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Analysis of Decimation on Finite Frames with Sigma-Delta Quantization

  • Kung-Ching LinEmail author
Article
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Abstract

In analog-to-digital conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the \(\Sigma \Delta \) quantization scheme, the reconstruction error decays exponentially with respect to the bit-rate. In this study, similar results are proved for finite unitarily generated frames. We introduce a process called alternative decimation on finite frames that is compatible with first- and second-order \(\Sigma \Delta \) quantization. In both cases, alternative decimation results in exponential error decay with respect to the bit usage.

Keywords

Decimation Sigma-Delta quantization Unitarily generated frames 

Mathematics Subject Classification

42C15 

Notes

Acknowledgements

The author greatly acknowledges the support from ARO Grant W911NF-17-1-0014, and John Benedetto for the thoughtful advice and insights. Further, the author appreciates the constructive analysis and suggestions of the referees.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Norbert Wiener Center, Department of MathematicsUniversity of MarylandCollege ParkUSA

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