On optimal perfect reconstruction feedback quantizers

IEEE Transactions on Signal Processing

Volumn 56, Issue 8 II, 2008, Pages 3871-3890

  Derpich, Milan S ^a   Silva, Eduardo I ^a   Quevedo, Daniel E ^a   Goodwin, Graham C ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Differential pulse code modulation; Optimization; Quantization; Sigma delta modulation; Source coding

Indexed keywords

ACOUSTIC INTENSITY; ERROR ANALYSIS; FOOD ADDITIVES; IIR FILTERS; MEAN SQUARE ERROR; REPAIR; RESTORATION; STRAIN ENERGY; TRANSFER FUNCTIONS; WAVE FILTERS;

A-PRIORI; A/D CONVERTERS; ADDITIVE WHITE NOISE; ANALYTICAL EXPRESSIONS; DIFFERENTIAL PULSE CODE MODULATION; FEED BACK LOOPS; NOISE-SHAPING; OPTIMAL FILTERING; OPTIMIZATION; OVER-SAMPLING RATIO; PERFECT RECONSTRUCTION; QUANTIZATION; QUANTIZATION ERRORS; QUANTIZATION NOISES; QUANTIZERS; SCALAR QUANTIZER; SIGMA-DELTA; SIGMA-DELTA MODULATION; SIGNAL TRANSFER FUNCTIONS; SOURCE CODING;

SIGNAL TO NOISE RATIO;

EID: 48849089331     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.925577     Document Type: Article

References (36)

1. N. Jayant and P. Noll, Digital Coding of Waveforms. Principles and Approaches to Speech and Video. Englewood Cliffs, NJ: Prentice-Hall, 1984.
2. S. R. Norsworthy, R. Schreier, and G. C. Temes, Eds., Delta-Sigma Data Converters: Theory, Design and Simulation Piscataway, NJ, IEEE, 1997.
3. R. A. Wannamaker, "Psycho-acoustically optimal noise shaping," J. Audio Eng. Soc., vol. 40, no. 7/8, pp. 611-620, Jul./Aug. 1992.
4. S. K. Tewksbury and R. W. Hallock, "Oversampled, linear predictive and noise-shaping coders of order N >1," IEEE Trans. Circuits Syst., vol. 25, pp. 436-447, Jul. 1978.
5. H. Bölcskei and F. Hlawatsch, "Noise reduction in oversampled filter banks using predictive quantization," IEEE Trans. Inf. Theory, vol. 47, pp. 155-172, Jan. 2001.
6. F. Baqai, J.-H. Lee, A. Agar, and J. Allebach, "Digital color halftoning," IEEE Signal Process. Mag., vol. 22, no. 1, pp. 87-96, Jan. 2005.
7. C. H. Bae, J. H. Ryu, and K. W. Lee, "Suppression of harmonic spikes in switching converter output using dithered sigma-delta modulation," IEEE Trans. Ind. Appl., vol. 38, pp. 159-166, Jan./Feb. 2002.
8. E. I. Silva, G. C. Goodwin, D. E. Quevedo, and M. S. Derpich, "Optimal noise shaping for networked control systems," in Proc. Europ. Contr. Conf. Kos., Greece, 2007.
9. A. Gersho, "Principles of quantization," IEEE Trans. Circuits Syst. vol. 25, pp. 427-436, Jul. 1978.
10. R. A. Wannamaker, S. P. Lipshitz, J. Vanderkooy, and J. N. Wright, "A theory of nonsubtractive dither," IEEE Trans. Signal Process., vol. 48, pp. 499-516, Feb. 2000.
11. D. E. Quevedo and G. C. Goodwin, "Multistep optimal analog-to-digital conversion," IEEE Trans. Circuits Syst. I, vol. 52, pp. 503-515, Mar. 2005.
12. H. Spang, III and P. Schultheiss, "Reduction of quantizing noise by use of feedback," IRE Trans. Commun. Syst., vol. CS-10, no. 4, pp. 373-380, Dec. 1962.
13. R. Schreier and G. Temes, Understanding Delta-Sigma Data Converters New York: Wiley-IEEE, 2004.
14. P. Noll, "On predictive quantizing schemes," Bell. Syst. Tech. J. vol. 57, no. 5, pp. 1499-1532, May-Jun. 1978.
15. M. Gerzon and P. G. Craven, "Optimal noise shaping and dither of digital signals," in 87th Convention AES, New York, Oct. 1989, preprint 2822.
16. R. Brainard and J. Candy, "Direct-feedback coders: Design and performance with television signals," Proc. IEEE, vol. 57, pp. 776-786, Jul. 1969.
17. B. S. Atal and M. Schroeder, "Predictive coding of speech signals and subjective error criteria," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-27, pp. 247-254, Jun. 1979.
18. D. Stacey, R. Frost, and G. Ware, "Error spectrum shaping quantizers with nonideal reconstruction filters and saturating quantizers," in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., 1991, vol. 3, pp. 1905-1908.
19. S. P. Lipschitz, J. Vanderkooy, and R. A. Wannamaker, "Minimally audible noise shaping," J. Audio Eng. Soc., vol. 39, no. 11, pp. 836-852, Nov. 1991.
20. H. Bölcskei, "Noise shaping quantizers of order L > 1 for "general" frame expansions," in 2006, Presented at the Workshop on Coarsely Quantized Redundant Representations of Signals, Banff, Alberta, Canada, 2006.
21. J. Tuqan and P. P. Vaidyanathan, "Statistically optimum pre- and post-filtering in quantization," IEEE Trans. Circuits Syst. II, vol. 44, pp. 1015-1031, Dec. 1997.
22. O. Guleryuz and M. Orchard, "On the DPCM conpression of Gaussian autoregressive sequences," IEEE Trans. Inf. Theory, vol. 47, pp. 945-956, Mar. 2001.
23. G. F. Carrier, M. Krook, and C. Pearson, Functions of a Complex Variable: Theory and Technique. Ithaca, NY: Hod Books, 1983.
24. M. M. Serón, J. H. Braslavsky, and G. C. Goodwin, Fundamental Limitations in Filtering and Control. London, U.K.: Springer-Verlag, 1997.
25. R. L. Burden and J. D. Faires, Numerical Analysis. Boston, MA: PWS-Kent, 1993, The Prindle, Weber & Schmidt series in Math..
26. S. Boyd and L. Vandenberghe, Convex Optimization. New York: Springer, 2004.
27. T. Berger, Rate Distortion Theory: A Mathematical Basis for Data Compression. Englewood Cliffs, NJ: Prentice-Hall, 1971.
28. J. O'Neal, Jr, "Bounds on subjective performance measures for source encoding systems," IEEE Trans. Inf. Theory, vol. IT-17, pp. 224-231, May 1971.
29. W. R. Bennet, "Spectrum of quantized signals," Bell Syst. Tech. J. vol. 27, pp. 446-472, Jul. 1948.
30. D. Hui and D. L. Neuhoff, "Asymptotic analysis of optimal fixed-rate uniform scalar quantization," IEEE Trans. Inf. Theory, vol. 47, pp. 957-977, Mar. 2001.
31. I. Daubechies and R. DeVore, "Approximating a bandlimited function using very coarsely quantized data: A family of stable sigmadelta modulators of arbitrary order," Ann. Math., vol. 158, no. 2, pp. 679-710, 2003.
32. C. S. Güntürk, "One-bit sigma-delta quantization with exponential accuracy," Commun. Pure Appl. Math., vol. 56, no. 11, pp. 1608-1630, 2003.
33. M. S. Derpich, J. Østergaard, and G. C. Goodwin, "The quadratic Gaussian rate-distortion function for source uncorrelated distortions," in Proc. Data Compress. Conf., Snowbird, UT, Mar. 2008, pp. 73-82.
34. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities. Cambridge, U.K.: Cambridge Univ. Press, 1959.
35. R.Weinstock, Calculus of Variations with Applications to Physics and Engineering. New York: Dover Publications, Inc., 1974.
36. I. M. Gelfand and S. V. Fomin, Calculus of Variations. Englewood Cliffs, NJ: Prentice-Hall, 1963.