Skip to main content

Advertisement

Springer Nature Link
Log in

An Improved Lattice Filter Structure with Minimum Roundoff Noise Gain

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Trivial parameters are defined as that are 0 and \(\pm 1\). Other parameters are, therefore, referred to as nontrivial parameters.

References

  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)

    Article  MathSciNet  Google Scholar 

  2. M. Gevers, G. Li, Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects. Communication and Control Engineering Series (Springer, London, 1993)

    Book  MATH  Google Scholar 

  3. A.H. Gray Jr, J.D. Markrl, Digital lattice and ladder filter synthesis. IEEE Trans. Audio Electroacoust. 21, 491–500 (1973)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  7. S.Y. Hwang, Minimum uncorrelated unit noise in state-space digital filtering. IEEE Trans. Acoust. Speech Signal Process. ASSP 25, 273–281 (1977)

    Article  MATH  Google Scholar 

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  12. G. Li, Y.C. Lim, C.G. Huang, Very robust low complexity lattice filters. IEEE Trans. Signal Process. 58(12), 6093–6104 (2010)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  19. R.A. Roberts, C.T. Mullis, Digital Signal Processing (Addison Wesley, Reading, MA, 1987)

    MATH  Google Scholar 

  20. P.P. Vaidyanathan, On error-spectrum shaping in state-space digital filters. IEEE Trans. Circuits Syst. 32, 88–92 (1985)

    Article  Google Scholar 

  21. D. Williamson, Delay replacement in direct form structures. IEEE Trans. Acoust. Speech Signal Process. 36, 453–460 (1988)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. School of Information, Zhejiang University of Finance and Economics, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Chao-Geng Huang, Hou-Qi Zhang & Jian Lin

  2. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, Zhejiang, People’s Republic of China

    Hong Xu & Xiong-Xiong He

Authors
  1. Chao-Geng Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hou-Qi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiong-Xiong He
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jian Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chao-Geng Huang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, CG., Zhang, HQ., Xu, H. et al. An Improved Lattice Filter Structure with Minimum Roundoff Noise Gain. Circuits Syst Signal Process 35, 4170–4182 (2016). https://doi.org/10.1007/s00034-016-0247-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-016-0247-1

Keywords