Deterministic analysis of sigma-delta modulation for linear and non-linear signal reconstruction

International Journal of Circuit Theory and Applications

Volumn 25, Issue 5, 1997, Pages 369-391

  Thao, Nguyen T ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Decoding; Deterministic; Nonlinear; Sigma delta; Signal reconstruction

Indexed keywords

DECODING; INFORMATION RETRIEVAL; MATHEMATICAL TECHNIQUES; SIGNAL PROCESSING;

DELTA-SIGMA MODULATION; DETERMINISTIC ANALYSIS;

MODULATION;

EID: 0031236036     PISSN: 00989886     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-007x(199709/10)25:5<369::aid-cta979>3.0.co;2-g     Document Type: Article

References (36)

1. J. C. Candy and G. C. Ternes (eds), Oversampling Delta-Sigma Data Converters. Theory, Design and Simulation, IEEE, New York, 1992, Introductory chapter.
2. O. Feely and L. O. Chua, 'The effect of integrator leak in ΣΔ modulation', IEEE Trans. Circuits and Systems, CAS-38, 1293-1305 (1991).
3. H. Wang, 'Sigma delta modulation from the perspective of nonlinear dynamics', Proc. IEEE Int. Symp. on Circuits and Systems, Vol. 3, IEEE, New York, 1992, pp. 1296-1299.
4. R. Schreier, 'On the use of chaos to reduce idle-channel tones in delta-sigma modulators', IEEE Trans. Circuits and Systems I, CAS-41, 539-547 (1994).
5. A. Zakhor and K. Ibraham, 'Lower bounds on the MSE of the single loop sigma delta modulator', Proc. 23rd Asilomar Conf. on Signals, Systems and Computers, 1989, Mapple Press, pp. 849-853.
6. R. Schreier, 'Noise-shaped coding', Ph.D. Dissertation, Department of Electrical Engineering, University of Toronto, 1991.
7. N. T. Thao and M. Vetterli, 'Convex coders and oversampled A/D conversion: theory and algorithms', Tech. Rep. CU/CTR/TR 289-91-71, Columbia University, 1991.
8. N. T. Thao and M. Vetterli, 'Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates', IEEE Trans. Signal Process., SP-42, 519-531 (1994).
9. N. T. Thao and M. Vetterli, 'Oversampled A/D conversion using alternate projections', Proc. Conf. on Information Sciences and Systems, Johns Hopkins University Press, Baltimore, MD, 1991, pp. 241-248.
10. N. T. Thao, 'Analysis framework for the digital inversion of nonlinear deterministic characteristics in ΣΔ modulation', Proc. IEEE Int. Symp. on Circuits and Systems, IEEE, New York, 1997, pp. 405-408.
11. S. K. Tewksbury and R. W. Hallock, 'Oversampled, linear predictive and noise shaping coders of order N>1', IEEE Trans. Circuits and Systems, CAS-25, 436-447 (1978).
12. K. C. H. Chao, S. Nadeem, W. L. Lee and C. G. Sodini, 'A higher order topology for interpolative modulators for oversampling A/D conversion', IEEE Trans. Circuits and Systems, CAS-37, 309-318 (1990).
13. J. C. Candy and O. J. Benjamin, 'The structure of quantization noise from sigma-delta modulation', IEEE Trans. Commun., COM-29, 1316-1323. (1981).
14. G. R. Ritchie, 'Higher order interpolation analog to digital converters', Ph.D. Dissertation, University of Pennsylvania, 1977.
15. J. C. Candy, 'A use of double integration in sigma-delta modulation', IEEE Trans. Commun., COM-33, 249-258 (1985).
16. R. M. Gray, 'Spectral analysis of quantization noise in a single loop sigma-delta modulator with dc input', IEEE Trans. Commun., COM-37, 588-599 (1989).
17. N. He, F. Kuhlmann and A. Buzo, 'Multi-loop sigma-delta quantization', IEEE Trans. Info. Theory, IT-38, 1015-1028 (1992).
18. J. C. Willems, The Analysis of Feedback Systems, MIT Press, Cambridge, MA, 1971.
19. N. T. Thao, 'Unified principle for digital correction in ΣΔ modulation with ADC-DAC imperfections', Tech. Rep., EEE Department, The Hong Kong University of Science and Technology, 1997.
20. T. Cataltepe, A. R. Kramer, L. E. Larson, G. C. Ternes and R. H. Walden, 'Digitally corrected multi-bit ΣΔ data converters', Proc. IEEE Int. Symp. on Circuits and Systems, IEEE, New York, 1989, pp. 647-650.
21. M. Sarhang-Nejad and G. C. Temes, 'A high-resolution multibit ΣΔ ADC with digital correction and relaxed amplifier requirements', IEEE J. Solid-State Cire., SC-28, 648-660 (1993).
22. I. Galton, 'Spectral shaping of circuit errors in digital-to-analog converters', IEEE Trans. Circuits and Systems II, in press.
23. R. T. Baird and T. S. Fiez, 'Linearity enhancement of multibit ΣΔ A/D and D/A converters using data weighted averaging', IEEE Trans. Circuits and Systems II, CAS-42, 753-762 (1995).
24. J. C. Candy, 'A use of limit cycle oscillations to obtain robust analog-to-digital converters', IEEE Trans. Commun., COM-22, 298-305 (1974).
25. A. Gersho and R. M. Gray, Vector Quantization and Signal Compression, Kluwer, Dordrecht, 1992.
26. S. Hein, K. Ibraham and A. Zakhor, 'New properties of sigma-delta modulators with dc inputs', IEEE Trans. Commun., COM-40, 1375-1387 (1992).
27. R. M. Gray, W. Chou and P. -W. Wong, 'Quantization noise in single-loop sigma-delta modulation with sinusoidal input', IEEE Trans. Commun., COM-37, 956-968 (1989).
28. S. Hein and A. Zakhor, 'Optimal decoding for data acquisition applications of sigma delta modulators', IEEE Trans. Signal Process., SP-41, 602-616 (1993).
29. N. T. Thao, 'Vector quantization analysis of ΣΔ modulation', IEEE Trans. on Signal Process., SP-44, 808-817 (1996).
30. N. T. Thao and M. Vetterli, 'Lower bound on the mean squared error in oversampled quantization of periodic signals using vector quantization analysis', IEEE Trans. Info. Theory, IT-42, 469-479 (1996).
31. P. L. Combettes, 'The foundations of set theoretic estimation', Proc. IEEE, 81, 1175-1186 (1993).
32. D. C. Youla, 'Generalized image restoration by the method of alternating orthogonal projections', IEEE Trans. Circuits and Systems, CAS-25, 694-702 (1978).
33. S. Hein and A. Zakhor, 'Reconstruction of oversampled band-limited signals from ΣΔ encoded binary sequences', IEEE Trans. Signal Process., SP-42, 799-811 (1994).
34. S. Hein, 'A fast block-based nonlinear decoding algorithm for ΣΔ modulators', IEEE Trans. Signal Process., SP-43, 1360-1367 (1995).
35. R. J. Marks II, Introduction to Shannon Sampling and Interpolation Theory,. Springer, New York, 1991.
36. T. T. Nguyen, 'Deterministic analysis of oversampled A/D conversion and ΣΔ modulation, and decoding improvements using consistent estimates', Ph.D. Dissertation, Department of Electrical Engineering, Columbia University, 1993.