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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation
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by C. Sı̇nan Güntürk PDF
J. Amer. Math. Soc. 17 (2004), 229-242 Request permission

Abstract:

Sigma-delta quantization is a method of representing bandlimited signals by $0{-}1$ sequences that are computed from regularly spaced samples of these signals; as the sampling density $\lambda \to \infty$, convolving these one-bit sequences with appropriately chosen kernels produces increasingly close approximations of the original signals. This method is widely used for analog-to-digital and digital-to-analog conversion, because it is less expensive and simpler to implement than the more familiar critical sampling followed by fine-resolution quantization. We present examples of how tools from number theory and harmonic analysis are employed in sharpening the error estimates in sigma-delta quantization.
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Additional Information
  • C. Sı̇nan Güntürk
  • Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185
  • Email: gunturk@cims.nyu.edu
  • Received by editor(s): April 11, 2003
  • Published electronically: August 1, 2003
  • Additional Notes: The author’s research was supported in part by the Francis Robbins Upton honorific fellowship from Princeton University, the NSF Grant 97-29992 at the Institute for Advanced Study, and the NSF Grant DMS-0219072.
  • © Copyright 2003 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 17 (2004), 229-242
  • MSC (2000): Primary 94A20, 11K06; Secondary 11L07, 41A25
  • DOI: https://doi.org/10.1090/S0894-0347-03-00436-3
  • MathSciNet review: 2015335