Performance of Sigma-Delta Quantizations in Finite Frames

In this paper, we extend the results that we derived in [1], [2] to the case of filter banks (FBs) based transmission. We consider first- and second-order sigma-delta (SD) quantization in the context of an oversampled digital Fourier transform (DFT) FBs (DFT-FBs). In this context, we investigate the case of Odd- and Even-stacked DFT FBs. We establish the set of conditions that guarantee that the reconstruction minimum squares error (MSE) behaves 1/r(2) as where r denotes the frame redundancy and we derive the corresponding MSE upper-bounds closed-form expressions. The obtained results demonstrate that overoversampled FBs that are subject to the first- and second-order SD can exhibit a reconstruction error behavior according to 1/r(2). Furthermore, the established results are shown to be true under the quantization model used in [3]-[6], as well as under the widely used additive white quantization noise assumption.