Ten lectures on wavelets
Multirate systems and filter banks
Multirate systems and filter banks
Oversampled filter banks: Optimal noise shaping, design freedom, and noise analysis
ICASSP '97 Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97)-Volume 3 - Volume 3
Quantization noise shaping on arbitrary frame expansions
EURASIP Journal on Applied Signal Processing
Vector quantization analysis of ΣΔ modulation
IEEE Transactions on Signal Processing
Optimization of filter banks using cyclostationary spectralanalysis
IEEE Transactions on Signal Processing
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms
IEEE Transactions on Information Theory
Noise reduction in oversampled filter banks using predictive quantization
IEEE Transactions on Information Theory
Efficient quantization for overcomplete expansions in RN
IEEE Transactions on Information Theory
Sigma-delta (ΣΔ) quantization and finite frames
IEEE Transactions on Information Theory
Single-Bit Oversampled A/D Conversion With Exponential Accuracy in the Bit Rate
IEEE Transactions on Information Theory
Performance of Sigma–Delta Quantizations in Finite Frames
IEEE Transactions on Information Theory
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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 as 1/r2 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/r2. 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.