Algorithms for Accurate Spectral Analysis in the Presence of Arbitrary Non-coherency and Large Distortion

  • Yuming Zhuang
  • Degang Chen


In spectral analysis, achieving coherent sampling, especially when signals have large distortion, has been a challenge for many years. This chapter introduces three algorithms to resolve this issue. In comparison to previous algorithms, and two widely used methods in industry (windowing and four-parameter sine wave fit), these new algorithms are capable of obtaining accurate spectral results of the signal while achieving high accuracy and computational efficiency. The novel contribution of this chapter is not only the proposal of three new algorithms but also the analysis of their advantages and limitations in detail, providing their trade-offs and different fields of applications. Extensive simulations and measurements were performed to validate these algorithms. Combined with the high accuracy, computational efficiency, and robustness of these algorithms against signal purity, they are readily available to be implemented for bench or on-chip testing. In addition, it is suitable for data converter spectral testing when non-coherent sampling is present and spectrally pure test signal source is not available.


  1. 1.
    Y. Zhuang, D. Chen, Algorithms for accurate spectral analysis in the presence of arbitrary noncoherency and large distortion. IEEE Trans. Instrum. Meas. 66(10), 2556–2565 (2017)CrossRefGoogle Scholar
  2. 2.
    Y. Zhuang, D. Chen, Accurate spectral testing with non-coherent sampling for large distortion to noise ratios,” in Proc. IEEE 34th VLSI Test Symp. (VTS) (2016), pp. 1–6.Google Scholar
  3. 3.
    Y. Zhuang, D. Chen, New strategies in removing non-coherency from signals with large distortion to noise ratios, in Proc. IEEE Int. Symp. Circuits Syst., (2016), p. 2901.Google Scholar
  4. 4.
    Y. Zhuang, D. Chen, New strategies in removing non-coherency from signals with large distortion to noise ratios. IEEE Trans. on Circ. and Syst. II: Express Brief 63(12), 1136–1140 (2016)Google Scholar
  5. 5.
    J.L. Huertas, Test and Design-for-Testability in Mixed-Signal Integrated Circuits (Springer, New York, 2004)CrossRefGoogle Scholar
  6. 6.
    P. Stoica, R. Moses, Spectral Analysis of Signals (Prentice-Hall, Englewood Cliffs, 2005)Google Scholar
  7. 7.
    M. Burns, G.W. Roberts, An Introduction to Mixed-Signal IC Test and Measurement (Oxford Univ. Press, New York, 2012)Google Scholar
  8. 8.
    P. Stoica, R.L. Moses, Spectral Analysis of Signals (Prentice-Hall, Englewood Cliffs, 2011)Google Scholar
  9. 9.
    S.M. Alessio, Digital Signal Processing and Spectral Analysis for Scientists: Concepts and Applications (Springer, Cham, 2016)CrossRefzbMATHGoogle Scholar
  10. 10.
    IEEE standard for terminology and test methods for analg-to-digital converters, IEEE Std. 1241, (2010).Google Scholar
  11. 11.
    IEEE standard for terminology and test methods of digital-to-analog converter devices, IEEE Std.1658, (2011)Google Scholar
  12. 12.
    IEEE standard for digitizing waveform recorders, IEEE Std.1057, (2007)Google Scholar
  13. 13.
    B. Razavi, RF Microelectronics (Prentice-Hall, Englewood Cliffs, 2012)Google Scholar
  14. 14.
    F.J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66(1), 51–83 (1978)CrossRefGoogle Scholar
  15. 15.
    M. Bertocco, P. Carbone, E. Nunzi, D. Petri, Windows for ADC dynamic testing via frequency-domain analysis. IEEE Trans. Instrum. Meas. 50(6), 1571–1576 (2000)Google Scholar
  16. 16.
    S. Raze, D. Dallet, P. Marchegay, Non coherent spectral analysis of ADC using FFT windows: An alternative approach, in Proc. IEEE Workshop Intell. Data Acquisition Adv. Comput. Syst. (2005), pp. 474–478.Google Scholar
  17. 17.
    T.Z. Bilau, T. Megyeri, A. Sárhegyi, J. Márkus, I. Kollár, Four parameter fitting of sine wave testing result: Iteration and convergence. Comput. Stand. Interfaces 26(1), 51–56 (2004)CrossRefGoogle Scholar
  18. 18.
    K.F. Chen, Estimating parameters of a sine wave by separable nonlinear least squares fitting. IEEE Trans. Instrum. Meas. 59(12), 3214–3217 (2010)CrossRefGoogle Scholar
  19. 19.
    P. Handel, Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm. IEEE Trans. Instrum. Meas. 49(6), 1189–1193 (2000)CrossRefGoogle Scholar
  20. 20.
    G. Simon, R. Pintelon, L. Sujbert, J. Schoukens, An efficient nonlinear least square multisine fitting algorithm. IEEE Trans. Instrum. Meas. 51(4), 750–755 (2002)CrossRefGoogle Scholar
  21. 21.
    V. Palfi, I. Kollar, Acceleration of the ADC test with sine-wave fit. IEEE Trans. Instrum. Meas. 62(5), 880–888 (2013)CrossRefGoogle Scholar
  22. 22.
    D.K. Mishra, ADC testing using interpolated fast Fourier transform (IFFT) technique. Int. J. Electron. 90(7), 459–469 (2003)CrossRefGoogle Scholar
  23. 23.
    J. Schoukens, R. Pintelon, H. Van Hamme, The interpolated fast Fourier transform: A comparative study. IEEE Trans. Instrum. Meas. 41(2), 226–232 (1992)CrossRefGoogle Scholar
  24. 24.
    D. Belega, D. Dallet, Multipoint interpolated DFT method for frequency estimation. Proc. Int. Multi-Conf. Syst. Signals Devices, 1–6 (2009)Google Scholar
  25. 25.
    D. Belega, D. Dallet, D. Petri, Estimation of the effective number of bits of ADCs using the interpolated DFT method, in Proc. IEEE Instrum. Meas. Technol. Conf. (2010), pp. 30–35Google Scholar
  26. 26.
    D. Belega, D. Dallet, D. Stoiciu, Choice of the window used in the interpolated discrete Fourier transform method. Revue Roumaine Sci. Techn. Serie Electrotechn. Energetique 54(4), 365–374 (2009)Google Scholar
  27. 27.
    X.M. Gao, S.J. Ovaska, S. Shenghe, Y.C. Jenq, Analysis of second-order harmonic distortion of ADC using bispectrum. IEEE Trans. Instrum. Meas. 45(1), 50–55 (1996)CrossRefGoogle Scholar
  28. 28.
    C. Rebai, D. Dallet, P. Marchegay, Noncoherent spectral analysis of ADC using filter Bank. IEEE Trans. Instrum. Meas. 53(3), 652–660 (2004)CrossRefGoogle Scholar
  29. 29.
    A.R. Varkonyi-Koczy, G. Simon, L. Sujbert, M. Fek, A fast filter bank for adaptive Fourier analysis. IEEE Trans. Instrum. Meas. 47(5), 1124–1128 (1998)CrossRefGoogle Scholar
  30. 30.
    S. Sudani, C. Degang, G. Randy, A 2-FFT method for on chip spectral testing without requiring coherency, in Proc. IEEE Int. Instrum. Meas. Technol. Conf., Hangzhou, China 2011, pp. 1–6.Google Scholar
  31. 31.
    S. Sudani, M. Wu, D. Chen, A novel robust and accurate spectral testing method for non-coherent sampling, in Proc. Int. Test Conf. (2011), pp. 1–10.Google Scholar
  32. 32.
    S. Sudani, D. Chen, FIRE: A fundamental identification and replacement method for accurate spectral test without requiring coherency. IEEE Trans. Instrum. Meas. 62(11), 15–25 (2013)CrossRefGoogle Scholar
  33. 33.
    A. Bergamin, G. Cavagnero, G. Mana, Accuracy assessment of a least-squares estimator for scanning X-ray interferometry. Meas. Sci. Technol. 2(8), 725–734 (1991)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Yuming Zhuang
    • 1
  • Degang Chen
    • 2
  1. 1.Qualcomm IncSan DiegoUSA
  2. 2.Iowa State UniversityAmesUSA

Personalised recommendations