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Distortion-Free 1-Bit PWM Coding for Digital Audio Signals


Although uniformly sampled pulse width modulation (UPWM) represents a very efficient digital audio coding scheme for digital-to-analog conversion and full-digital amplification, it suffers from strong harmonic distortions, as opposed to benign non-harmonic artifacts present in analog PWM (naturally sampled PWM, NPWM). Complete elimination of these distortions usually requires excessive oversampling of the source PCM audio signal, which results to impractical realizations of digital PWM systems. In this paper, a description of digital PWM distortion generation mechanism is given and a novel principle for their minimization is proposed, based on a process having some similarity to the dithering principle employed in multibit signal quantization. This conditioning signal is termed "jither" and it can be applied either in the PCM amplitude or the PWM time domain. It is shown that the proposed method achieves significant decrement of the harmonic distortions, rendering digital PWM performance equivalent to that of source PCM audio, for mild oversampling (e.g.,) resulting to typical PWM clock rates of 90 MHz.


  1. 1.

    Nishio A, Ichimura G, Inazawa Y, Horikawa N, Suzuki T: Direct stream digital audio system. Proceedings of the 100th Convention of Audio Engineering Society (AES '96), May 1996, Copenhagen, Denmark preprint 4163

    Google Scholar 

  2. 2.

    Verbakel J, van de Kerkhof L, Maeda M, Inazawa Y: Super audio CD format. Proceedings of the 104th Convention of Audio Engineering Society (AES '98), May 1998, Amsterdam, The Netherlands preprint 4705

    Google Scholar 

  3. 3.

    Goldberg JM, Sandler MB: Pseudo-natural pulse width modulation for high accuracy digital-to-analogue conversion. Electronics Letters 1991,27(16):1491-1492. 10.1049/el:19910933

    Article  Google Scholar 

  4. 4.

    Nielsen K: A review and comparison of pulse width modulation (PWM) methods for analog and digital input switching power amplifiers. Proceedings of the 102nd Convention of Audio Engineering Society (AES '97), March 1997, Munich, Germany preprint 4446

    Google Scholar 

  5. 5.

    Nielsen K: Linearity and efficiency performance of switching audio power amplifier output stages—a fundamental analysis. Proceedings of the 105th Convention of Audio Engineering Society (AES '98), September 1998, San Francisco, Calif, USA preprint 4838

    Google Scholar 

  6. 6.

    Hawksford MJ: Modulation and system techniques in PWM and SDM switching amplifiers. Journal of the Audio Engineering Society 2006,54(3):107-139.

    Google Scholar 

  7. 7.

    Esslinger R, Gruhler G, Stewart RW: Digital power amplification based on pulse-width modulation and sigma-delta loops. A comparison of current solutions. Proceedings of the Institute of Radio Electronics, Czech and Slovak Radio Engineering Society (RADIOELEKTRONIKA '99), April 1999, Brno, Czech Republic

    Google Scholar 

  8. 8.

    Magrath AJ, Sandler MB: Digital power amplification using sigma-delta modulation and bit flipping. Journal of the Audio Engineering Society 1997,45(6):476-487.

    Google Scholar 

  9. 9.

    Hawksford MJ: SDM versus PWM power digital-to-analogue converters (PDAC) in high-resolution digital audio applications. Proceedings of the 118th Convention of Audio Engineering Society (AES '05), May 2005, Barcelona, Spain preprint 6471

    Google Scholar 

  10. 10.

    Bowes SR: New sinusoidal pulsewidth-modulated invertor. IEE Proceedings 1975,122(11):1279-1285.

    Google Scholar 

  11. 11.

    Hawksford MJ: Linearization of multilevel, multiwidth digital PWM with applications in digital-to-analog conversion. Journal of the Audio Engineering Society 1995,43(10):787-798.

    Google Scholar 

  12. 12.

    Jung J-W, Hawksford MJ: An oversampled digital PWM linearization technique for digital-to-analog conversion. IEEE Transactions on Circuits and Systems 2004,51(9):1781-1789. 10.1109/TCSI.2004.834487

    Article  Google Scholar 

  13. 13.

    Nielsen K: High-fidelity PWM-based amplifier concept for active loudspeaker systems with very low energy consumption. Journal of the Audio Engineering Society 1997,45(7-8):554-570.

    Google Scholar 

  14. 14.

    Black HS: Modulation Theory. Van Nostrand, Princeton, NJ, USA; 1953.

    MATH  Google Scholar 

  15. 15.

    Mellor PH, Leigh SP, Cheetham BMG: Reduction of spectral distortion in class D amplifiers by an enhanced pulse width modulation sampling process. IEE Proceedings—Part G: Circuits, Devices and Systems 1991,138(4):441-448. 10.1049/ip-g-2.1991.0076

    Google Scholar 

  16. 16.

    Bowes SR, Lai Y-S: Relationship between space-vector modulation and regular-sampled PWM. IEEE Transactions on Industrial Electronics 1997,44(5):670-679. 10.1109/41.633469

    Article  Google Scholar 

  17. 17.

    Bowes SR, Bird BM: Novel approach to the analysis and synthesis of modulation processes in power converters. IEE Proceedings 1975,122(5):507-513.

    Google Scholar 

  18. 18.

    Floros A, Mourjopoulos J: Analytic derivation of audio PWM signals and spectra. Journal of the Audio Engineering Society 1998,46(7):621-633.

    Google Scholar 

  19. 19.

    Lipshitz S, Wannamaker R, Vanderkooy J: Quantization and dither: a theoretical survey. Journal of the Audio Engineering Society 1992,40(5):355-375.

    Google Scholar 

  20. 20.

    Gray RM: Quantization noise spectra. IEEE Transactions on Information Theory 1990,36(6):1220-1244. 10.1109/18.59924

    Article  Google Scholar 

  21. 21.

    Blesser BA: Digitization of audio: a comprehensive examination of theory, implementation, and current practice. Journal of the Audio Engineering Society 1978,26(10):739-771.

    Google Scholar 

  22. 22.

    Floros A, Mourjopoulos J: A study of the distortions and audibility of PCM to PWM mapping. Proceedings of the 104th Convention of Audio Engineering Society (AES '98), May 1998, Amsterdam, The Netherlands preprint 4669

    Google Scholar 

  23. 23.

    Floros A, Mourjopoulos J, Tsoukalas DE: Jither: the effects of jitter and dither for 1-bit audio PWM signals. Proceedings of the 106th Convention of Audio Engineering Society (AES '99), May 1999, Munich, Germany preprint 4656

    Google Scholar 

  24. 24.

    Craven P: Toward the 24-bit DAC: novel noise-shaping topologies incorporating correction for the nonlinearity in a PWM output stage. Journal of the Audio Engineering Society 1993,41(5):291-313.

    Google Scholar 

  25. 25.

    Floros A, Mourjopoulos J: On the nature of digital audio PWM distortions. Proceedings of the 108th Convention of Audio Engineering Society (AES '00), February 2000, Porte Maillot, Paris, France preprint 5123

    Google Scholar 

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Correspondence to Andreas Floros.

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Floros, A., Mourjopoulos, J. Distortion-Free 1-Bit PWM Coding for Digital Audio Signals. EURASIP J. Adv. Signal Process. 2007, 094386 (2007).

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  • Pulse Width
  • Quantum Information
  • Generation Mechanism
  • Audio Signal
  • Pulse Width Modulation