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Biorthogonal Recombination Nonuniform Cosine-Modulated Filter Banks and their Multiplier-Less Realizations

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Abstract.

This paper studies the theory, design and multiplier-less (ML) realization of a class of perfect reconstruction (PR) low-delay biorthogonal nonuniform cosine-modulated filter banks (CMFBs). It is based on a recombination (or merging) structure previously proposed by the authors. By relaxing the original CMFB and the recombination transmultiplexer (TMUX) in the recombination structure to be biorthogonal, nonuniform CMFBs with lower system delay can be obtained. This also increases the possible choices of the prototype filters to meet different design objectives. A matching condition is introduced to suppress the spurious response resulting from the mismatch in the transition bands of the two biorthogonal CMFBs. A complete factorization of biorthgonal CMFB using the lifting scheme is employed to obtain structurally PR biorthogonal nonuniform filter banks (FBs), which are robust to coefficient quantization. In addition, by approximating the lifting coefficients and the modulation matrices by the sum of powers-of-two (SOPOT) coefficients, ML realization with very low implementation complexity is obtained. Design examples and comparison are given to illustrate the effectiveness of the proposed method.

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References

  1. P.P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice Hall, 1992.

    Google Scholar 

  2. T. Blu, “An Iterated Rational Filter Bank for Audio Coding Time-frequency and time-scale Analysis,” IEEE-SP International Symposium on, pp. 81–84, 1996.

  3. R.V. Cox, “The design of Uniformly and Nonuniformly Spaced Pseudoquadrature Mirror Filters,” IEEE Trans. on ASSP, vol. 24, 1986 pp. 1090–1096.

    Article  Google Scholar 

  4. J. Kovacevic and M. Vetterli, “Perfect Reconstruction Filter Banks with Rational Sampling Factors,” IEEE Trans. on SP, vol. 41, 1993, pp. 2047–2066.

    Article  MATH  Google Scholar 

  5. P.Q. Hoang and P.P. Vaidyanathan, “Nonuniform Multirate Filter Banks: Theory and Design,” in Proc. IEEE ISCAS, 1989, pp. 371–374.

  6. S. Akkarakaran and P.P. Vaidyanathan, “New Results and open Problems on Nonuniform Filter-banks,” in Proc. IEEE ICASSP, 1999, vol. 3, pp. 1501–1504.

    Google Scholar 

  7. S.C. Chan, X.M. Xie and T.I. Yuk, “Theory and Design of a Class of Cosine-modulated Nonuniform filter banks,” in Proc. IEEE ICASSP, 2000, vol. 1, pp. 504–507.

    Google Scholar 

  8. C.W. Kok, Y. Hui, and T.Q. Nguyen, “Nonuiform Modulated Filter Banks,” SPIE Vol. 3169, 1997.

  9. X.M. Xie, S.C. Chan, and T.I. Yuk, “A Class of Perfect-Reconstruction Nonuniform Cosine-Modulated Filter-Banks with Dynamic Recombination,” in Proc. Eusipco, 2002, vol. 2, pp. 549–552.

    Google Scholar 

  10. M.J.T. Smith and T.P. Barnwell III, “Exact Reconstruction Techniques for Tree-structured Sub-band coders,” IEEE Trans. on ASSP., pp. 434–441, June 1986.

  11. J. Li, T.Q. Nguyen and S. Tantaratana, “A Simple Design Method for Near-perfect Reconstruction Nonuniform Filter Banks,” IEEE Trans. on SP., vol.45, 1997, pp.2105–2109, Aug.

    Article  Google Scholar 

  12. R.L. Querioz, “Uniform Filter Banks with Nonuniform Bands: Post Processing Design,” in Proc. IEEE ICASSP, 1998, vol. 3, pp. 1341–1344.

    MATH  Google Scholar 

  13. F. Argenti, B. Brogelli and E. Del Re, “Design of Pseudo-QMF Banks with Rational Sampling Factors Using Several Prototype Filters,” IEEE Trans. on SP, vol. 46, 1998, pp. 1709–1715.

    Article  Google Scholar 

  14. T.W. Chen, L. Qiu and E. W. Bai, “General Multirate Building Structures with Application to Nonuniform Filter Banks,” IEEE Trans. on Circuits and Sys. II, vol. 45, 1998, pp. 948–958.

    Article  Google Scholar 

  15. K. Nayebi, T.P. Barnwell III, and M.J.T. Smith, “Nonuniform Filter Banks: A Reconstruction and Design Theory,” IEEE Trans. on SP, vol. 41, 1993, pp. 1114–1127.

    Article  MATH  Google Scholar 

  16. J. Princen, “The Design of Nonuniform Modulated Filter Banks,” in Proc. IEEE-SP, Time-Frequency and Time-Scale Analysis, International Symposium, 1994, pp. 112–115.

  17. R.D. Koilpillai, T.Q. Nguyen and P.P. Vaidyanathan, “Some results in the theory of crosstalk-free transmultiplexers,” IEEE Trans. on SP, vol. 39, 1991, pp. 2174–2183.

    Article  Google Scholar 

  18. T.Q. Nguyen and P.N. Heller, “Biorthogonal Cosine-modulated Filter Bank,” in Proc. IEEE ICASSP, 1996, vol. 3, pp. 1471–1474.

    Google Scholar 

  19. N.P. Heller, T. Karp and T.Q. Nguyen, “A General Formulation of Modulated Filter Banks,” IEEE Trans. on SP, vol. 47, Apr. 1999, pp. 986–1002.

    Article  Google Scholar 

  20. X.M. Xie, “New Design and Realization Methods for Perfect Reconstruction Nonuniform Filter Banks,” Ph.D thesis, Dept. of Elect & Electronic Engg., The University of Hong Kong, 2004.

  21. T. Karp, A. Mertins and G. Schuller, “Efficient Biorthogonal Cosine-modulated Filter banks,” EURASP Signal Processing, vol. 81, 2001, pp. 997–1016.

    Article  MATH  Google Scholar 

  22. R.D. Koilpillai and P.P. Vaidyanathan, “Cosine-modulated FIR filter banks satisfying perfect reconstruction,” IEEE Trans. on SP, vol. 40, 1992, pp. 770–783.

    Article  Google Scholar 

  23. J.S. Mao, “New Design and Factorization Methods for Perfect Reconstruction Filter Banks,” Ph.D thesis, Dept. of Elect & Electronic Engg., The University of Hong Kong, 2000.

  24. I. Daubechies and W. Swedens, “Factoring Wavelet Transform into Lifting Steps,” J. Fourier Anal. Appl., vol. 4 no. 3, 1998, pp. 247–269.

    Article  MathSciNet  Google Scholar 

  25. S.C. Chan, W. Liu and K.L. Ho, “Perfect Reconstruction Modulated Filter Banks with sum of Powers-of-two Coefficients,” IEEE Signal Processing Letter, vol. 8, 2001, pp. 163–166.

    Article  Google Scholar 

  26. Y.C. Lam and S.R. Parker, “FIR filter design over a discrete power-of-two coefficient space,” IEEE Trans. ASSP, vol. 31, 1983, pp. 583–591.

    Google Scholar 

  27. S.C. Chan and K.M. Tsui, “Multiplier-less Real-valued FFT-like Transformation (ML-RFFT) and Related Real-valued Transformations,” in Proc. IEEE ISCAS, 03, vol. 4, pp. 257–260.

    Google Scholar 

  28. Z. Wang, “Fast Algorithms for the Discrete W Transform and for the discrete Fourier Transform,” IEEE Trans. on ASSP, vol. 32, 1986, pp. 803–816.

    Article  Google Scholar 

  29. S.C. Chan and K.L. Ho, “Fast Algorithms for Computing the discrete Cosine Transform,” IEEE Trans. on Circuits Syst. II, vol. 39, 1992, pp. 185–190.

    Article  MATH  Google Scholar 

  30. T.S. Chang, J.I. Guo and C.W. Jen, “Hardware-efficient DFT Designs with Cyclic Convolution and Sub-expression Sharing,” IEEE Trans. on Circuits Syst. II, vol. 47, 2000, pp. 886–892.

    Article  Google Scholar 

  31. C.M. Rader, “Discrete Fourier Transforms when the Number of Data Samples is Prime,” in Proc. IEEE, vol. 56, 1968, pp. 1107–1108.

    Article  Google Scholar 

  32. C.S. Burrus, “Efficient Fourier Transform and Convolution Algorithm,” in Advanced Topic in Signal Processing, J.S. Lim and A.V. Oppenheim, Eds. Englewood Cliffs, NJ: Prentice-Hall, 1988, pp. 199–215.

    Google Scholar 

  33. M.T. Heideman, C.S. Burrus and H.W. Johnson, “Prime factor FFT algorithms for real-valued series,” in Proc. IEEE ICASSP, 84, pp. 28A.7.1–28A.7.4.

  34. J.G. Proakis, C.M. Rader, F.Y. Ling, C.L. Nikias, M.Moonen and L.K. Proudler, Algorithm for Statistical Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 2001.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, University of Hong Kong, Pokfulam Road, Hong Kong

    S. C. Chan & X. M. Xie

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  1. S. C. Chan
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  2. X. M. Xie
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Correspondence to S. C. Chan.

Additional information

S. C. Chan received his B.Sc. (Eng) and Ph.D. degrees in electrical engineering from the University of Hong Kong, Hong Kong, in 1986 and 1992, respectively. He joined City Polytechnic of Hong Kong in 1990 as an assistant Lecturer and later as a University Lecturer. Since 1994, he has been with the department of electrical and electronic engineering, the University of Hong Kong, Hong Kong, and is now an associate Professor. He was a visiting researcher in Microsoft Corporation, Redmond, USA and Microsoft China at 1998 and 1999, respectively. Dr. Chan is currently a member of the Digital Signal Processing Technical Committee of the IEEE Circuits and Systems Society. He was Chairman of the IEEE Hong Kong Chapter of Signal Processing from 2000 to 2002. His research interests include fast transform algorithms, filter design and realization, multirate signal processing, communications signal processing, and image-based rendering.

X. M. Xie received the M.S. degree in electronic engineering from Xidian University in 1996, and the Ph.D degree in electrical & electronic engineering from the University of Hong Kong in 2004. She is now with the school of electronic engineering, Xidian University. Her research interests are in digital signal processing, multirate filter bank and wavelet transform.

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Chan, S.C., Xie, X.M. Biorthogonal Recombination Nonuniform Cosine-Modulated Filter Banks and their Multiplier-Less Realizations. J VLSI Sign Process Syst Sign Image Video Technol 44, 5–23 (2006). https://doi.org/10.1007/s11265-005-4175-8

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  • DOI: https://doi.org/10.1007/s11265-005-4175-8

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