Sigma—Delta Modulation with I.I.D. Gaussian Inputs

IEEE Transactions on Information Theory

Volumn 36, Issue 4, 1990, Pages 784-798

  Wong, Ping Wah ^a   Gray, Robert M ^b  

^a CLARKSON UNIVERSITY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NOISE, SPURIOUS SIGNAL; PROBABILITY--RANDOM PROCESSES;

GAUSSIAN PROCESSES; POWER SPECTRA; QUANTIZATION NOISE; SIGMA-DELTA MODULATION; STOCHASTIC MODELS; WIENER PROCESSES;

MODULATION;

EID: 0025462763     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.53738     Document Type: Article

References (30)

1. H. Inose, Y. Yasuda, and J. Murakami, “A telemetering system by code modulation— modulation,” IRE Trans. Space Electron. Telemetry, vol. SET-8, pp. 204–209, Sept. 1962.
2. H. Inose and Y. Yasuda, “A unity bit coding method by negative feedback,” Proc. IEEE, vol. 51, pp. 1524–1535, Nov. 1963.
3. J. C. Candy, “A use of limit cycle oscillations to obtain robust analog-to-digital converters,” IEEE Trans. Commun., vol. COM-22, pp. 298–305, Mar. 1974.
4. J. C. Candy, Y. C. Ching, and D. S. Alexander, “Using triangularly weighted interpolation to get 13-bit PCM from a sigma-delta modulator,” IEEE Trans. Commun., vol. COM-24, pp. 1268–1275, Nov. 1976.
5. J. C. Candy, “A use of double integration in sigma-delta modulation,” IEEE Trans. Commun., vol. COM-33, pp. 249–258, Mar. 1985.
6. C. H. Giancarlo and C. G. Sodini, “A slope adaptive delta modulator for VLSI signal processing systems,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 51–58, Jan. 1986.
7. L. R. Carley, “An oversampling analog-to-digital converter topology for high-resolution signal acquisition systems,” IEEE Trans. Circuits Syst., vol. CAS-34, pp. 83–90, Jan. 1987.
8. B. E. Boser and B. A. Wooley, “The design of sigma-delta modulation analog-to-digital converters,” IEEE J. Solid-State Circuits, vol. SC-23, pp. 1298–1308, Dec. 1988.
9. Y. Matsuya, K. Uchimura, A. Iwata, T. Kobayashi, M. Ishikawa, and T. Yoshitome, “A 16-bit oversampling A to D conversion technology using triple-integration noise shaping,” IEEE J. Solid-State Circuits, vol. SC-22, pp. 921–929, Dec. 1987.
10. K. Uchimura, T. Hayashi, T. Kimura, and A. Iwata, “Oversampling A to D and D to A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-36, pp. 1899–1905, Dec. 1988.
11. W. R. Bennett, “Spectra of quantized signals,” Bell Syst. Tech. J., vol. 27, pp. 446–472, 1948.
12. B. Widrow, “A study of rough amplitude quantization by means of Nyqist sampling theory,” IRE Trans. Professional Group Circuit Theory, vol. CT-3, pp. 266–276, Dec. 1956.
13. A. B. Sripad and D. L. Snyder, “A necessary and sufficient condition for quantization errors to be uniform and white,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-25, pp. 442–448, Oct. 1977.
14. R. M. Gray, “Oversampled sigma-delta modulation,” IEEE Trans. Commun., vol. COM-35, pp. 481–489, May 1987.
15. J. E. Iwersen, “Calculated quantizing noise of single-integration delta-modulation coders,” Bell Syst. Tech. J., pp. 2359–2389, Sept. 1969.
16. J. C. Candy and O. J. Benjamin, “The structure of quantization noise from sigma-delta modulation,” IEEE Trans. Commun., vol. COM-29, pp. 1316–1323, Sept. 1981.
17. R. M. Gray, “Spectral analysis of quantization noise in a single-loop sigma-delta modulator with dc input,” IEEE Trans. Commun., vol. COM-37, pp. 588–599, June 1989.
18. R. M. Gray, W. Chou, and P. W. Wong, “Quantization noise in single-loop sigma-delta modulation with sinusoidal inputs,” IEEE Trans. Commun., vol. COM-37, 956–968, 1989.
19. N. He, F. Kuhlmann and A. Buzo, “Double-loop sigma-delta modulation with DC input,” IEEE Trans. Commun., vol. COM-38, Apr. 1990.
20. P. W. Wong and R. M. Gray, “Two-stage sigma-delta modulation,” IEEE Trans. Acoust. Speech Signal Processing, accepted for publication.
21. W. Chou, P. W. Wong, and R. M. Gray, “Multistage sigma-delta modulation,” IEEE Trans. Inform. Theory, vol. IT-35, pp. 784–796, July 1989.
22. B. H. Leung, R. Neff, P. R. Gray, and R. W. Brodersen, “Area-efficient multichannel oversampled PCM voice-band coder,” IEEE J. Solid-State Circuits, vol. SC-23, pp. 1351–1357, Dec. 1988.
23. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol., vol. COM-12, pp. 162–165, December, 1964.
24. N. S. Jayant and L. R. Rabiner, “The application of dither to the quantization of speech signals,” Bell Syst. Tech. J., vol. 51, no. 6, pp. 1293–1304, July-Aug. 1972.
25. L. G. Roberts, “Picture coding using pseudorandom noise,” IEEE Trans. Inform. Theory, vol. IT-8, pp. 145–154, Feb. 1962.
26. W. Chou and R. M. Gray, “Dithering and its effects on sigma-delta and multistage sigma-delta modulation,” IEEE Trans. Inform. Theory, to appear.
27. K. L. Chung, A Course in Probability Theory, 2nd ed. New York: Academic Press, 1974.
28. R. M. Gray and L. D. Davisson, Random Processes: A Mathematical Approach for Engineers. Englewood Cliffs, NJ: Prentice-Hall, 1986.
29. S. Karlin and H. M. Taylor, A First Course in Stochastic Processes, 2nd ed. New York: Academic Press, 1975.
30. J. M. Harrison, Brownian Motion and Stochastic Flow Systems. New York: John Wiley, 1985.