Discrete Lagrangian methods for optimizing the design of multiplierless QMF banks

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

Volumn 46, Issue 9, 1999, Pages 1179-1191

  Wah, Benjamin W ^a   Shang, Yi ^a   Wu, Zhe ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; DIGITAL ARITHMETIC; DIGITAL FILTERS; LAGRANGE MULTIPLIERS; LOW PASS FILTERS; MATHEMATICAL MODELS; OPTIMIZATION;

ADAPTIVE WEIGHTED LAGRANGIAN SEARCH; CANONICAL SIGNED DIGIT REPRESENTATION; MULTIPLIERLESS FILTER BANKS;

INTEGRATED CIRCUIT LAYOUT;

EID: 0033189034     PISSN: 10577130     EISSN: None     Source Type: Journal    
DOI: 10.1109/82.793708     Document Type: Article

References (29)

1. A. D. Booth, "A signed binary multiplication technique," Quart. J. Mech. Appl. Math., vol. 4, pp. 236-240, 1951.
2. R. A. Caruana and B. J. Coffey, "Searching for optimal FIR multiplierless digital filters with simulated annealing," Philips Laboratories, Tech. Rep., 1988.
3. C.-K. Chen and J.-H. Lee, "Design of quadrature mirror filters with linear phase in the frequency domain," IEEE Trans. Circuits Syst. II, vol. 39, pp. 593-605, Sept. 1992.
4. _, "Design of linear-phase quadrature mirror filters with powers-of-two coefficients," IEEE. Trans. Circuits Syst. I, vol. 41, pp. 445-456, July 1994.
5. C. D. Creusere and S. K. Mitra, "A simple method for designing high-quality prototype filters for m-band pseudo QMF banks," IEEE Trans. Signal Processing, vol. 43, pp. 1005-1007, Apr. 1995.
6. M. H. Er and C. K. Slew, "Design of FIR filters using quadrature programming approach," IEEE Trans. Circuits Syst. II, vol. 42, pp. 217-220, Mar. 1995.
7. A. M. Geoffrion, "Lagrangian relaxation and its uses in integer programming," Math. Prog. Study, vol. 2, pp. 82-114, 1974.
8. B. R. Horng and A. N. Willon, Jr., "Lagrange multiplier approaches to the design of two-channel perfect-reconstruction linear-phase FIR filter banks," IEEE Trans. Signal Processing, vol. 40, pp. 364-374, Feb. 1992.
9. V. K. Jain and R. E. Crochiere, "Quadrature mirror filter design in the time domain," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 353-361, Apr. 1984.
10. J. D. Johnston, "A filter family designed for use in quadrature mirror filter banks," Proc. IEEE Proc. Int. Conf. ASSP, 1980, pp. 291-294.
11. D. Kodek and K. Steiglitz, "Comparison of optimal and local search methods for designing finite word length FIR digital filters," IEEE Trans. Circuits Syst., vol. CAS-28, pp. 28-32, Jan. 1981.
12. R. D. Koilpillai and P. P. Vaidyanathan, "A spectral factorization approach to pseudo-QMF design," IEEE Trans. Signal Processing, vol. 41, pp. 82-92, Jan. 1993.
13. Y. C. Lim and S. R. Parker, "FIR filter design over a discrete power-of-two coefficient space," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 583-519, June 1983.
14. D. G. Luenberger, Linear and Nonlinear Programming. Reading, MA: Addison-Wesley, 1984.
15. K. Nayebi, T. P. Barnwell, III, and M. J. T. Smith, "Time-domain filter bank analysis: A new design theory," IEEE Trans. Signal Processing, vol. 40, pp. 1412-1429, June 1992.
16. T. Q. Nguyen, "Digital filter bank design quadratic-constrained formulation," IEEE Trans. Signal Processing, vol. 43, pp. 2103-2108, Sept. 1995.
17. H. Samueli, "An improved search algorithm for the design of multiplierless FIR filters with powers-of-two coefficients," IEEE Trans. Circuits Syst., vol. 36, pp. 1044-1047, July 1989.
18. J. D. Schaffer and L. J. Eshelman, "Designing multiplierless digital filters using genetic algorithms," Proc. Int. Conf. Genetic Algorithms. San Mateo, CA: Morgan Kaufmann, 1993, pp. 439-444.
19. Y. Shang and B. W. Wah, "A discrete Lagrangian based global search method for solving satisfiability problems," J. Global Optimization, vol. 12, no. 1, pp. 61-99, Jan. 1998.
20. J.-J. Shyu and Y.-C. Lin, "A new approach to the design of discrete coefficient FIR digital filters," IEEE Trans. Signal Processing, vol. 43, pp. 310-314, Jan. 1995.
21. M. J. T. Smith and T. P. Barnwell, III, "Exact reconstruction techniques for tree-structured subband coders," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 434-441, June 1986.
22. I. Sodagar, K. Naybei, and T. P. Barnwell, III, "Time-varying filter banks and wavelets," IEEE Trans. Signal Processing, vol. 42, pp. 2983-2996, Nov. 1994.
23. A. K. Soman, P. P. Vaidyanathan, and T. Q. Nguyen, "Linear phase paraunitary filter banks: Theory, factorizations and designs," IEEE Trans. Signal Processing, vol. 41, pp. 3480-3496, Dec. 1993.
24. T. E. Tuncer and T. Q. Nguyen, "General analysis of two-band QMF banks," IEEE Trans. Signal Processing, vol. 43, pp. 544-548, Feb. 1995.
25. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
26. B. W. Wah and Y. Shang, "A discrete Lagrangian-based global-search method for solving satisfiability problems," Satisfiability Problem: Theory and Applications, D.-Z. Du, J. Gu, and P. Pardalos, Eds.. :Singapore American Mathematical Society, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1997, pp. 365-392.
27. B. W. Wah, Y. Shang, T. Wang, and T. Yu, "Global optimization of QMF filter-bank design using NOVEL," Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Munich, Germany, Apr. 1997, vol. 3, pp. 2081-2084.
28. B. W. Wah, Y. Shang, and Z. Wu, "Discrete Lagrangian method for optimizing the design of multiplierless QMF filter banks, in Proc. IEEE Int. Conf. Application-Specific Array Processors, July 1997, pp. 529-538.
29. Z. Wu, "Discrete Lagrangian methods for solving nonlinear discrete constrained optimization problems," M.Sc. thesis, Dept. Comput. Sei., Univ. of Illinois, Urbana, IL, May 1998.