In this paper, we show that an NPR M-channel filter bank with a diagonal system inserted between the analysis and synthesis filter banks may be used to decompose an FIR system of order L into M complex subband components each of order L K , where K is the downsampling rate. This decomposition is at the expense of using complex arithmetic for the subband processing. The theory surrounding the proposed filter bank structure leads to a new understanding of subbanded adaptive filtering implementations. It also leads naturally to a delayless subbanded adaptive filter scheme. Using conditions on the analysis and synthesis filters, the formulas for the subband components and their respective properties are developed. Simulation results for an acoustic echo cancellation example are given to support the developed theory.

In this paper, 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 which are sensitive to aliasing, such as subband adaptive filters. Our 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 filter bank, 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. 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. * A condensed version of this report has been accepted, subject to minor revisions, for publication in the IEEE Transactions on Signal Processing

In this paper, 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 which are sensitive to aliasing, such as subband adaptive filters. Our 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 filter bank, 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. 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. * A condensed version of this report has been accepted, subject to minor revisions, for publication in the IEEE Transactions on Signal Processing

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