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Effects of fractional order integration on ASDM signals

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Abstract

Pulse density modulation (PDM) can find applications in consumer electronics, power and switch control systems. PDM signals can be generated by asynchronous sigma delta modulator (ASDM) structures and improvement of ASDM performance provides significant contribution for practical applications. This study numerically investigates effects of fractional order integration (FOI) on the PDM signal, produced by ASDM. We implemented fractional order integratorin ASDM structure and present numerical analysis to discuss effects of fractional order integrator on PDM signals, obtained for bipolar digital signal transmission application. Theoretical analysis indicates that FOI provides finer pulse trains and thus improves representation of original signal. In simulations, we tested FOI for various fractional-order values. Signal to noise ratio and signal to noise and distortion ratio (SINAD) levels of demodulated signals are reported for sinusoidal and audio test signals. Simulation results demonstrate that FOI can improve SNR and SINAD performance of ASDMs.

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References

  1. Gutierrez RE, Rosario JM, Machado JAT (2010) Fractional order calculus: basic concepts and engineering applications, mathematical problems in engineering. Hindawi Publishing Corporation, Cairo

    MATH  Google Scholar 

  2. Petras I (2010) Fractional order nonlinear system, modeling, analysis and simulation. Springer, London

  3. Podlubny I (1999) Fractional differential equations, mathematics in science and engineering. Academic press, Cambridge

    MATH  Google Scholar 

  4. Ross B (1975) Fractional calculus and its applications. Springer, London

    Book  Google Scholar 

  5. Yeroglu C, Ates A (2014) A stochastic multi-parameters divergence method for online auto-tuning of fractional order PID controller. J Frank Inst 351:2411–2429

    Article  MathSciNet  Google Scholar 

  6. Correa JM, Hutto ED, Farret FA, Simoes MG (2003) A fuzzy-controlled pulse density modulation strategy for a series resonant inverter with wide load range. In: Power electronics specialist conference, vol 4, pp 1650–1655

  7. Essadaoui J, Sicard P, Ngandui E, Cheriti A (2003) Power inverter control for induction heating by pulse density modulation with improved power factor. IEEE CCECE Can Conf 1:515–520

    Google Scholar 

  8. Stauth JT, Sanders SR (2008) Pulse-density modulation for RF applications: the radio-frequency power amplifier (RF PA) as a power converter. Power electronics specialists conference, 2008. PESC 2008. IEEE

  9. Lee YS, Park YO (2004) BER performance of AGC in high-speed portable Internet system. Vehicular Technol Conf 7:4794–4797

    Google Scholar 

  10. Kite TD (2012) Understanding PDM digital audio. Application note from audio precision. http://users.ece.utexas.edu/~bevans/courses/rtdsp/lectures/10_Data_Conversion/AP_Understanding_PDM_Digital_Audio.pdf. Accessed 25 March 2016

  11. Senay S, Chaparro LF, Sun M, Sclabassi R, Akan A (2011) Asynchronous signal processing for brain–computer interfaces. Turk J Elect Eng Comput Sci 19(2):275–289

    Google Scholar 

  12. Lazar AA, Tóth LT (2004) Perfect recovery and sensitivity analysis of time encoded bandlimited signals. Circuits Syst I 51(10):2060–2073

    Article  MathSciNet  Google Scholar 

  13. Kikkert CJ, Miller DJ (1975) Asynchronous delta sigma modulation. Proc IREE 36:83–88

    Google Scholar 

  14. Kavuran G, Yeroglu C (2015) Investigation of periodic modes in nonlinear systems with fractional order integrator. Signal processing and communications applications conference (SIU), 2015 23rd, Malatya

  15. Chen YQ, Vinagre BM, Podlubny I (2004) Continued fraction expansion approaches to discretizing fractional order derivatives an expository review. Nonlinear Dyn 38(1–4):155–170

    Article  MathSciNet  MATH  Google Scholar 

  16. Özyetkin MM, Yeroğlu C, Tan N, Tağluk ME (2010) Design of PI and PID controllers for fractional order time delay systems. In: Proceedings of the 9th IFAC workshop on time-delay systems, TDS, Prague

  17. Kavuran G, Ates A, Alagoz BB, Yeroglu C (2015) A note on effects of fractional order integration on ASDM signals. The international symposium on fractional signals and systems 2015 (FSS2015). Cluj Napoca, Romania

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Authors and Affiliations

  1. Mechatronics Engineering, Technology Faculty, Fırat University, Elazig, Turkey

    Gurkan Kavuran

  2. Computer Engineering, Engineering Faculty, Inonu University, Malatya, Turkey

    Celaleddin Yeroğlu, Abdullah Ateş & Baris Baykant Alagoz

Authors
  1. Gurkan Kavuran
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  2. Celaleddin Yeroğlu
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  3. Abdullah Ateş
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  4. Baris Baykant Alagoz
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Correspondence to Gurkan Kavuran.

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Kavuran, G., Yeroğlu, C., Ateş, A. et al. Effects of fractional order integration on ASDM signals. Int. J. Dynam. Control 5, 10–17 (2017). https://doi.org/10.1007/s40435-016-0240-3

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  • DOI: https://doi.org/10.1007/s40435-016-0240-3

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