One-Bit Sigma-Delta Quantization with Exponential Accuracy

Communications on Pure and Applied Mathematics

Volumn 56, Issue 11, 2003, Pages 1608-1630

  Güntürk, C Sinan ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346513750     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.3044     Document Type: Article

References (19)

1. Anastassiou, D. Error diffusion coding for A/D conversion. IEEE Trans. Circuits and Systems 36 (1989), no. 3, 1175-1186.
2. Boas, R. P. Entire functions. Academic, New York, 1954.
3. Calderbank, A. R.; Daubechies, I. The pros and cons of democracy. IEEE Trans. Inform. Theory 48 (2002), no. 6, 1721-1725.
4. Chou, W; Wong, P. W; Gray, R. M. Multistage ΣΔ modulation. IEEE Trans. Inform. Theory 35 (1989), no. 4, 784-796.
5. Daubechies, I; DeVore, R. Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order. Ann. of Math. 158 (2003), no. 2, in press.
6. de Boor, C. On calculating with B-splines. J. Approximation Theory 6 (1972), 50-62.
7. Delta-sigma data converters: Theory, design and simulation. S. R. Norsworthy, R. Schreier, and G. C. Temes, eds. Wiley-IEEE, 1996.
8. DeVore, R. A; Lorentz, G. G. Constructive approximation. Springer, 1993.
9. Gray, R. M. Oversampled sigma-delta modulation. IEEE Trans. Comm. 35 (1987), 481-489.
10. Gray, R. M. Spectral analysis of quantization noise in a single-loop sigma-delta modulator with dc input. IEEE Trans. Comm. 37 (1989), 588-599.
11. He, N; Kuhlmann, F; Buzo, A. Multi-loop ΣΔ quantization. IEEE Trans. Inform. Theory 38 (1992), 1015-1028.
12. Kolmogorov, A. N.; Tihomirov, V. M. ε-entropy and ε-capacity of sets in function spaces. Uspehi Mat. Nauk 14 (1959), no. 2 (86), 3-86. (Also in Amer. Math. Soc. Transl., Ser. 2 17 (1961), 277-364.)
13. Kolmogorov, A. N.; Tihomirov, V. M. ε-entropy and ε-capacity of sets in function spaces. Uspehi Mat. Nauk 14 (1959), no. 2 (86), 3-86. (Also in Amer. Math. Soc. Transl., Ser. 2 17 (1961), 277-364.)
14. Konyagin, S. Personal communication, 1999.
15. Meyer, Y. Wavelets and operators. Cambridge Studies in Advanced Mathematics, 37. Cambridge University, Cambridge, 1992.
16. Oversampling delta-sigma data converters: Theory, design and simulation. J. C. Candy and G. C. Temes, eds. Wiley-IEEE, 1992.
17. Risbo, L. Σ-Δ modulators-Stability analysis and optimization. Doctoral dissertation, Electronics Institute, Technical University of Denmark, 1994.
18. Schreier, R. An empirical study of high-order single-bit delta-sigma modulators. IEEE Trans. Circuits Syst. II 40 (1993), no. 8, 461-466.
19. Schreier, R; Snelgrove, M. Stability in a general ΣΔ modulator. Acoustics, Speech, and Signal Processing (ICASSP-91), IEEE Proceedings 3 (1991), 1769-1772.