Matthew R. Wilbur, Timothy N. Davidson and James P. Reilly.
Efficient design of oversampled NPR GDFT filter banks.
IEEE Transactions on Signal Processing,
52(7):1947-1963,
July 2004.
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.
An abridged version of this paper appears in the Proceedings of the 2003 International Conference on Acoustics, Speech and Signal Processing, VI:489-492, Hong Kong, April 2003.
A technical report which contains additional examples is available as a pdf file.
The principles of this design method have also been applied to the design of the prototype filter in a Filtered Multitone Modulation (FMT) scheme. That work appears in the IEEE Transactions on Communications in May 2006.
A Matlab m-file for equation (39) of the technical report (equation (38) of the paper in the IEEE Transactions on Signal Processing) is available here.
To run that file, you'll also need the little Matlab function vectransT.m.
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