Quantization of filter bank frame expansions through moving horizon optimization

IEEE Transactions on Signal Processing

Volumn 57, Issue 2, 2009, Pages 503-515

  Quevedo, Daniel E ^a   Bölcskei, Helmut ^b   Goodwin, Graham C ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b ETH ZURICH   (Switzerland)

Author keywords

Filter banks; Frame expansions; Oversampling; Quantization

Indexed keywords

ADDITIVE WHITE NOISE; FRAME EXPANSIONS; MOVING HORIZON OPTIMIZATIONS; NONLINEAR FEEDBACKS; OVERSAMPLED FILTER BANKS; OVERSAMPLING; QUANTIZATION; QUANTIZERS; SUB BANDS;

FILTER BANKS;

EID: 60549096752     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.2008259     Document Type: Article

References (49)

1. R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1983.
2. M. Vetterli and J. Kovačević, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice-Hall, 1995.
3. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
4. N. Fliege, Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets. New York: Wiley, 1994.
5. G. Strang and T. Nguyen, Wavelets and Filter Banks. Wellesley, MA: Wellesley-Cambridge, 1996.
6. Collected Papers on Digital Audio Bit-Rate Reduction, N. Gilchrist and C. Grewin, Eds. New York: Audio Eng. Soc., 1996.
7. Z. Cvetković and J. D. Johnson, "Nonuniform oversampled filter banks for audio signal processing," IEEE Trans. Speech Audio Process., vol. 11, pp. 393-399, Sep. 2003.
8. 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.
9. H. Vikalo, B. Hassibi, A. T. Erdogan, and T. Kailath, "On robust signal reconstruction in noisy filter banks," Signal Process., vol. 85, no. 1, pp. 1-14, Jan. 2005.
10. Y. -M. Cheng, B. -S. Chen, and L. -M. Chen, "Minimax deconvolution design of multirate systems with channel noises: A unified approach," IEEE Trans. Signal Process., vol. 47, pp. 3145-3149, Nov. 1999.
11. A. Makur and M. Arunkumar, "Minimization of quantization noise amplification in biorthogonal subband coders," IEEE Trans. Circuits Syst. I, vol. 51, pp. 2088-2097, Oct. 2004.
12. 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.
13. Delta-Sigma Data Converters: Theory, Design and Simulation, S. R. Norsworthy, R. Schreier, and G. C. Temes, Eds. Piscataway, NJ: IEEE, 1997.
14. D. E. Quevedo, G. C. Goodwin, and J. A. De Doná, "Finite constraint set receding horizon quadratic control," Int. J. Robust Nonlin. Contr., vol. 14, no. 4, pp. 355-377, Mar. 2004.
15. G. C. Goodwin, D. E. Quevedo, and D. McGrath, "Moving-horizon optimal quantizer for audio signals," J. Audio Eng. Soc., vol. 51, no. 3, pp. 138-149, Mar. 2003.
16. 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.
17. D. E. Quevedo and G. C. Goodwin, "Moving horizon design of discrete coefficient FIR filters," IEEE Trans. Signal Process., vol. 53, pp. 2262-2267, Jun. 2005.
18. D. E. Quevedo, G. C. Goodwin, and J. A. De Doná, "Multistep detector for linear ISI-channels incorporating degrees of belief in past estimates," IEEE Trans. Commun., vol. 55, pp. 2092-2103, Nov. 2007.
19. C. S. Güntürk, T. Nguyen, A. M. Powell, and O. Yilmaz, "Coarsely Quantized Redundant Representations of Signals, Final Workshop Report," Int. Res. Station for Math. Innovat. Disc., Banff, 2006.
20. I. Daubechies and R. DeVore, "Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order," Ann. Math., vol. 158, no. 2, pp. 679-710, Sep. 2003.
21. J. J. Benedetto, A. M. Powell, and O. Yilmaz, "Sigma-delta (ΣΔ) quantization and finite frames," IEEE Trans. Inf. Theory, vol. 52, pp. 1990-2005, May 2006.
22. J. J. Benedetto, A. M. Powell, and O. Yilmaz, "Second-order sigma-delta (ΣΔ) quantization of finite frame expansions," Appl. Comput. Harmon. Anal., vol. 20, no. 1, pp. 126-148, Jan. 2006.
23. I. Daubechies, R. DeVore, C. S. Güntürk, and V. A. Vaishampayan, "A/D conversion with imperfect quantizers," IEEE Trans. Inf. Theory vol. 52, pp. 874-885, Mar. 2006.
24. C. S. Güntürk and N. T. Thao, "Refined error analysis in second-order ΣΔ modulation with constant inputs," IEEE Trans. Inf. Theory, vol. 50, pp. 839-860, May 2004.
25. M. S. Derpich, E. I. Silva, D. E. Quevedo, and G. C. Goodwin, "On optimal perfect reconstruction feedback quantizers," IEEE Trans. Signal Process., vol. 56, pp. 3871-3890, Aug. 2008.
26. Z. Cvetković and M. Vetterli, "Oversampled filter banks," IEEE Trans. Signal Process., vol. 46, pp. 1245-1255, May 1998.
27. H. Bölcskei, F. Hlawatsch, and H. G. Feichtinger, "Frame-theoretic analysis of oversampled filter banks," IEEE Trans. Signal Process. vol. 46, pp. 3256-3268, Dec. 1998.
28. B. -S. Chen, C. -W. Lin, and Y. -L. Chen, "Optimal signal reconstruction in noisy filter bank systems: Multirate Kalman synthesis filtering approach," IEEE Trans. Signal Process., vol. 43, pp. 2496-2504, Nov. 1995.
29. D. Marco and D. L. Neuhoff, "The validity of the additive noise model for uniform scalar quantizers," IEEE Trans. Inf. Theory, vol. 51, pp. 1739-1755, May 2005.
30. P. Westerink, J. Biemond, and D. E. Boekee, "Scalar quantization error analysis for image subband coding using QMF's," IEEE Trans. Signal Process., vol. 40, pp. 421-428, Feb. 1992.
31. O. Feely, "Nonlinear dynamics of discrete-time circuits: A survey," Int. J. Circuit Theory Appl., vol. 35, no. 5-6, pp. 515-531, Sep.-Dec. 2007.
32. R. A. Haddad and K. Park, "Modeling, analysis, and optimum design of quantized M-band filter banks," IEEE Trans. Signal Process. vol. 43, pp. 2540-2549, Nov. 1995.
33. N. Jayant, J. Johnston, and R. Safranek, "Signal compression based on models of human perception," Proc. IEEE, vol. 81, pp. 1385-1421, Oct. 1993.
34. A. Eshraghi and T. S. Fiez, "A comparative analysis of parallel delta-sigma ADC converter architectures," IEEE Trans. Circuits Syst. I, vol. 51, pp. 450-458, Mar. 2004.
35. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Optimality and stability," Automatica, vol. 36, no. 6, pp. 789-814, Jun. 2000.
36. G. C. Goodwin, M. M. Serón, and J. A. De Doná, Constrained Control and Estimation - An Optimization Perspective. London, U.K.: Springer-Verlag, 2005.
37. T. Kailath, Linear systems. Englewood Cliffs, N.J: Prentice-Hall, 1980.
38. B. D. O. Anderson and J. Moore, Optimal filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
39. Z. Pan, K. Kotani, and T. Ohmi, "A unified projection method for fast search of vector quantization," IEEE Signal Process. Lett., vol. 11, pp. 637-640, Jul. 2004.
40. J. -S. Pan, Z. -M. Lu, and S. -H. Sun, "An efficient encoding algorithm for vector quantization based on subvector technique," IEEE Trans. Image Process., vol. 12, pp. 265-270, Mar. 2003.
41. G. D. Forney, "Maximum likelihood sequence estimation of digital sequences in the presence of intersymbol interference," IEEE Trans. Inf. Theory, vol. 18, pp. 363-378, May 1972.
42. D. F. Delchamps, "Nonlinear dynamics of oversampling A-to-D converters," in Proc. IEEE Conf. Decision Contr., Dec. 1993, vol. 1, pp. 480-485.
43. P. J. Ramadge, "On the periodicity of symbolic observations of piece-wise smooth discrete-time systems," IEEE Trans. Autom. Control vol. 35, pp. 807-813, Jul. 1990.
44. Y.-P. Lin and P. P. Vaidyanathan, "Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction," IEEE Trans. Signal Process., vol. 42, pp. 2525-2539, Nov. 1995.
45. R. D. Koilpillai and P. P. Vaidyanathan, "Cosine-modulated FIR filter banks satisfying perfect reconstruction," IEEE Trans. Signal Process., vol. 40, pp. 770-783, Apr. 1992.
46. W.-S. Lu, T. Saramäki, and R. Bregović, "Design of practically perfect-reconstruction cosine-modulated filter banks: A second-order cone programming approach," IEEE Trans. Circuits Syst. I, vol. 51, pp. 552-563, Mar. 2004.
47. H. Bölcskei and F. Hlawatsch, "Oversampled cosine modulated filter banks with perfect reconstruction," IEEE Trans. Circuits Syst. II vol. 45, pp. 1057-1071, Aug. 1998.
48. J. L. Mannos and D. J. Sakrison, "The effect of a visual fidelity criterion on the encoding of images," IEEE Trans. Inf. Theory, vol. 20, pp. 525-536, Jul. 1974.
49. H. Bölcskei, P. Duhamel, and R. Hleiss, "Orthogonalization of OFDM/OQAM pulse shaping filters using the discrete Zak transform," Signal Process., vol. 83, no. 7, pp. 1379-1391, Jul. 2003.