Advertisement

Analog Integrated Circuits and Signal Processing

, Volume 77, Issue 2, pp 113–122 | Cite as

Efficient signal reconstruction scheme for M-channel time-interleaved ADCs

  • Anu Kalidas Muralidharan Pillai
  • Håkan Johansson
Article

Abstract

In time-interleaved analog-to-digital converters (TI-ADCs), the timing mismatches between the channels result in a periodically nonuniformly sampled sequence at the output. Such nonuniformly sampled output limits the achievable resolution of the TI-ADC. In order to correct the errors due to timing mismatches, the output of the TI-ADC is passed through a digital time-varying finite-length impulse response reconstructor. Such reconstructors convert the nonuniformly sampled output sequence to a uniformly spaced output. Since the reconstructor runs at the output rate of the TI-ADC, it is beneficial to reduce the number of coefficient multipliers in the reconstructor. Also, it is advantageous to have as few coefficient updates as possible when the timing errors change. Reconstructors that reduce the number of multipliers to be updated online do so at a cost of increased number of multiplications per corrected output sample. This paper proposes a technique which can be used to reduce the number of reconstructor coefficients that need to be updated online without increasing the number of multiplications per corrected output sample.

Keywords

Finite-length impulse response (FIR) filters Least-squares design Two-rate approach Periodically nonuniform sampling Time-interleaved analog-to-digital converters (TI-ADCs) Reconstruction filters 

Notes

Acknowledgments

This work was supported by the Swedish Research Council.

References

  1. 1.
    Black, W. C., & Hodges, D. A. (1980). Time interleaved converter arrays. IEEE Journal of Solid-State Circuits, 15(6), 1022–1029.CrossRefGoogle Scholar
  2. 2.
    El-Chammas, M., & Murmann, B. (2011). A 12-GS/s 81-mW 5-bit time-interleaved flash ADC with background timing skew calibration. EEE Journal of Solid-State Circuits, 46(4), 838–847.CrossRefGoogle Scholar
  3. 3.
    Vogel, C. (2005). The impact of combined channel mismatch effects in time-interleaved ADCs. IEEE Transactions on Instrumentation and Measurement, 54(1), 415–427.CrossRefGoogle Scholar
  4. 4.
    Kopmannm, H., & Göckler, H. G. (2004). Error analysis of ultra-wideband hybrid analogue-to-digital conversion. In Proceedings of the XII European Signal Processing Conference (EUSIPCO) (pp. 6–10). Austria: Vienna.Google Scholar
  5. 5.
    Tsui, K. M., & Chan, S. C. (2011). New iterative framework for frequency response mismatch correction in time-interleaved ADCs: Design and performance analysis. IIEEE Transactions on Instrumentation and Measurement, 60(12), 3792–3805.CrossRefGoogle Scholar
  6. 6.
    Vogel, C., & Mendel, S. (2009). A flexible and scalable structure to compensate frequency response mismatches in time-interleaved ADCs. IEEE Journal of Solid-State Circuits, 56(11), 2463–2475.MathSciNetGoogle Scholar
  7. 7.
    Johansson, H. (2009). A polynomial-based time-varying filter structure for the compensation of frequency-response mismatch errors in time-interleaved ADCs. IEEE Journal of Solid-State Circuits, 3(3), 384–396.Google Scholar
  8. 8.
    Saleem S., & Vogel, C. (2011). Adaptive blind background calibration of polynomial-represented frequency response mismatches in a two-channel time-interleaved ADC. IEEE Transactions on Circuits and Systems, 58(6), 1300–1310.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Marvasti, F. (Ed.). (2001). Nonuniform sampling: Theory and practice. Newyork, NY: Kluwer Academic.Google Scholar
  10. 10.
    Selva, J. (2009). Functionally weighted lagrange interpolation of band-limited signals from nonuniform samples. IEEE Transactions on Signal Processing, 57(1), 168–181.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Strohmer, T., & Tanner, J. (2007). Fast reconstruction algorithms for periodic nonuniform sampling with applications to time-interleaved ADCs. In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2007, vol. 3.Google Scholar
  12. 12.
    Margolis, E., & Eldar, Y. C. (2008). Nonuniform sampling of periodic bandlimited signals. IEEE Transactions on Signal Processing, 56(7), 2728–2745.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Johansson, H., & Löwenborg, P. (2006). Reconstruction of nonuniformly sampled bandlimited signals by means of time-varying discrete-time FIR filters. EURASIP Journal of Advances Signal Process, 2006, 064185.Google Scholar
  14. 14.
    Pillai, A. K. M., & Johansson, H.: Two-rate based low-complexity time-varying discrete-time FIR reconstructors for two-periodic nonuniformly sampled signals. Sampling Theory in Signal and Image Processing—Special Issue on SampTA 2011 accepted.Google Scholar
  15. 15.
    Johansson, H., Löwenborg, P., & Vengattaramane, P. (2007). Least-squares and minimax design of polynomial impulse response FIR filters for reconstruction of two-periodic nonuniformly sampled signals. IEEE Transactions on Circuits and Systems, 54(4), 877–888.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Tertinek, S., & Vogel, C. (2008). Reconstruction of nonuniformly sampled bandlimited signals using a differentiator–multiplier cascade. IEEE Transactions on Circuits and Systems, 55(8), 2273–2286.MathSciNetGoogle Scholar
  17. 17.
    Pillai, A. K. M., & Johansson, H. (2013). Low-complexity two-rate based multivariate impulse response reconstructor for time-skew error correction in M-channel time-interleaved ADCs. In Proceedings of the International Symposium on Circuits and Systems ISCAS.Google Scholar
  18. 18.
    Johansson, H., Löwenborg, P., & Vengattaramane, K. (2006). Reconstruction of M-periodic nonuniformly sampled signals using multivariate impulse response time-varying FIR filters. In Proceedings of the XII European Signal Processing Conference.Google Scholar
  19. 19.
    Pillai, A. K. M., & Johansson, H. (2012). Efficient signal reconstruction scheme for time-interleaved ADCs. In Proceedings of the IEEE 10th International New Circuits and Systems Conference (NEWCAS) (pp. 357–360).Google Scholar
  20. 20.
    Renfors, M., & Neuvo, Y. (1981). The maximum sampling rate of digital filters under hardware speed constraints. IEEE Transactions on Circuits and Systems, 28(3), 196–202.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Fettweis, A. (1990). On assessing robustness of recursive digital filters. European Transactions on Telecommunications Related Technologies, 1(2), 103–109.CrossRefGoogle Scholar
  22. 22.
    Seo, M., Rodwell, M., & Madhow, U. (2007). Generalized blind mismatch correction for two-channel time-interleaved a-to-d converters. In Proceedings of IEEE International Conference Acoustics, Speech and Signal Processing ICASSP 2007, vol. 3.Google Scholar
  23. 23.
    Vaidyanathan, P. P. (1993). Multirate systems and Fflter banks. Englewood Cliffs, NJ, USA: Prentice-Hall.MATHGoogle Scholar
  24. 24.
    Murphy, N. P., Krukowski, A., & Kale, I. (1994). Implementation of wideband integer and fractional delay element. Electronics Letters, 30(20), 1658–1659.CrossRefGoogle Scholar
  25. 25.
    Johansson, H., & Hermanowicz, E. (2013). Two-rate based low-complexity variable fractional-delay FIR filter structures. IEEE Transactions on Circuits and Systems, 60(1), 136–149.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Saramäki, T. (1993). Finite impulse response filter design. In A. Mitra & S. Kaiser (Eds.), Handbook for digital signal processing (pp. 155–277). Newyork: Wiley.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Anu Kalidas Muralidharan Pillai
    • 1
  • Håkan Johansson
    • 1
  1. 1.Division of Electronics Systems, Department of Electrical EngineeringLinköping UniversityLinköpingSweden

Personalised recommendations