Authors

Mohammed Danish, Stefan Bilbao, Michele Ducceschi

Abstract

This paper presents an application of the port Hamiltonian formalism to the nonlinear simulation of the OTA-based Korg35 filter circuit and the Moog 4-pole ladder filter circuit. Lyapunov analysis is used with their state-space representations to guarantee zero-input stability over the range of parameters consistent with the actual circuits. A zero-input stable non-iterative discrete-time scheme based on a discrete gradient and a change of state variables is shown along with numerical simulations. Simulations show behavior consistent with the actual operation of the circuits, e.g., self-oscillation, and are found to be stable and have lower computational cost compared to iterative methods.

Citation

  • Journal: 2021 24th International Conference on Digital Audio Effects (DAFx)
  • Year: 2021
  • Volume:
  • Issue:
  • Pages: 33–40
  • Publisher: IEEE
  • DOI: 10.23919/dafx51585.2021.9768301

BibTeX

@inproceedings{Danish_2021,
  title={{Applications of Port Hamiltonian Methods to Non-Iterative Stable Simulations of the KORG35 and MOOG 4-Pole VCF}},
  DOI={10.23919/dafx51585.2021.9768301},
  booktitle={{2021 24th International Conference on Digital Audio Effects (DAFx)}},
  publisher={IEEE},
  author={Danish, Mohammed and Bilbao, Stefan and Ducceschi, Michele},
  year={2021},
  pages={33--40}
}

Download the bib file

References

  • holters, Antiderivative Antialiasing for Stateful Systems. Intl Conf on Digital Audio Effects (2019)
  • esqueda, Aliasing Reduction in Nonlinear Audio Signal Processing (2018)
  • Veberič, D. Lambert W function for applications in physics. Computer Physics Communications 183, 2622–2628 (2012) – 10.1016/j.cpc.2012.07.008
  • bilbao, Lyapunov function for the nonlinear Moog voltage-controlled filter (2021)
  • muller, Trajectory Anti-Aliasing on Guaranteed-Passive Simulation of Nonlinear Physical Systems. Intl Conf on Digital Audio Effects (2017)
  • carson, Aliasing Reduction in Virtual Analogue Mod-elling (2020)
  • holters, Antiderivative Antialiasing for Stateful Systems. Applied Sciences (2020)
  • Yeh, D. T., Abel, J. S. & Smith, J. O. Automated Physical Modeling of Nonlinear Audio Circuits For Real-Time Audio Effects—Part I: Theoretical Development. IEEE Trans. Audio Speech Lang. Process. 18, 728–737 (2010) – 10.1109/tasl.2009.2033978
  • Yeh, D. T. Automated Physical Modeling of Nonlinear Audio Circuits for Real-Time Audio Effects—Part II: BJT and Vacuum Tube Examples. IEEE Trans. Audio Speech Lang. Process. 20, 1207–1216 (2012) – 10.1109/tasl.2011.2173677
  • Fettweis, A. Wave digital filters: Theory and practice. Proc. IEEE 74, 270–327 (1986) – 10.1109/proc.1986.13458
  • Sarti, A. & De Poli, G. Toward nonlinear wave digital filters. IEEE Trans. Signal Process. 47, 1654–1668 (1999) – 10.1109/78.765137
  • Karjalainen, M. & Pakarinen, J. Wave Digital Simulation of a Vacuum-Tube Amplifier. 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings vol. 5 V-153-V–156 – 10.1109/icassp.2006.1661235
  • werner, A gen-eral and explicit formulation for wave digital filters with mul-tiple/multiport nonlinearities and complicated topologies. 2015 IEEE Workshop on App Sig Proces Audio and Acous-tics (WASPAA) (0)
  • van der schaft, Port-Hamiltonian Systems: An Intro-ductory Survey. Proc Int Cong Math (0)
  • hélie, Lyapunov Stability Analysis of the Moog Ladder Filter and Dissipativity Aspects in Numerical Solutions. Proc 14th Int Conf Digital Audio Effects (0)
  • Lopes, N., Hélie, T. & Falaize, A. Explicit second-order accurate method for the passive guaranteed simulation of port-Hamiltonian systems. IFAC-PapersOnLine 48, 223–228 (2015) – 10.1016/j.ifacol.2015.10.243
  • Falaize, A. & Hélie, T. Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach. Applied Sciences 6, 273 (2016) – 10.3390/app6100273
  • D’Angelo, S. & Valimaki, V. An improved virtual analog model of the Moog ladder filter. 2013 IEEE International Conference on Acoustics, Speech and Signal Processing 729–733 (2013) doi:10.1109/icassp.2013.6637744 – 10.1109/icassp.2013.6637744
  • schimmel, Non-linear Dynamics Processing. J Audio Eng Soc (2003)
  • Helie, T. Volterra Series and State Transformation for Real-Time Simulations of Audio Circuits Including Saturations: Application to the Moog Ladder Filter. IEEE Trans. Audio Speech Lang. Process. 18, 747–759 (2010) – 10.1109/tasl.2009.2035211
  • schimmel, Using Nonlinear Amplifier Simulation in Dy-namic Range Comtrollers. Proc 6th Int Conf Digital Audio Effects (2003)
  • yeh, Simulation of the Diode Limiter in Guitar Distortion Circuits by Numerical Solution of Ordinary Differential Equations. Proc 10th Int Conf Digital Audio Effects (2007)
  • stinchcombe, Analysis of the Moog Transistor Ladder and Derivative Filters (2008)
  • huovilainen, Non-Linear Digital Implementation of the Moog Ladder Filter. Proc 7th Int Conf Digital Audio Effects (2004)
  • yeh, Nonlinear Modeling of a Guitar Loudspeaker Cabinet. Proc 11 th Int Conf Digital Audio Effects (2008)
  • yeh, Simplified, Physically-Informed Models of Distortion and Overdrive Guitar Effects Pedals. Proc 10th Int Conf Digital Audio Effects (2007)
  • yeh, Discretization of the ‘59 Fender Bassman Tone Stack. Proc 9th Int Conf Digital Audio Effects (2006)
  • yeh, Simulating Guitar Distortion Circuits Using Wave Digital and Nonlinear State-Space For-mulations. Proc 11 th Int Conf Digital Audio Effects (2008)
  • stilson, Analyzing the Moog VCF with Considerations for Digital Implementation. Proc Int Computer Music Conf (1996)
  • khalil, Nonlinear Systems (2002)
  • Falaize, A. & Hélie, T. Passive modelling of the electrodynamic loudspeaker: from the Thiele–Small model to nonlinear port-Hamiltonian systems. Acta Acust. 4, 1 (2020) – 10.1051/aacus/2019001
  • Falaize, A. & Hélie, T. Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano. Journal of Sound and Vibration 390, 289–309 (2017) – 10.1016/j.jsv.2016.11.008
  • paiva, Em-ulation of Operational Amplifiers and Diodes in Audio Dis-tortion Circuits. IEEE Trans Circ Syst II Express Briefs (2012)
  • Esqueda, F., Pöntynen, H., Parker, J. & Bilbao, S. Virtual Analog Models of the Lockhart and Serge Wavefolders. Applied Sciences 7, 1328 (2017) – 10.3390/app7121328
  • hélie, On the Use of Volterra Series for Real-time Sim-ulations of Weakly Nonlinear Analog Audio Devices: Application to the Moog Ladder Filter. Proc 9th Int Conf Digital Audio Effects (2006)
  • stinchcombe, A Study of the Korg MS10 and MS20 Filters (2006)