On the Use of Chaos to Reduce Idle-Channel Tones in Delta-Sigma Modulators

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

Volumn 41, Issue 8, 1994, Pages 539-547

  Schreier, Richard ^a  

^a OREGON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALOG TO DIGITAL CONVERSION; CHAOS THEORY; DIGITAL TO ANALOG CONVERSION; PERFORMANCE; SPURIOUS SIGNAL NOISE; SYSTEM STABILITY; WHITE NOISE;

ANALOG TO DIGITAL CONVERTERS; DELTA SIGMA MODULATORS; DIGITAL TO ANALOG CONVERTERS; DITHER; LIMIT CYCLES; PHASE LOCKING; QUANTIZATION NOISE; SUBHARMONICS;

MODULATORS;

EID: 0028482840     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.311537     Document Type: Article

References (25)

1. J. C. Candy and G. C. Temes, “Oversampling methods for A/D and D/A conversion,” in Oversampling Delta-Sigma Data Converters, J. C. Candy and G. C. Temes, Eds. New York: IEEE Press, 1991.
2. J. C. Candy and O. J. Benjamin, “The structure of quantization noise from sigma-delta modulation,” IEEE Trans. Commun., vol. COM-29, no. 9, pp. 1316–1323, Sept. 1981.
3. V. Friedman, “The structure of the limit cycles in sigma-delta modulation,” IEEE Trans. Commun., vol. 36, no. 8, pp. 972–979, Aug. 1988.
4. S. H. Ardalan and J. J. Paulos, “Analysis of nonlinear behavior in delta-sigma modulators,” IEEE Trans. Circuits and Syst., vol. 34, pp. 593–603, June 1987.
5. R. M. Gray, “Spectral analysis of quantization noise in a single-loop sigma-delta modulator with dc input,” IEEE Trans. Commun., vol. 37, no. 6, pp. 588–599, June 1989.
6. R. M. Gray, W. Chou, and P. W. Wong, “Quantization noise in single-loop sigma-delta modulation with sinusoidal inputs,” IEEE Trans. Commun., vol. 37, no. 9, pp. 956–968, Sept. 1989.
7. N. He, F. Kuhlmann, and A. Buzo, “Double-loop sigma-delta modulation with dc input,” IEEE Trans. Commun., vol. 38, no. 4, pp. 487–495, Apr. 1990.
8. H. Wang, “A geometric view of ऱख modulations,” IEEE Trans. Circuits and Syst.-II: Analog and Digital Signal Processing, vol. 39, no. 2, pp. 402–405, June 1992.
9. O. Feely and L. O. Chua, “Nonlinear dynamics of a class of analog-to-digital converters,” Int. J. Bifurcation and Chaos, vol. 2, no. 2, pp. 325–340, June 1992.
10. D. F. Delchamps, “Exact asymptotic statistics for sigma-delta quantization noise,” in Proc. 28th Annual Allerton Conf. Commun. Cont. and Computing, Oct. 1990.
11. I. Galton, “Granular quantization noise in a class of delta-sigma modulators,” IEEE Trans. Informat. Theory, to appear, May, 1994.
12. R. Schreier and Y. Yang, “Stability tests for single-bit sigma-delta modulators with second-order FIR noise transfer functions,” in Proc. IEEE Int. Symp. Circuits and Syst., 1992, pp. 1316–1319.
13. R. Schreier, “An empirical study of high-order single-bit delta-sigma modulators,” submitted to IEEE Trans. Circuits and Syst.
14. R. Schreier, “Destabilizing limit cycles in delta-sigma modulators with chaos,” in Proc. IEEE Inter. Symp. Circuits and Syst., 1993, pp. 1369–1372.
15. S. R. Norsworthy, “Effective dithering of sigma-delta modulators,” Proc. IEEE Int. Symp. Circuits and Syst., 1992, pp. 1304–1307.
16. M. W. Hauser, “Principles of oversampling A/D conversion,” J. Audio Eng. Soc., vol. 39, no. 1/2, pp. 3–26, Jan./Feb. 1991.
17. W. Chou and R. M. Gray, “Dithering and its effects on sigma delta and multistage sigma delta modulation,” in Proc. 1990 IEEE Int. Symp. Circuits and Syst., vol. 3, pp. 368—371, May 1990.
18. R. Schreier and W. M. Snelgrove, “ऱख modulation is a mapping,” in Proc. 1991 IEEE Int. Symp. Circuits and Syst., vol. 3, pp. 1769–1772, May 1991.
19. D. Delchamps, “Invariant densities and the macroscopic asymptotic behavior of digitally controlled continuous-time systems,” 1992 SIAM Conf. Applicat. Dynamical Syst., 1992.
20. H. Wang, “ऱख modulation from the perspective of nonlinear dynamics,” in Proc. 1992 IEEE Int. Symp. on Circuits and Syst., pp. 1296–1299, 1992.
21. S. Hein, “Exploiting chaos to suppress spurious tones in general double-loop sigma delta modulators,” submitted to IEEE Trans. Circuits and Syst. II, vol. 40, no. 10, pp. 651–659, Oct. 1993.
22. J. C. Candy, “Decimation for sigma-delta modulation,” IEEE Trans. Commun., vol. COM-34, no. 1, pp. 72–76, Jan. 1986.
23. S. R. Norsworthy, private communication, Sept. 1991.
24. O. Feely and L. O. Chua, “The effect of integrator leak in E — A modulation,” IEEE Trans. Circuits and Syst., vol. 38, no. 11, pp. 1293–1305, Nov. 1991.
25. M. R. Spiegel, Mathematical Handbook. New York: McGraw-Hill, 1968, p. 1.