Virtual Analog Synthesis and Audio Effects

Virtual analog synthesis refers to the real-time simulation of electronic music synthesis, which has been traditionally implemented using analog electronics.

Around 1995, music technology companies started to develop digital musical instruments based on the virtual analog approach. In some products, samples are used to play back old sounds. We are developing discrete-time algorithms to simulate the analog filters and the waveform generation of analog music synthesizers. This work can be seen parallel to our physical modeling research, where we design computational simulations of acoustic systems - in virtual analog synthesis, computational simulations of electronic systems are designed. A related topic is the simulation of tube amplifiers used by electric guitar, bass, and electric organ players. This problem is difficult due to nonlinearities in the tube behavior. Our goal is to obtain physically valid digital models for tube amplifiers. This implies accurate imitations of all electrical parts of the amplifier. A further topic of interest is the modeling of analog effects processing boxes, such as phasers and flangers.

Selected Publications

Publication Short Description
D'Angelo, S., Pakarinen, J., Välimäki V., "New Family of Wave-Digital Triode Models," IEEE Transactions on Audio, Speech, and Language Processing, 2013. Vol. 21, nro 2, 313-321. A new family of highly accurante wave-digital vacuum tube triode
models is presented. The proposed algorithms were found to produce a richer static harmonic response, introducing comparable or less aliasing and requiring approximately 50% less CPU time than previous models.
Lehtonen, H.-M., Pekonen, J., and Välimäki, V., ''Audibility of aliasing distortion in sawtooth signals and its implications for oscillator algorithm design,'' Journal of the Acoustical Society of America, vol. 132, no. 4, pp. 2721-2733, October 2012. Formal listening tests are conducted in order to find how much the aliased components in computer-generated sawtooth signals must be attenuated for them to be audible. It is shown that the frequency-masking phenomenon affects the perception of aliasing and that the masking effect is more significant above the fundamental than below it. Additionally, general rules for antialiasing sawtooth oscillators are derived.
Paiva, R. C. D., D’Angelo, S., Pakarinen, J., Välimäki, V., "Emulation of operational amplifiers and diodes in audio distortion circuits," IEEE Transactions on Circuits and Systems. Part 2: Express Briefs, 2012. Vol. 59, nro 10, 688-692. The article presents a new model for an ideal operational amplifier that is suitable for implementation using wave digital filters (WDFs). Furthermore, a novel WDF model for a diode is proposed using the Lambert W function. A comparison of output signals of the proposed models to those obtained from a reference simulation using SPICE shows that the distortion characteristics are accurately reproduced over a wide frequency range.
D’Angelo, S., Välimäki, V., "Wave-digital polarity and current inverters and their application to virtual analog audio processing," The 37th International Conference on Acoustics, Speech, and Signal Processing (ICASSP); Kyoto, Japan; March 25-30, 2012. Kyoto, Japan, 2012, IEEE, 469-472. Two new non-energic two-port WDF adaptors are introduced to enable interconnections among subnetworks using different polarity and sign conventions, and the definitions of absorbed instantaneous and steady-state pseudopower are extended accordingly. The correctness of the obtained results is verified in a concrete case study.
J. Parker, “Efficient Dispersion Generation Structures for Spring Reverb Emulation,” EURASIP Journal on Advances in Signal Processing, article ID 646134, 8 pages, 2011. In this paper, a refinement of the dispersion generation structure of a spring reverb model is proposed. This refinement lowers the computational complexity by applying multi-rate techniques, and modelling the dispersion in different frequency bands separately.
J. Parker, “A Simple Digital Model of the Diode-Based Ring-Modulator” in Proc. Int. Conf. Digital Audio Effects (DAFx-11), Paris, France, Sept.19-23,2011. In this paper, the diode-based ring modulator, an important device in early electronic music (and radio) is examined. The circuit is analysed, and a number of simplifications proposed which allow for the construction of a simple digital algorithm that emulates the circuit for musical use.
S. Oksanen, V. Välimäki, “Modeling of the carbon microphone nonlinearity for a vintage telephone sound effect”, in Proc. 14th International Conference on Audio Effects (DAFx-11), Sept 19-23, 2011, Paris, France This paper presents a digital model of the carbon microphone nonlinearity which can be used to produce a vintage telephone sound effect. The model is constructed based on measurements taken from a real carbon microphone and supplemented with added noise. Companion web page.
S. Oksanen, V. Välimäki, “Digital modeling of the vintage telephone sound”, in Proc. International Computer Music Conference (ICMC) 2011, July 31–Aug. 5, 2011, Huddersfield, UK This paper presents a digital model of a vintage telephone sound effect. The effect is derived based on the physical principles of a single-button carbon microphone. The model is realized by using a sandwiched model which consists of a cascade of second-order equalizer filters followed by nonlinearity function and additive noise generator and concluded by band limiting linear filter. Companion web page.
V. Välimäki, J. Parker, and J. S.Abel, “Parametric spring reverberation effect,” Journal of the Audio Engineering Society, vol. 58, no. 7/8, pp. 547–562, July/August 2010. In this paper a parametric model of the spring reverberator, based on standard signal processing elements, is proposed. The structure uses all pass filters to generate the required dispersion. The resulting model is suitable for real-time musical use.
S. Bilbao and J. Parker, “A virtual model of spring reverberation,” IEEE Transactions on Audio, Speech and Language Processing, vol. 18, no. 4, pp. 799-808, May 2010. Mathematical models of helical spring vibration are analysed, and related to the operation of early artificial reverberation devices that use such springs. A discretisation of one of the mathematical models via the finite difference method is proposed, which allows digital simulation of the behaviour of a spring reverberator.
V. Välimäki and A. Huovilainen, "Antialiasing oscillators in subtractive synthesis," IEEE Signal Processing Magazine, vol. 24, no. 2, pp. 116–125, March 2007. Signal processing techniques for implementing digital waveform oscillators with reduced aliasing are reviewed. Currently known methods are classified, briefly reviewed, and compared. A new method based on polynomial bandlimited step functions (PolyBLEP) is introduced. An auditory error measure, the noise-to-mask ratio (NMR), is used for evaluating the sound quality. 
M. Karjalainen and J. Pakarinen, "Wave digital simulation of a vacuum-tube amplifier", in the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'06), Toulouse, France, May 15-19, 2006. This paper discusses wave digital simulation of tube amplifier stages, typical e.g. in guitar amplifiers. A new real-time model is introduced and different implementation techniques are presented. 
V. Välimäki and A. Huovilainen, "Oscillator and Filter Algorithms for Virtual Analog Synthesis", in Computer Music Journal, vol. 30, no. 2, 2006. New algorithms for the generation of alias-free digital versions of classical analog waveforms (the sawtooth, pulse, and triangular wave) are introduced. Modifications and simplifications to the digital nonlinear model of the Moog ladder filter proposed previously by Huovilainen are given.
A. Huovilainen, "Enhanced digital models for analog modulation effects", in Proc. 8th Int. Conf. on Digital Audio Effects (DAFx'05), pp. 155-160, Madrid, Spain, Sept. 2005. The operation and non-idealities of analog phaser and flanger / chorus effects are discussed. Two new digital models for phaser and one for flanger / chorus are presented that more closely match the operation of the analog implementations.
R. Trausmuth and A. Huovilainen, "Powerwave - A high performance single chip interpolating wavetable synthesizer", in Proc. 8th Int. Conf. on Digital Audio Effects (DAFx'05), pp. 293-296, Madrid, Spain, Sept. 2005. Design for a high quality wavetable synthesizer is presented. The synthesizer is implemented with a single Xilinx FPGA chip containing both audio generation and control functions. 
A. Huovilainen and V. Välimäki, "New Approaches to Digital Subtractive Synthesis", in Proc. Int. Computer Music Conf. (ICMC'05), Barcelona, Spain, pp. 399-402, Sept. 2005. This paper presents new methods for digital subtractive synthesis that have both low computational cost and relatively high quality. The DPW algorithm for producing reduced alias sawtooth waveform is reviewed. A new variant of the digital Moog filter with multiple responses and low cost non-linearity is also shown. 
V. Välimäki and A. Huovilainen, "Virtuaalista nostalgiaa - digitaalinen vähentävä äänisynteesi", Musiikki, vol. 35, no. 1-2, pp. 78-98, 2005. This is a review of oscillators and resonant filters for digital subtractive music synthesis in the Finnish language. The DPW sawtooth algorithm, the simplified nonlinear Moog filter, and two examples of digital synthesizer patches are briefly explained. 
V. Välimäki, "Discrete-Time Synthesis of the Sawtooth Waveform with Reduced Aliasing", IEEE Signal Processing Letters, vol. 12, no. 3, pp. 214-217, March 2005.  This paper introduces a new efficient signal processing technique, called the DPW, to generate an alias-free sawtooth waveform for virtual analog synthesis. The algorithm differentiates a piecewise parabolic waveform, and it is easy to implement with a computer. Two variants of the algorithm are given, one of which employes multirate signal processing.
M. Karjalainen, T. Mäki-Patola, A. Kanerva, A. Huovilainen, and P. Jänis, ''Virtual Air Guitar,'' in Proceedings of AES 117th Convention, preprint no. 6203, San Francisco, CA, USA, October 28-31, 2004. Signal processing and gesture-control methods are discussed that enable playing of an electric guitar synthesizer by waving your hands in the air. Highly entertaining real-time demonstrations have been implemented using these techniques. For more info, see
A. Huovilainen, "Non-linear Digital Implementation of the Moog Ladder Filter", in Proc. 7th Int. Conf. Digital Audio Effects (DAFx'04), pp. 61-64, Naples, Italy, October 5-8, 2004. This paper analyzes the structure and behaviour of the Moog ladder filter. A large-signal model is presented and discretized to yield a digital model that correctly simulates the non-linear behaviour. An alternative method of tuning correction is also presented.
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