An algorithm for computing convex positively invariant sets for deltasigma modulators

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 44, Issue 1, 1997, Pages 3844-

  Schreier, Richard ^a   Goodson, Montgomery V ^a   Zhang, Bo ^a  

^a 1148 Kelley Engineering Center Corvallis   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747841690     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. J. C. Candy and G. C. Temes, Oversampling methods for A/D and D/A conversion, in Oversampling DeltaSigma Data Converters, J. C. Candy and G. C. Temes, Eds. New York: IEEE Press, 1991.
2. D. A. Kerth, D. B. Kasha, T. G. Mellissionos, D. S. Piasecki, and E. J. Swanson, A 120 dB linear switchedcapacitor deltasigma modulator, ISSCC Dig. Tech. Papers, pp. 196197, Feb. 1994.
3. R. W. Adams, P. F. Ferguson, A. Ganesan, S. Vincelette, A. Volpe, and R. Libert, Theory and practical implementation of a fifthorder sigmadelta A/D converter, J. Audio Eng. Soc., vol. 39, pp. 515528, July 1991.
4. J. G. Kenney and L. R. Carley, CLANS: A highlevel synthesis tool for high resolution data converters, in Proc. IEEE Conf. ComputerAided Design, Nov. 1988, pp. 496499.
5. D. Anastassiou, Error diffusion coding for A/D conversion, IEEE Trans. Circuits Syst., vol. 36, pp. 11751186, Sept. 1989.
6. S. Hein and A. Zakhor, On the stability of interpolative sigma delta modulators, in Proc. 1991 IEEE Int. Symp. Circuits Syst., June 1991, vol. 3, pp. 16211624.
7. H. Wang, ∑Δ modulation from the perspective of nonlinear dynamics, in Proc. 1992 IEEE Int. Symp. Circuits Syst., May 1013, 1992, pp. 12961299.
8. A geometric view of SD modulations, IEEE Trans. Circuits Syst. II, vol. 39, pp. 402405, June 1992.
9. On the stability of thirdorder sigmadelta modulation, in Proc. 1993 IEEE Int. Symp. Circuits Syst., May 36, 1993, pp. 13771380.
10. S. C. Pinault and P. V. Lopresti, On the behavior of the doubleloop sigmadelta modulator, IEEE Trans. Circuits Syst. II, vol. 40, pp. 467479, Aug. 1993.
11. B. P. Agrawal and K. Shenoi, Design methodology of SDM, IEEE Trans. Commun., vol. COM31, pp. 360370, Mar. 1983.
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 Syst., vol. 37, pp. 309318, Mar. 1990.
13. S. H. Ardalan and J. J. Paulos, Analysis of nonlinear behavior in deltasigma modulators, IEEE Trans. Circuits Syst., vol. CAS34, pp. 593603, June 1987.
14. T. Ritoniemi, T. Karema, and H. Tenhunen, Design of stable high order 1bit sigmadelta modulators, in Proc. 1990 IEEE Int. Symp. Circuits Syst., May 1990, vol. 4, pp. 32673270.
15. L. Risbo, ∑Δ modulators Stability analysis and optimization, Ph.D. dissertation, Tech. Univ. Denmark, June 1994.
16. R. Schreier, An empirical study of highorder singlebit deltasigma modulators, IEEE Trans. Circuits Syst. II, vol. 40, pp. 461466, Aug. 1993.
17. M. Motamed, A. Zakhor, and S. Sanders, Tones, saturation and SNR in double loop ∑Δ modulators, in Proc. 1993 IEEE Int. Symp. Circuits Syst., May 36, 1993, vol. 2, pp. 13451348.
18. R. Schreier and B. Zhang, Deltasigma modulators employing continuoustime circuitry, IEEE Trans. Circuits Syst. I, to be published.
19. S. Hein and A. Zakhor, On the stability of sigma delta modulators, IEEE Trans. Signal Processing, vol. 41, pp. 23222348, July 1993.
20. C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, The QuickHull algorithm for convex hull, The Geometry Center Tech. Rep. GCG53, ftp://geom.umn.edu/pub/documents/preprints/GCG53, Minneapolis, MN, 1993.
21. M. Goodson, B. Zhang, and R. Schreier, Proving stability of deltasigma modulators using invariant sets, in Proc. IEEE Int. Symp. Circuits Syst., May 1995, vol. 1, pp. 633636.
22. P. Steiner and W. Yang, Stability analysis of the secondorder ∑Δ modulator, in Proc. 1994 IEEE Int. Symp. Circuits Syst., May 30June 2, 1994, pp. 365368.
23. V. Klee, On the complexity of ddimensional Voronoi diagrams, Archiv. Mathem., vol. 34, pp. 7580, 1980.
24. J. O'Rourke, Computational Geometry in C. Cambridge, England: Cambridge Univ. Press, 1994, chs. 34.
25. S. Hein, Exploiting chaos to suppress spurious tones in general doubleloop sigma delta modulators, IEEE Trans. Circuits Syst. II, vol. 40, pp. 651659, Oct. 1993.
26. O. Feely, Nonlinear dynamics of chaotic doubleloop sigmadelta modulation, in Proc. 1994 IEEE Int. Symp. Circuits Syst., May 1994, vol. 6, pp. 101104.
27. R. Schreier, On the use of chaos to reduce idlechannel tones in deltasigma modulators, IEEE Trans. Circuits Syst. I, vol. 41, pp. 539547, Aug. 1994.