Circuits, Systems, and Signal Processing

, Volume 35, Issue 11, pp 4170–4182 | Cite as

An Improved Lattice Filter Structure with Minimum Roundoff Noise Gain

  • Chao-Geng Huang
  • Hou-Qi Zhang
  • Hong Xu
  • Xiong-Xiong He
  • Jian Lin
Short Paper
First Online:
Received:
Revised:
Accepted:
  • 136 Downloads

Abstract

In this paper, a new filter structure is derived by combining the lattice structure and error feedback technique, which contains a free parameter used for structure optimization. The roundoff noise of the proposed structure is analyzed, and the corresponding mathematical expression is deduced. The problem of how to optimize the free parameter is investigated in terms of minimizing the roundoff noise gain. When the free parameter is expressed as an integer power-of-two, for an Nth-order digital filter, the proposed structure requires \(5N+1\) multipliers, which yields the same implementation complexity as the normalized lattice structure. A numerical example is given to show the finite wordlength performance of the proposed structure.

Keywords

Lattice filters Digital filter structures Roundoff noise gain Error feedback Finite wordlength 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

This work was supported by the NSFC Grants 61503330, 61503331, 61273195 and 61473262, ZJNSF Grant LQ14F030008, Zhejiang Key Laboratory for Signal Processing and Zhejiang Hua Yue Institute of Information and Data Processing.

References

  1. 1.
    L. Chai, J.X. Zhang, Y.X. Sheng, Optimal design of oversampled synthesis FBs with lattice structure constraints. IEEE Trans. Signal Process. 59(8), 3549–3559 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    M. Gevers, G. Li, Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects. Communication and Control Engineering Series (Springer, London, 1993)CrossRefMATHGoogle Scholar
  3. 3.
    A.H. Gray Jr, J.D. Markrl, Digital lattice and ladder filter synthesis. IEEE Trans. Audio Electroacoust. 21, 491–500 (1973)CrossRefGoogle Scholar
  4. 4.
    T. Hinamoto, A. Doi, W.-S. Lu, Jointly optimal high-order error feedback and realization for roundoff noise minimization in 1-D and 2-D state-space digital filters. IEEE Trans. Signal Process. 61(23), 5893–5904 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    C.G. Huang, G. Li, Z.X. Xu, A.H. Yu, L.P. Chang, Design of optimal digital lattice filter structures based on genetic algorithm. Signal Process. 92(4), 989–998 (2012)CrossRefGoogle Scholar
  6. 6.
    C.G. Huang, Y.C. Lim, G. Li, A generalized lattice filter for finite wordlength implementation with reduced number of multipliers. IEEE Trans. Signal Process. 62(8), 2080–2089 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    S.Y. Hwang, Minimum uncorrelated unit noise in state-space digital filtering. IEEE Trans. Acoust. Speech Signal Process. ASSP 25, 273–281 (1977)CrossRefMATHGoogle Scholar
  8. 8.
    F. Itakura, S. Saito, Digital filtering techniques for speech analysis and synthesis. in 7th International Congress on Acoustics, Budapest Hungary 3, 261–264 (1971)Google Scholar
  9. 9.
    G. Li, M. Gevers, Comparative study of finite wordlength effects in shift and delta operator parameterizations. IEEE Trans. Automat. Contr. 38, 803–807 (1993)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    G. Li, M. Gevers, Y.X. Sun, Performance analysis of a new structure for digital filter implementation. IEEE Trans. Circuits Syst. I 47(4), 474–482 (2000)CrossRefGoogle Scholar
  11. 11.
    G. Li, J.Y. Hua, G.A. Bi, An efficient and robust orthogonal structure for linear discrete-time systems. J. Circuits Syst. Signal Process. 29(4), 727–743 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    G. Li, Y.C. Lim, C.G. Huang, Very robust low complexity lattice filters. IEEE Trans. Signal Process. 58(12), 6093–6104 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    G. Li, C. Wan, G. Bi, An improved \(\rho \)DFIIt structure for digital filters with minimum roundoff noise. IEEE Trans. Circuits Syst II Express Br. 52(4), 199–203 (2005)CrossRefGoogle Scholar
  14. 14.
    G. Li, Z. Zhao, On the generalized DFIIt structure and its statespace realization in digital filter implementation. IEEE Trans. Circuits Syst. I 51(4), 769–778 (2004)CrossRefGoogle Scholar
  15. 15.
    Y.C. Lim, On the synthesis of IIR digital filters derived from single channel AR lattice network. IEEE Trans. Acoust. Speech Signal Process. ASSP 32(4), 741–749 (1984)CrossRefGoogle Scholar
  16. 16.
    W.-S. Lu, T. Hinamoto, Jointly optimized error-feedback and realization for roundoff noise minimization in state-space digital filters. IEEE Trans. Signal Process. 53(6), 2135–2145 (2005)MathSciNetCrossRefGoogle Scholar
  17. 17.
    J.D. Markrl, A.H. Gray Jr, Fixed-point implementation algorithms for a class of orthogonal polynomial filter structures. IEEE Trans. Acoust. Speech Signal Process. ASSP 23(5), 486–494 (1975)CrossRefGoogle Scholar
  18. 18.
    C.T. Mullis, R.A. Roberts, Synthesis of minimum roundoff noise fixed-point digital filters. IEEE Trans. Circuits Syst. CAS 23, 551–562 (1976)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    R.A. Roberts, C.T. Mullis, Digital Signal Processing (Addison Wesley, Reading, MA, 1987)MATHGoogle Scholar
  20. 20.
    P.P. Vaidyanathan, On error-spectrum shaping in state-space digital filters. IEEE Trans. Circuits Syst. 32, 88–92 (1985)CrossRefGoogle Scholar
  21. 21.
    D. Williamson, Delay replacement in direct form structures. IEEE Trans. Acoust. Speech Signal Process. 36, 453–460 (1988)CrossRefMATHGoogle Scholar
  22. 22.
    N. Wong, T.S. Ng, A generalized direct-form delta operator-based IIR filter with minimum noise gain and sensitivity. IEEE Trans. Circuits Syst. II 48(4), 425–431 (2001)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Chao-Geng Huang
    • 1
  • Hou-Qi Zhang
    • 1
  • Hong Xu
    • 2
  • Xiong-Xiong He
    • 2
  • Jian Lin
    • 1
  1. 1.School of InformationZhejiang University of Finance and EconomicsHangzhouPeople’s Republic of China
  2. 2.College of Information EngineeringZhejiang University of TechnologyHangzhouPeople’s Republic of China

Personalised recommendations