Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigmadelta modulation
Author:
C. Sı̇nan Güntürk
Journal:
J. Amer. Math. Soc. 17 (2004), 229242
MSC (2000):
Primary 94A20, 11K06; Secondary 11L07, 41A25
DOI:
https://doi.org/10.1090/S0894034703004363
Published electronically:
August 1, 2003
MathSciNet review:
2015335
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Abstract  References  Similar Articles  Additional Information
Abstract: Sigmadelta 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 onebit sequences with appropriately chosen kernels produces increasingly close approximations of the original signals. This method is widely used for analogtodigital and digitaltoanalog conversion, because it is less expensive and simpler to implement than the more familiar critical sampling followed by fineresolution quantization. We present examples of how tools from number theory and harmonic analysis are employed in sharpening the error estimates in sigmadelta quantization.

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Additional Information
C. Sı̇nan Güntürk
Affiliation:
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 100121185
Email:
gunturk@cims.nyu.edu
Keywords:
A/D conversion,
sigmadelta 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 9729992 at the Institute for Advanced Study, and the NSF Grant DMS0219072.
Article copyright:
© Copyright 2003
American Mathematical Society