subband adaptive filters. The design criteria for the prototype filter are explicit bounds (derived herein) on the aliased components in the subbands and the output, the distortion induced by the filterbank, and the imaged subband errors in the output. It is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem, which can be efficiently solved. The proposed design technique provides an efficient and effective tool for exploring many of the inherent tradeoffs in the design of the prototype filter, including the tradeoff between aliasing in the subbands and the distortion induced by the filterbank. We calculate several examples of these tradeoffs and demonstrate that the proposed method can generate filters with significantly better performance than filters obtained using current design methods.