Advertisement

Quantization Noise Shaping on Arbitrary Frame Expansions

  • Petros T. BoufounosEmail author
  • Alan V. Oppenheim
Open Access
Research Article
Part of the following topical collections:
  1. Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory

Abstract

Quantization noise shaping is commonly used in oversampled A/D and D/A converters with uniform sampling. This paper considers quantization noise shaping for arbitrary finite frame expansions based on generalizing the view of first-order classical oversampled noise shaping as a compensation of the quantization error through projections. Two levels of generalization are developed, one a special case of the other, and two different cost models are proposed to evaluate the quantizer structures. Within our framework, the synthesis frame vectors are assumed given, and the computational complexity is in the initial determination of frame vector ordering, carried out off-line as part of the quantizer design. We consider the extension of the results to infinite shift-invariant frames and consider in particular filtering and oversampled filter banks.

Keywords

Information Technology Computational Complexity Quantum Information Cost Model Filter Bank 

References

  1. 1.
    Daubechies I: Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, Pa, USA; 1992.Google Scholar
  2. 2.
    Cvetkovic Z, Vetterli M: Overcomplete expansions and robustness. Proceedings of IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, June 1996, Paris, France 325–328.Google Scholar
  3. 3.
    Goyal VK, Vetterli M, Thao NT:Quantized overcomplete expansions inOpen image in new window : analysis, synthesis, and algorithms. IEEE Transactions on Information Theory 1998, 44(1):16–31. 10.1109/18.650985MathSciNetCrossRefGoogle Scholar
  4. 4.
    Thao NT, Vetterli M:Reduction of the MSE inOpen image in new window-times oversampled A/D conversionOpen image in new window toOpen image in new window. IEEE Transactions on Signal Processing 1994, 42(1):200–203. 10.1109/78.258137CrossRefGoogle Scholar
  5. 5.
    Benedetto JJ, Powell AM, Yilmaz Ö:Sigma-DeltaOpen image in new window quantization and finite frames. to appear in IEEE Transactions on Information Theory, available at: https://doi.org/www.math.umd.edu/~jjb/ffsd.pdf to appear in IEEE Transactions on Information Theory, available at:
  6. 6.
    Benedetto JJ, Yilmaz Ö, Powell AM: Sigma-delta quantization and finite frames. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 3: 937–940.zbMATHGoogle Scholar
  7. 7.
    Bolcskei H, Hlawatsch F: Noise reduction in oversampled filter banks using predictive quantization. IEEE Transactions on Information Theory 2001, 47(1):155–172. 10.1109/18.904519MathSciNetCrossRefGoogle Scholar
  8. 8.
    Boufounos PT, Oppenheim AV: Quantization noise shaping on arbitrary frame expansion. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 4: 205–208.Google Scholar
  9. 9.
    Strang G, Nguyen T: Wavelets and Filter Banks. Wellesley-Cambridge Press, Wellesley, Mass, USA; 1996.zbMATHGoogle Scholar
  10. 10.
    Candy JC, Temes GC (Eds): Oversampling Delta-Sigma Data Converters: Theory, Design and Simulation. IEEE Press, New York, NY, USA; 1992.Google Scholar
  11. 11.
    Cormen TH, Leiserson CE, Rivest RL, Stein C: Introduction to Algorithms. 2nd edition. MIT Press, Cambridge, Mass, USA; 2001.zbMATHGoogle Scholar

Copyright information

© Boufounos and Oppenheim 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Digital Signal Processing GroupMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations