Geodesic
Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation
Güntürk, C.1
1 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185
Journal of the American Mathematical Society, Tome 17 (2004) no. 1, pp. 229-242

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-03-00436-3

Güntürk, C. 1

1 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185 
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Güntürk, C. Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation. Journal of the American Mathematical Society, Tome 17 (2004) no. 1, pp. 229-242. doi: 10.1090/S0894-0347-03-00436-3

[1] Kuipers, L., Niederreiter, H. Uniform distribution of sequences 1974

[2] Wavelets 1992

[3] Montgomery, Hugh L. Ten lectures on the interface between analytic number theory and harmonic analysis 1994

[4] Stein, Elias M. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals 1993

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