Circuits, Systems, and Signal Processing

, Volume 38, Issue 5, pp 2165–2186 | Cite as

Analysis, Design, and Order Estimation of Least-Squares FIR Equalizers for Bandwidth Extension of ADCs

  • Yinan WangEmail author
  • Håkan Johansson
  • Nan Li
  • Qingjiang Li


In modern mixed-signal systems, it is important to build the conversion components with a flat frequency response over their full Nyquist frequency band. However, with increasing circuit speed, it is becoming more difficult to achieve this, due to limitations of the analog front-end circuits. This paper considers finite-length impulse-response (FIR) filters, designed in the least-squares sense, for the bandwidth extension of analog-to-digital converters, which is one of the most important applications in frequency response equalization. The main contributions of this paper are as follows: Firstly, based on extensive simulations, filter order-estimation expressions of the least-squares designed equalizers are derived. It appears to be the first time that order-estimation expressions are presented for any least-squares designed FIR filter. These expressions accurately estimate the order required for given specifications on the targeted extended bandwidth systems. Secondly, based on the derived order-estimation expressions, systematic design procedures are presented, which contribute to reducing the design time. Finally, a relation between the dynamic-range degradation and the system parameters is also derived and verified in the paper.


ADC Bandwidth extension FIR filter Frequency response equalization Filter order estimation Least-squares design 



This work was supported by the National Natural Science Foundation of China (Nos. 61701509 and 61704191).


  1. 1.
    J. Hancock, Advantages and disadvantages of using DSP filtering on oscilloscope waveforms. Application Note 1494, Agilent Technologies (2004),
  2. 2.
    S.C. Chapra, R.P. Canale, Numerical Methods for Engineers (McGraw-Hill, Maidenherd, 2012)Google Scholar
  3. 3.
    S. Dhabu, A.P. Vinod, A new time-domain approach for the design of variable FIR filters using the spectral parameter approximation technique. Circuits Syst. Signal Process. 36(5), 2154–2165 (2017)CrossRefGoogle Scholar
  4. 4.
    Z. Hao, Y. Peng, Research on analog bandwidth enhancement technology for digital storage oscilloscope. in Proceedings of IEEE International Conference on Electronic Measurement and Instruments (2011), pp. 217–220Google Scholar
  5. 5.
    L. Hars, Frequency response compensation with DSP. IEEE Signal Process. Mag. 20(4), 91–95 (2003)CrossRefGoogle Scholar
  6. 6.
    X. Huang, Y. Wang, Z. Yan, H. Xian, M. Liu, Closed-form FIR filter design with accurately controllable cut-off frequency. Circuits Syst. Signal Process. 36(2), 721–741 (2017)CrossRefzbMATHGoogle Scholar
  7. 7.
    K. Ichige, M. Iwaki, R. Ishii, Accurate estimation of minimum filter length for optimum FIR digital filters. IEEE Trans. Circuits Syst. II 47(10), 1008–1016 (2000)CrossRefGoogle Scholar
  8. 8.
    H. Johansson, P. Löwenborg, A least-squares filter design technique for the compensation of frequency-response mismatch errors in time-interleaved A/D converters. IEEE Trans. Circuits Syst. II: Express Briefs 55(11), 1154–1158 (2008)CrossRefGoogle Scholar
  9. 9.
    W.J. Kenneth, Digital Signal Processing (DSP) in Oscilloscopes. Application Note (LeCroy Corporation, New York, 2010)Google Scholar
  10. 10.
    N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, K. Kobayashi, Explicit analysis of channel mismatch effects in time-interleaved ADC systems. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 48, 261–271 (2001)CrossRefGoogle Scholar
  11. 11.
    W.R. Lee, L. Caccetta, K.L. Teo, V. Rehbock, A unified approach to multistage frequency-response masking filter design using the WLS technique. IEEE Trans. Signal process. 54(9), 3459–3467 (2006)CrossRefzbMATHGoogle Scholar
  12. 12.
    S.M. Louwsma, A.J.M. Van Tuijl, M. Vertregt, B. Nauta, A 1.35 GS/s, 10 b, 175 mw time-interleaved AD converter in 0.13 \(\mu \)m CMOS. IEEE J. Solid-State Circuits 43(4), 778–786 (2008)CrossRefGoogle Scholar
  13. 13.
    B. Murmann, C. Vogel, H. Koeppl, Digitally enhanced analog circuits: system aspects. in Proceedings of IEEE International Symposium on Circuits and Systems (2008), pp. 560–563Google Scholar
  14. 14.
    A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing (Prentice Hall, Englewood Cliffs, 1989)zbMATHGoogle Scholar
  15. 15.
    J.J. Pickerd, DSP in high performance oscilloscopes. TektronixTM White Paper (2005)Google Scholar
  16. 16.
    L. Rabiner, J. McClellan, T. Parks, FIR digital filter design technique using weighted-Chebyshev approximation. IEEE Proc. 63(4), 595–610 (1975)CrossRefGoogle Scholar
  17. 17.
    Z.U. Sheikh, H. Johansson, A class of wide-band linear-phase FIR differentiators using a two-rate approach and the frequency-response masking technique. IEEE Trans. Circuits Syst. I: Reg. Pap. 58(8), 1827–1839 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Z.U. Sheikh, A. Eghbali, H. Johansson, Linear-phase FIR digital differentiator order estimation. in Proceedings of European Conference on Circuit Theory and Design (Linköping, Sweden, 2011), pp. 29–31Google Scholar
  19. 19.
    J.-J. Shyu, S.-C. Pei, C.-H. Chan, Y.-D. Huang, Minimax design of variable fractional-delay FIR digital filters by iterative weighted least-squares approach. IEEE Signal Process. Lett. 15, 693–696 (2008)CrossRefGoogle Scholar
  20. 20.
    P.P. Vaidyanathan, S.-M. Phoong, Y.-P. Lin, Signal Processing and Optimization for Transceiver Systems (Cambridge University Press, Cambridge, 2010)CrossRefzbMATHGoogle Scholar
  21. 21.
    R.J. Van de Plassche, CMOS Integrated Analog-to-Digital and Digital-to-Analog Converters (Kluwer Academic Publishers, Dordrecht, 2003)CrossRefzbMATHGoogle Scholar
  22. 22.
    Y. Wang, H. Johansson, H. Xu, J. Diao, Minimax design and order estimation of FIR filters for bandwidth extension of ADCs. in Proceedings of IEEE International Symposium on Circuits and Systems (2016), pp. 2186–2189Google Scholar
  23. 23.
    L. Wanhammar, H. Johansson, Digital Filters Using Matlab (Linköping University, Linköping, 2011)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Yinan Wang
    • 1
    Email author
  • Håkan Johansson
    • 2
  • Nan Li
    • 1
  • Qingjiang Li
    • 1
  1. 1.College of Electronic Science and EngineeringNational University of Defense TechnologyChangshaChina
  2. 2.Division of Communication Systems, Department of Electrical EngineeringLinköping UniversityLinköpingSweden

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