Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation

Author:
C. Sinan Güntürk

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

Published electronically:
August 1, 2003

MathSciNet review:
2015335

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Abstract | References | Similar Articles | Additional Information

Abstract: Sigma-delta quantization is a method of representing bandlimited signals by sequences that are computed from regularly spaced samples of these signals; as the sampling density , 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. Sinan Güntürk**

Affiliation:
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185

Email:
gunturk@cims.nyu.edu

DOI:
https://doi.org/10.1090/S0894-0347-03-00436-3

Keywords:
A/D conversion,
sigma-delta modulation,
sampling,
quantization,
uniform distribution,
discrepancy,
exponential sums.

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.

Article copyright:
© Copyright 2003
American Mathematical Society