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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

A Discrete Fourier Transform Based Dithering Signal Generation Method for Reduced Quantization Error

Journal of Vibration Testing and System Dynamics 2(1) (2018) 43--51 | DOI:10.5890/JVTSD.2018.03.005

Chang-Qing Ye, Xing-Zhong Xiong

Artificial Intelligence Key Laboratory of Sichuan Province, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China

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Abstract

Addressing the impact of quantization error in analog-to-digital converter (ADC) for signal processing, a Discrete Fourier Transform (DFT) based method for the generation of dithering signals is presented. Effective in reducing quantization error, the dithering signal generated using the method is not only independent of the input signal but also can improve the performance of the ADC. To illustrate the advantages of the dithering signal reconstructed using the method, three kinds of typical dithering effects, namely, Triangular Distribution Dithering, Gaussian Distribution Dithering and Uniform Distribution Dithering on the quantization error in an ADC are considered. The properties of three practical dithering signals are investigated. It is shown that while these typical dithering may be useful they are some potential problems. The dithering signals reconstructed using the DFT based generation scheme is shown to contribute significantly to reducing quantization error. Numerical experiments and theoretical analyses demonstrate that the DFT based dithering reconstruction can obtain prominent performance for ADC in comparison to typical dithering signals.

Acknowledgments

This work was supported by the Innovation Group Building Plan of Sichuan (No. 2015TD0022), Project of Talents of Sichuan University of Science and Engineering (No. 2014RC13), Initiation Project of Artificial Intelligence Key Laboratory of Sichuan Province (2017WZJ01), Initiation Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things (2017WZJ01), and Sichuan University of Science and Engineering Project of Talent Introduction (2017RCL11).

References

  1. [1]  Goodall, W.M. (1951), Television by pulse code modulation, Bell System Technical Journal, 30(1), 33-49.
  2. [2]  Roberts, L.G. (1962), Picture coding using pseudo-random noise, IRE Transactions on Information Theory, 8(2), 145-154.
  3. [3]  Widrow, B. (2012) Analysis of amplitude-quantized sampled-data systems, Transactions of the American Institute of Electrical Engineers, Part II Applications & Industry, 80(6), 450-450.
  4. [4]  Schuchman, L. (2003), Dither signals and their effect on quantization noise, IEEE Transactions on Communication Technology, 12(4), 162-165.
  5. [5]  Candy, J. and Temes, G. (2009), Reduction of quantizing noise by use of feedback, IRE Transactions on Communications Systems, 131-138.
  6. [6]  Blesser, B. (1974), An investigation of quantization noise, Journal of the Audio Engineering Society, 22(1), 20-22.
  7. [7]  Blesser, B. (1978), Digitization of audio: a comprehensive examination of theory, implementation and current practice, Journal of the Audio Engineering Society, 26(10), 739-771.
  8. [8]  Lipshitz, S.P., Pocock, M., and Vanderkooy, J. (1982), On the audibility of midrange phase distortion in audio systems, Journal of the Audio Engineering Society, 30(9), 580-595.
  9. [9]  Blesser, B.A. and Locanthi, B.N. (1986), Application of narrow-band dither operating at the nyquist frequency in digital systems to provide improved signal-to-noise ratio over conventional dithering, Journal of the Audio Engineering Society, 34(12), 446-454.
  10. [10]  Wagdy, M.F. (2002), Effect of various dither forms on quantization errors of ideal a/d converters, IEEE Transactions on Instrumentation & Measurement, 38(4), 850-855.
  11. [11]  Gray, R.M. (1990), Quantization noise spectra, IEEE Transactions on Information Theory, 36(6), 1220-1244.
  12. [12]  Gray, R.M. and Stockham, T.G.J. (1991), Dithered quantizers, IEEE Transactions on Information Theory, 39, 22-22.
  13. [13]  Carbone, P. and Petri, D. (1994), Effect of additive dither on the resolution of ideal quantizers, IEEE Transactions on Instrumentation & Measurement, 43(3), 389-396.
  14. [14]  Zames, G. and Shneydor, N. (1976), Dither in nonlinear systems, IEEE Transactions on Automatic Control, 21(5), 660-667.
  15. [15]  Wagdy, M.F. (1995), Effect of additive dither on the resolution of ADCs with single-bit or multi-bit errors, Instrumentation and Measurement Technology Conference, 1995. IMTC/95. IEEE Proceedings on Integrating Intelligent Instrumentation and Control, 45(2), 610-615.
  16. [16]  Carbone, P. (1997), Quantitative Criteria for the design of dithered-based quantizing systems, IEEE Transactions on Instrumentation and Measurement, 46, 656-659.
  17. [17]  Li, F., Duan, J., and Zhihua, A.W. (2008), A high linearity,13bit pipelined cmos adc, Journal of Semiconductors, 29(3), 487-501.
  18. [18]  Nair, K. (2004), A 96 dB SFDR 50 MS/s digitally enhanced CMOS pipeline A/D converter, Solid-State Circuits Conference, 2004. Digest of Technical Papers. ISSCC. 2004 IEEE International 1, 456-457.
  19. [19]  Siragusa, E. and Galton, I. (2004), A digitally enhanced 1.8-v 15-bit 40-msample/s cmos pipelined adc, IEEE Journal of Solid-State Circuits, 39(12), 2126-2138.
  20. [20]  Liu, H.C., Lee, Z.M., and Wu, J.T. (2005), A 15-b 40-ms/s cmos pipelined analog-to-digital converter with digital background calibration, IEEE Journal of Solid-State Circuits, 40(5), 1047-1056.
  21. [21]  Balestrieri, E., Daponte, P., and Rapuano, S. (2005) A state of the art on adc error compensation methods, IEEE Transactions on Instrumentation & Measurement, 54(4), 1388-1394.
  22. [22]  Bogner, P., Kuttner, F., Kropf, C., and Hartig, T. (2006), A 14b 100MS/s digitally self-calibrated pipelined ADC in 0.13/spl mu/m CMOS. Solid-State Circuits Conference, 2006. ISSCC 2006. Digest of Technical Papers, IEEE International, 832-841.
  23. [23]  Tatsuo, K., Birnbaum, Z.W., and Lukacs, E. (1972), Fourier Analysis in Probability Theory, Academic Press: New York-London, 566-566.
  24. [24]  Wannamaker, R.A., Lipshitz, S.P., Vanderkooy, J., and Wright, J.N. (2000), A theory of nonsubtractive dither, IEEE Transactions on Signal Processing, 48(2), 499-516.
  25. [25]  Bernard, W. and István, K. (2015), Quantization noise: roundoff error in digital computation, signal processing, control, and communications - preface, Cambridge University Press, 11(Supplement s1), 704-704.
  26. [26]  Luo, A.C.J. (2017), Memorized Discrete Systems and Time-delay, Springer: New York.

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