Aliasing Reduction in Nonlinear Audio Signal Processing

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School of Electrical Engineering | Doctoral thesis (article-based) | Defence date: 2018-05-18
Degree programme
64 + app. 88
Aalto University publication series DOCTORAL DISSERTATIONS, 74/2018
Most real-world audio devices, particularly those of interest in musical applications, fall under the category of nonlinear systems. Examples of these devices include overdrive and distortion circuits used by guitar and bass players, dynamic range processors, and vintage synthesizer circuits. Nonlinear algorithms are known to expand the bandwidth of the input signal by introducing harmonic and intermodulation distortion. Naive digital emulations of these systems are susceptible to aliasing due to the inherent frequency constraints of discrete systems.  This thesis focuses on new digital signal processing techniques designed to reduce the level of aliasing introduced by memoryless nonlinearities. The underlying motivation of this work is to incorporate these tools within the framework of virtual analog (VA) modeling, an area of study that concentrates on the emulation of analog audio devices in the digital domain. In VA modeling, aliasing reduction has been studied extensive for the case of synthesis of classical oscillator waveforms like those used in subtractive synthesis. However, in audio effects processing oversampling has traditionally been the only available tool to ameliorate this problem. The first part of this work proposes the use of bandlimited correction functions previously used in waveform synthesis, to reduce the aliasing caused by special nonlinearities that introduce discontinuities in the derivatives of a signal. This family of novel methods includes the use of the bandlimited ramp function (BLAMP), its efficient polynomial approximations, and its integrated form. A new VA model of a highly nonlinear wavefolder circuit, which incorporates one of these techniques, is proposed.  The second family of techniques elaborated in this thesis is that of the antiderivative method. This innovative approach to aliasing reduction is based on the discrete differentiation of integrated nonlinearities and can be applied to arbitrary explicit memoryless nonlinearities regardless of their form. The use of the antiderivative forms in VA modeling is proposed by introducing two novel transistor/diode-based wavefolder models, and two static diode clipper models that incorporate these techniques.  Results obtained show the proposed algorithms effectively reduce the level of aliasing in nonlinear processing and can help reduce, and in some cases even eliminate, the oversampling requirements of the system. The proposed algorithms are suitable for real-time software implementations of VA instruments and effects processors.
Supervising professor
Välimäki, Vesa, Prof., Aalto Univeristy, Department of Signal Processing and Acoustics, Finland
Thesis advisor
Bilbao, Stefan, Dr., University of Edinburgh, UK
acoustic signal processing, digital signal processing, antialiasing, nonlinear systems, circuit simulation, real-time systems
Other note
  • [Publication 1]: Fabián Esqueda, Stefan Bilbao and Vesa Välimäki. Aliasing reduction in clipped signals. IEEE Transactions on Signal Processing, Vol. 64, No. 20, pp. 5255–5267, October 2016.
    DOI: 10.1109/TSP.2016.2585091 View at publisher
  • [Publication 2]: Fabián Esqueda, Vesa Välimäki, Stefan Bilbao. Rounding corners with BLAMP. In Proceedings of the 19th International Conference on Digital Audio Effects (DAFx-16), Brno, Czech Republic, pp. 121–128, September 2016.
  • [Publication 3]: Fabián Esqueda, Henri Pöntynen, Vesa Välimäki, Julian D. Parker. Virtual analog Buchla 259 wavefolder. In Proceedings of the 20th International Conference on Digital Audio Effects (DAFx-17), Edinburgh, UK, pp. 192–199, September 2017.
  • [Publication 4]: Fabián Esqueda, Vesa Välimäki, Stefan Bilbao. Antialiased soft clipping using an integrated bandlimited ramp. In Proceedings of the 24th European Signal Processing Conference (EUSIPCO), Budapest, Hungary, pp. 1043–1047, August–September 2016.
    DOI: 10.1109/EUSIPCO.2016.7760407 View at publisher
  • [Publication 5]: Stefan Bilbao, Fabián Esqueda, Julian D. Parker, Vesa Välimäki. Antiderivative antialiasing for memoryless nonlinearities. IEEE Signal Processing Letters, Vol. 24, No. 7, pp. 1049–1053, July 2017.
    DOI: 10.1109/LSP.2017.2675541 View at publisher
  • [Publication 6]: Fabián Esqueda, Henri Pöntynen, Julian D. Parker, Stefan Bilbao. Virtual analog models of the Lockhart and Serge wavefolders. Applied Sciences, Vol. 7, No. 12, December 2017.
    DOI: 10.3390/app7121328 View at publisher
  • [Publication 7]: Fabián Esqueda, Vesa Välimäki. Alias-free simulation of static audio distortion circuits using the Lambert-W function. Submitted to IEEE Transactions on Circuits and Systems II: Express Briefs, March 2018.