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A Simple Non-linear Transfer Function for a Wiener-Hammerstein Model to Simulate Guitar Distortion and Overdrive Effects

In: Integral Methods in Science and Engineering

Author

Listed:
  • Adalberto Schuck Jr.

    (Federal University of Rio Grande do Sul (UFRGS), Electrical Engineering Department (DELET))

  • Luiz F. Ferreira

    (Federal University of Rio Grande do Sul (UFRGS), Electrical Engineering Department (DELET))

  • Ronaldo Husemann

    (Federal University of Rio Grande do Sul (UFRGS), Electrical Engineering Department (DELET))

  • Bardo E. J. Bodmann

    (Federal University of Rio Grande do Sul (UFRGS), Mechanical Engineering Department (DEMEC))

Abstract

Valve amplifiers have been modulated recently by digital signal processing techniques, using the Wiener-Hammerstein cell. The key of this approach is to identify the non-linear static transfer function. In the present contribution we model audio distortion pedal effects and propose a transfer function model derived from a modification of the Shockley equation. Six limiter circuits with different types of diodes (silicon, germanium and LED) were evaluated using a voltage sine wave of 10 Hz and amplitude such as to provide a 10 mA input current. Ten seconds of input and output signals were sampled (100 kSamples/s) and the model was fitted to the data using the Levenberg-Marquardt non-linear least square method. The model worked well, providing a root mean square standard error between the data and best fit less than 10−4, except for the LED limiter circuit. The present approach resulted in an analytical representation of the non-linear transfer function, which can generate directly from a discretised input signal the corresponding output signal according to a desired response of a chosen limiter model.

Suggested Citation

  • Adalberto Schuck Jr. & Luiz F. Ferreira & Ronaldo Husemann & Bardo E. J. Bodmann, 2019. "A Simple Non-linear Transfer Function for a Wiener-Hammerstein Model to Simulate Guitar Distortion and Overdrive Effects," Springer Books, in: Christian Constanda & Paul Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 425-436, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-16077-7_33
    DOI: 10.1007/978-3-030-16077-7_33
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