Table of Contents
ISRN Signal Processing
Volume 2013 (2013), Article ID 815619, 10 pages
http://dx.doi.org/10.1155/2013/815619
Review Article

Two-Channel Quadrature Mirror Filter Bank: An Overview

Department of Electronics and Communication Engineering, National Institute of Technology, Kurukshetra, Haryana 136119, India

Received 28 June 2013; Accepted 1 August 2013

Academic Editors: C.-W. Kok and C.-M. Kuo

Copyright © 2013 S. K. Agrawal and O. P. Sahu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Croisier, D. Esteban, and C. Galand, “Perfect channel splitting by use of interpolation/decimation/tree decomposition techniques,” in Proceedings of the International Symposium on Information Circuis and Systems, Patras, Greece, 1976.
  2. D. Esteban and C. Galand, “Application of quadrature mirror filter to split band voice coding schemes,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ASSP '77), pp. 191–195, 1977.
  3. R. E. Crochiere, “Sub-band coding,” The Bell System Technical Journal, vol. 60, no. 7, pp. 1633–1653, 1981. View at Google Scholar · View at Scopus
  4. S. C. Chan, C. K. S. Pun, and K. L. Ho, “New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases,” IEEE Transactions on Signal Processing, vol. 52, no. 7, pp. 2135–2141, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Sablatash, “Designs and architectures of filter bank trees for spectrally efficient multi-user communications: review, modifications and extensions of wavelet packet filter bank trees,” Signal, Image and Video Processing, vol. 2, no. 1, pp. 9–37, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. M. J. T. Smith and S. L. Eddins, “Analysis/synthesis techniques for subband image coding,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 8, pp. 1446–1456, 1990. View at Publisher · View at Google Scholar · View at Scopus
  7. J. W. Woods and S. D. O’Neil, “Sub-band coding of images,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, no. 10, pp. 1278–1288, 1986. View at Google Scholar
  8. M. G. Bellanger and J. L. Daguet, “TDM-FDM transmultiplexer: digital polyphase and FFT,” IEEE Transactions on Communications, vol. 22, no. 9, pp. 1199–1205, 1974. View at Google Scholar · View at Scopus
  9. M. Vetterly, “Perfect transmultiplexers,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ASSP '86), vol. 4, pp. 2567–2570, 1986.
  10. Y.-P. Lin and S.-M. Phoong, “ISI-free FIR filterbank transceivers for frequency-selective channels,” IEEE Transactions on Signal Processing, vol. 49, no. 11, pp. 2648–2658, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. J. H. Husøy and T. Gjerde, “Computationally efficient sub-band coding of ECG signals,” Medical Engineering and Physics, vol. 18, no. 2, pp. 132–142, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. S. O. Aase, “Filter bank design for sub-band ECG compression,” in Proceedings of the 18th Annual International Conference of IEEE Engineering in Medicine and Biology Society, Amsterdam, The Netherlands, 1996.
  13. S. Chandran, “A novel scheme for a sub-band adaptive beam forming array implementation using quadrature mirror filter banks,” Electronics Letters, vol. 39, no. 12, pp. 891–892, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Painter and A. Spanias, “Perceptual coding of digital audio,” Proceedings of the IEEE, vol. 88, no. 4, pp. 451–512, 2000. View at Publisher · View at Google Scholar · View at Scopus
  15. V. X. Afonso, W. J. Tompkins, T. Q. Nguyen, and S. Luo, “ECG beat detection using filter banks,” IEEE Transactions on Biomedical Engineering, vol. 46, no. 2, pp. 192–202, 1999. View at Publisher · View at Google Scholar · View at Scopus
  16. G. Gu and E. F. Badran, “Optimal design for channel equalization via the filterbank approach,” IEEE Transactions on Signal Processing, vol. 52, no. 2, pp. 536–545, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. R. V. Cox, D. E. Bock, K. B. Bauer, J. D. Johnston, and J. H. Synder, “The analog voice privacy systems,” AT&T Technical Journal, vol. 66, no. 1, pp. 119–131, 1987. View at Google Scholar · View at Scopus
  18. R. E. Crochiere, “A novel approach for implementing pitch prediction in sub-band coding,” in Proceeding of the International Conference on Acoustics, Speech, and Signal Processing (ASSP '79), Washington, DC, USA, April 1979.
  19. A. J. Barabell and R. E. Crochiere, “Sub-band coder design incorporating quadrature filters and pitch prediction,” in Proceeding of the International Conference on Acoustics, Speech, and Signal Processing (ASSP '79), Washington, DC, USA, April 1979.
  20. R. Bregovic and T. Saramaki, “A general-purpose optimization approach for designing two-channel fir filterbanks,” IEEE Transactions on Signal Processing, vol. 51, no. 7, pp. 1783–1791, 2003. View at Publisher · View at Google Scholar · View at Scopus
  21. P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, Englewood Cliffs, NJ, USA, 1993.
  22. R. Bregovic and T. Saramaki, “Two-channel FIR filterbanks—a tutorial review and new results,” in Proceedings of the 2nd International Workshop on Transforms Filter banks, vol. 4, pp. 507–558, Brandenburg, Germany, 1999.
  23. M. J. T. Smith and T. P. Barnwell III, “Exact reconstruction techniques for tree structured sub-band coders,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, no. 3, pp. 434–441, 1986. View at Google Scholar · View at Scopus
  24. M. J. T. Smith and T. P. Barnwell III, “A procedure fo designing Exact reconstruction filter bank for tree structured sub-band coders,” in Proceeding of the International Conference on Acoustics, Speech, and Signal Processing (ASSP '84), pp. 27.1.1–27.1.4, 1984.
  25. P. P. Vaidyanathan, “Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial,” Proceedings of the IEEE, vol. 78, no. 1, pp. 56–93, 1990. View at Publisher · View at Google Scholar · View at Scopus
  26. J. D. Johnston, “A filter family designed for use in quadrature mirror filter banks,” in Proceeding of the International Conference on Acoustics, Speech, and Signal Processing (ASSP '80), pp. 292–294, April 1980.
  27. V. K. Jain and R. E. Crochiere, “Quadrature mirror filter design in time domain,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 32, no. 2, pp. 353–361, 1984. View at Google Scholar · View at Scopus
  28. C. K. Chen and J. H. Lee, “Design of quadrature mirror filters with linear phase in the frequency domain,” IEEE Transactions on Circuits and Systems, vol. 39, no. 9, pp. 593–605, 1992. View at Google Scholar
  29. H. Xu, W.-S. Lu, and A. Antoniou, “An improved method for the design of fir quadrature mirror-image filter banks,” IEEE Transactions on Signal Processing, vol. 46, no. 5, pp. 1275–1281, 1998. View at Publisher · View at Google Scholar · View at Scopus
  30. W.-S. Lu, H. Xu, and A. Antoniou, “A new method for the design of FIR quadrature mirror-image filter banks,” IEEE Transactions on Circuits and Systems II, vol. 45, no. 7, pp. 922–926, 1998. View at Publisher · View at Google Scholar · View at Scopus
  31. O. P. Sahu, M. K. Soni, and I. M. Talwar, “Marquardt optimization method to design two-channel quadrature mirror filter banks,” Digital Signal Processing, vol. 16, no. 6, pp. 870–879, 2006. View at Publisher · View at Google Scholar · View at Scopus
  32. A. Kumar, G. K. Singh, and R. S. Anand, “An improved method for the design of quadrature mirror filter banks using the Levenberg-Marquardt optimization,” Signal, Image and Video Processing, vol. 7, pp. 209–220, 2013. View at Publisher · View at Google Scholar · View at Scopus
  33. J. Upendar, C. P. Gupta, and G. K. Singh, “Design of two-channel quadrature mirror filter bank using particle swarm optimization,” Digital Signal Processing, vol. 20, no. 2, pp. 304–313, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Kumar, G. K. Singh, and R. S. Anand, “A closed form design method for the two-channel quadrature mirror filter banks,” Signal, Image and Video Processing, vol. 5, no. 1, pp. 121–131, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Gupta and S. K. Agarwal, “Designing of two channel polyphase quadrature mirror filter bank using power optimization method,” in Proceedings of the 2nd International Conference on Computer and Communication Technology (ICCCT '11), pp. 280–284, September 2011. View at Publisher · View at Google Scholar · View at Scopus
  36. O. P. Sahu, M. K. Soni, and I. M. Talwar, “Designing quadrature mirror filter banks using steepest descent method,” Journal of Circuits, Systems and Computers, vol. 15, no. 1, pp. 29–41, 2006. View at Publisher · View at Google Scholar · View at Scopus
  37. O. P. Sahu, M. K. Soni, and I. M. Talwar, “On the design of two channel quadrature mirror filter,” Paritantra, vol. 11, no. 1, 2005. View at Google Scholar
  38. K. Swaminathan and P. P. Vaidyanathan, “Theory and design of uniform DFT, parallel QMF banks,” IEEE Transactions on Circuits and Systems, vol. 33, no. 12, pp. 1170–1191, 1986. View at Google Scholar · View at Scopus
  39. Y.-D. Jou, “Design of two-channel linear-phase quadrature mirror filter banks based on neural networks,” Signal Processing, vol. 87, no. 5, pp. 1031–1044, 2007. View at Publisher · View at Google Scholar · View at Scopus
  40. A. Kumar, S. M. Rafi, and G. K. Singh, “A hybrid method for designing linear-phase quadrature mirror filter bank,” Digital Signal Processing, vol. 22, no. 3, pp. 453–462, 2012. View at Publisher · View at Google Scholar · View at Scopus
  41. L. Andrew, V. T. Franques, and V. K. Jain, “Eigen design of quadrature mirror filters,” IEEE Transactions on Circuits and Systems II, vol. 44, no. 9, pp. 754–757, 1997. View at Publisher · View at Google Scholar · View at Scopus
  42. S. Nalbalwar, S. D. Joshi, and R. K. Patney, “A novel approach to design of signal matched QMF and DFT filter bank,” in Proceedings of the 15th International Conference on Software, Telecommunications and Computer Networks (SoftCOM '07), pp. 416–420, September 2007. View at Publisher · View at Google Scholar · View at Scopus
  43. M. Li and C.-W. Kok, “Norm induced QMF banks design using LMI constraints,” in Proceedings of the IEEE International Conference on Accoustics, Speech, and Signal Processing (ASSP '03), pp. 493–496, April 2003. View at Scopus
  44. A. Ghosh, R. Giri, A. Chowdhury, S. Das, and A. Abraham, “Two-channel quadrature mirror bank filter design using a Fitness-Adaptive Differential Evolution algorithm,” in Proceedings of the 2nd World Congress on Nature and Biologically Inspired Computing (NaBIC '10), pp. 634–641, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  45. F. Cruz-Roldán, I. Santamaría, and Á. M. Bravo, “Frequency sampling design of prototype filters for nearly perfect reconstruction cosine-modulated filter banks,” IEEE Signal Processing Letters, vol. 11, no. 3, pp. 397–400, 2004. View at Publisher · View at Google Scholar · View at Scopus
  46. P. Ghosh, S. Das, and H. Zafar, “Adaptive-differential-evolution-based design of two-channel quadrature mirror filter banks for sub-band coding and data transmission,” IEEE Transactions on Systems, Man, and Cybernetics C, vol. 42, no. 6, pp. 1613–1623, 2012. View at Google Scholar
  47. C. Y.-F. Ho, B. W.-K. Ling, L. Benmesbah, T. C.-W. Kok, W.-C. Siu, and K.-L. Teo, “Two-channel linear phase FIR QMF bank minimax design via global nonconvex optimization programming,” IEEE Transactions on Signal Processing, vol. 58, no. 8, pp. 4436–4441, 2010. View at Publisher · View at Google Scholar · View at Scopus
  48. G. S. Baicher, “Towards optimal implementation of a class of quadrature mirror filter using genetic algorithms,” in Proceedings of the IEEE 5th International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA '10), pp. 1663–1668, September 2010. View at Publisher · View at Google Scholar · View at Scopus
  49. Y. C. Lim, R. H. Yang, and S.-N. Koh, “Design of weighted minimax quadrature mirror filters,” IEEE Transactions on Signal Processing, vol. 41, no. 5, pp. 1780–1789, 1993. View at Publisher · View at Google Scholar · View at Scopus
  50. C.-K. Goh, Y. C. Lim, and C. S. Ng, “Improved weighted least squares algorithm for the design of quadrature mirror filters,” IEEE Transactions on Signal Processing, vol. 47, no. 7, pp. 1866–1877, 1999. View at Publisher · View at Google Scholar · View at Scopus
  51. S. K. Agrawal and O. P. Sahu, “Two-channel quadrature mirror filter bank design using FIR polyphase component,” International Journal on Signal Image Processing, vol. 4, no. 1, pp. 24–28, 2013. View at Google Scholar
  52. M. M. Ekanayake and K. Premaratne, “Two-channel IIR QMF banks with approximately linear-phase analysis and synthesis filters,” IEEE Transactions on Signal Processing, vol. 43, no. 10, pp. 2313–2322, 1995. View at Publisher · View at Google Scholar · View at Scopus
  53. P. P. Vaidyanathan, S. K. Mitra, and Y. Neuvo, “A new approach to the realization of low sensitivity IIR digital filters,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, no. 2, pp. 350–361, 1986. View at Google Scholar · View at Scopus
  54. P. P. Vaidyanathan, P. Regalia, and S. K. Mitra, “Design of doubly complementary IIR digital filters using a single complex all pass filter, with Multirate applications,” IEEE Transactions on Circuits and Systems, vol. 34, no. 4, pp. 378–389, 1987. View at Google Scholar · View at Scopus
  55. T. A. Ramstad, “IIR filter bank for sub band coding of images,” in Proceedings of the IEEE International Symposium on Circuits and Systems, pp. 827–830, Espoo, Finland, June 1988.
  56. T. Q. Nguyen, T. I. Laakso, and R. D. Koilpillai, “Eigenfilter approach for the design of allpass filters approximating a given phase response,” IEEE Transactions on Signal Processing, vol. 42, no. 9, pp. 2257–2263, 1994. View at Publisher · View at Google Scholar · View at Scopus
  57. M. M. Ekanayake and K. Premaratne, “Two-channel IIR QMF banks with approximately linear-phase analysis and synthesis filters,” in Proceedings of the 28th Annual Asilomar Conference on Signals, Systems, and Computers, pp. 1005–1009, November 1994.
  58. P. P. Vaidyanathan and P.-Q. Hoang, “Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, no. 1, pp. 81–94, 1988. View at Publisher · View at Google Scholar · View at Scopus
  59. B.-R. Horng and A. N. Willson Jr., “Lagrange multiplier approaches to the design of two-channel perfect-reconstruction linear-phase FIR filter banks,” IEEE Transactions on Signal Processing, vol. 40, no. 2, pp. 364–374, 1992. View at Publisher · View at Google Scholar · View at Scopus
  60. S.-J. Yang, J.-H. Lee, and B.-C. Chieu, “Perfect-reconstruction filter banks having linear-phase fir filters with equiripple response,” IEEE Transactions on Signal Processing, vol. 46, no. 12, pp. 3246–3255, 1998. View at Publisher · View at Google Scholar · View at Scopus
  61. T. Q. Nguyen and P. P. Vaidyanathan, “Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 5, pp. 676–690, 1989. View at Publisher · View at Google Scholar · View at Scopus
  62. K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, “Time-domain filter bank analysis: a new design theory,” IEEE Transactions on Signal Processing, vol. 40, no. 6, pp. 1412–1429, 1992. View at Publisher · View at Google Scholar · View at Scopus
  63. R. Bregovic and T. Saramaki, “New method for the design of two-channel perfect-reconstruction linear-phase FIR filter banks,” in Proceedings of the IEEE Internaitonal Symposium on Circuits and Systems, pp. 639–642, Geneva, Switzerland, May 2000. View at Scopus
  64. E. Abdel-Raheem, F. El-Guibaly, and A. Antoniou, “Design of low-delay two-channel FIR filter banks using constrained optimization,” Signal Processing, vol. 48, no. 3, pp. 183–192, 1996. View at Publisher · View at Google Scholar · View at Scopus
  65. A. K. Soman, P. P. Vaidyanathan, and T. Q. Nguyen, “Linear phase paraunitary filter banks: theory, factorizations and designs,” IEEE Transactions on Signal Processing, vol. 41, no. 12, pp. 3480–3496, 1993. View at Publisher · View at Google Scholar · View at Scopus
  66. M. S. Spurbeck and C. T. Mullis, “Least squares approximation of perfect reconstruction filter banks,” IEEE Transactions on Signal Processing, vol. 46, no. 4, pp. 968–978, 1998. View at Publisher · View at Google Scholar · View at Scopus
  67. C.-K. Goh and Y. C. Lim, “An efficient algorithm to design weighted minimax perfect reconstruction quadrature mirror filter banks,” IEEE Transactions on Signal Processing, vol. 47, no. 12, pp. 3303–3314, 1999. View at Publisher · View at Google Scholar · View at Scopus
  68. M. Vetterli and D. Le Gall, “Perfect reconstruction FIR filter banks: some properties and factorizations,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 7, pp. 1057–1071, 1989. View at Publisher · View at Google Scholar · View at Scopus
  69. S. R. K. Dutta and M. Vidyasagar, “New algorithms for constrained minimax optimization,” Mathematical Programming, vol. 13, no. 1, pp. 140–155, 1977. View at Publisher · View at Google Scholar · View at Scopus
  70. M. Vetterli, “Multi-dimensional sub-band coding: some theory and algorithms,” Signal Processing, vol. 6, no. 2, pp. 97–112, 1984. View at Google Scholar · View at Scopus
  71. S. Das and P. N. Suganthan, “Differential evolution: a survey of the state-of-the-art,” IEEE Transactions on Evolutionary Computation, vol. 15, no. 1, pp. 4–31, 2011. View at Publisher · View at Google Scholar · View at Scopus
  72. S. Hara, T. Matsuda, K. Ishikura, and N. Morinaga, “Co-existence problem of TDMA and DS-CDMA systems - application of complex multirate filter bank,” in Proceedings of the IEEE GLOBECOM, pp. 1281–1285, November 1996. View at Scopus
  73. S. Hara, H. Masutani, and T. Matsuda, “Filter bank-based adaptive interference canceler for co-existence problem of TDMA/CDMA systems,” in Proceedings of the IEEE VTS 50th Vehicular Technology Conference (VTC '99), pp. 1658–1662, September 1999. View at Publisher · View at Google Scholar · View at Scopus
  74. M. Konstantinos, A. Adamis, and P. Constantinou, “Receiver architectures for OFDMA systems with subband carrier allocation,” in Proceedings of the 14th European Wireless Conference (EW '08), pp. 1–7, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  75. T. D. Tran and T. Q. Nguyen, “On M-channel linear phase FIR filter banks and application in image compression,” IEEE Transactions on Signal Processing, vol. 45, no. 9, pp. 2175–2187, 1997. View at Publisher · View at Google Scholar · View at Scopus
  76. T. Xia and Q. Jiang, “Optimal multifilter banks: design, related symmetric extension transform, and application to image compression,” IEEE Transactions on Signal Processing, vol. 47, no. 7, pp. 1878–1889, 1999. View at Publisher · View at Google Scholar · View at Scopus
  77. M. Vetterly and J. Kovacevic, Wavelets and Sub-Band Coding, Prentice Hall, Englewood Cliffs, NJ, USA, 1995.
  78. I. Daubechies, “Ten Lectures on Wavelets,” CBMS series, SIAM, Philadelphia, Pa, USA, 1992. View at Google Scholar