Efficient Design of Oversampled NPR GDFT Filter Banks

We present a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized Discrete Fourier Transform (GDFT) filter bank. Such filter banks have several desirable properties for subband processing systems that are sensitive to aliasing; e.g., subband adaptive filters. Our design criteria for the prototype filter are explicit bounds on the aliased components in the subbands, the aliased components in the output, and the distortion induced by the filter bank. It is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem that can be efficiently solved. Our design technique provides an efficient and effective tool for exploring many of the inherent trade-offs in the design of the prototype filter, including the trade-off between aliasing in the subbands and the distortion induced by the filter bank. In our examples we calculate several of these trade-offs and demonstrate that our method can generate filters with significantly better performance than filters obtained using current design methods.