ArticlePDF Available

Oscillator and Filter Algorithms for Virtual Analog Synthesis

Authors:

Abstract

Virtual analog synthesis refers to computational methods that imitate the sound production principles used in electronic music synthesizers of the 1960s and 1970s. In practice, it means digital subtractive synthesis. In this paper, we introduce new methods to generate digital versions of classical analog waveforms with reduced aliasing. We also propose modifications to the digital nonlinear model of the Moog ladder filter. These virtual analog synthesis techniques enable the production of retro sounds with modern computers.
A preview of the PDF is not available
... The synthesiser has been planned as having a wavetable synthesis section to generate signal followed by a subtractive synthesis module. For the filter, it has been chosen to implement a Moog ladder filter emulation proposed in [4] so as to incorporate a vintage style timbre to a modern software construction. Filter's cutoff frequency has been chosen to operate in the 'pitch follow' mode. ...
... This concerns mostly waveforms which are rich in partials, such as a sawtooth or a square. That is why 'digital oscillator' algorithms have been developed since the 1980s to reduce distortion, but preserve computational efficiency [4]. These are described in Section 2.6. ...
... One of the main fields of interest was the algorithm for Moog ladder filter emulation (the filter itself is described in Section 2.4.2.3). Possible implementation can be found in [9] and [4]. The latter uses Fig. 2.10. ...
Thesis
Full-text available
The aim of the project was to create a library in the C++ programming language functioning as a thirty-two-voice sound synthesis engine. The wavetable section consists of three oscillators with octave, semitone, and cent transposition. Each of them can have its volume adjusted and two of them can be turned on or off. The basic waveforms have been implemented (sine, triangle, sawtooth, square) as well as their equivalents based on the Virtual Analog algorithms. This family of algorithms has also been used in implementing a digital Moog ladder filter emulation with an addition of the cutoff frequency envelope of Attack-Decay-Sustain-Release type. The final stages of sound synthesis are a waveshaper (non-linear transformation) and a volume envelope generator (in Attack-Decay1-Break-Decay2-Release form). A VST3 interface has been created using the JUCE framework. Library’s architecture has been designed in a flexible fashion allowing ease of feature extension and support. Strategy, Façade, Factory and Prototype design patterns have been used along with the PIMPL idiom.
... The trend of turning everything into a digital form has also impacted the musical domain, and in particular that of devices used in the production of electronic music [29], an endeavor that is commonly referred to as "virtual analog". Examples within this category include virtual analog synthesizers [22], virtual analog filters [30], virtual musical instruments [19,32], reverb emulations [31], and guitar amplifier models [21]. ...
... On the other hand, digital signal processing has limits and undesirable side-effects (e.g., quantization noise, aliasing), and research has devised a number of solutions to emulate the analog world in a realistic way (e.g., augmenting the quantization resolution, oversampling, antialiasing techniques) [20,28,30]. However, besides technical drawbacks related to the actual rendering of an analog device into the digital realm, downsides for virtual analog software may reside in their real-time control. ...
... For the case of analog VCFs, the digitizing started gradually several decades ago [4], [5] and has continued ever since. More recently, audio researchers have devised digital models for many other analog musical devices, such as synthesizer oscillators [6], guitar pedals [7]- [9], distortion circuits [10]- [12], audio transformers [13] and ring modulators [14]. ...
... Huovilainen derived a different digital model, which accounts for the nonlinear characteristics of the transistor ladder [15]. Huovilainen and Välimäki simplified the nonlinear Moog filter model so that it only uses one memoryless mapping function [6]. Other authors have derived digital variations of both the linear Moog filter [16] and the nonlinear one [17]- [21]. ...
Conference Paper
Full-text available
Abstract—The analog voltage-controlled filter used in historical music synthesizers by Moog is modeled using a digital system, which is then compared in terms of audio measurements with the original analog filter. The analog model is mainly borrowed from D’Angelo’s previous work. The digital implementation of the filter incorporates a recently proposed antialiasing method. This method enhances the clarity of output signals in the case of large-level input signals, which cause harmonic distortion. The combination of these two ideas leads to a novel digital model, which represents the state of the art in virtual analog musical filters. It is shown that without the antialiasing, the output signals in the nonlinear regime may be contaminated by undesirable spectral components, which are the consequence of aliasing, but that the antialiasing technique suppresses these components sufficiently. Comparison of measurements of the analog and digital filters show that the digital model is accurate within a few dB in the linear regime and has very similar behavior in the nonlinear regime in terms of distortion. The proposed digital filter model can be used as a building block in virtual analog music synthesizers.
... This system thus resembles the source-filter model, as discussed in speech synthesis. The early electronic synthesizers implementing subtractive synthesis produced a distinctive sound due to the many non-linear analogue effects, which can also be emulated with digital computers (Välimäki and Huovilainen, 2006). • Non-linear synthesis. ...
Article
Music is different from speech in that its role is not so much to convey linguistic and conceptual content as it is to evoke an aesthetic and emotional experiences. This chapter begins with the discussion of the formation of sounds in acoustical and electric musical instruments. It discusses shortly some basic properties of acoustic and electric instruments and their sounds. E.M. von Hornbostel and C. Sachs classified musical instruments into four different categories based on how they produce sound: idiophones, membranophones, chordophones, and aerophones. The classification of some instruments is the cause of some debate. The synthesis of musical sounds has been of interest for decades, and many musical instruments are based on such methods. The history of musical sound synthesis is different from the history of modelling of speech production, where the first models were based on the physics of speech organs, after which sampling methods were adopted.
... This also implies the use of the instrument's sensors as a replacement of the interface of the original analog equipment. For instance, this is the case of analog synthesizers or stompboxes for sound effects, which can be simulated by means of virtual analog techniques [117] and controlled via the embedded sensor interface. Such self-contained nature is one of the major strengths of SMIs compared to other interactive performance systems, which leads to benefits such as easiness of setup and portability, as well as the ubiquitous use of SMIs [110]. ...
Article
Full-text available
Smart Musical Instruments (SMIs) are a family of Internet of Musical Things devices for music creation. They are characterized by sensors, actuators, embedded intelligence, and wireless connectivity to local networks and to the Internet. In this article we depict a vision for this recent research area, which merges the research fields on digital musical instruments and smart objects, and fosters new types of interactions between the player and the instrument, between the player and other players, and between the player and audience members. We propose a set of capabilities and technical features characterizing SMIs, as well as a design for a technological architecture supporting them. To illustrate possible applications enabled by this vision we present a set of scenarios exploiting the intelligence embedded in SMIs. We also propose a set of guidelines that can help digital luthiers in the process of designing SMIs. Finally, we present a set of directions for future research.
... Such methods are applicable regardless of the particular form of the nonlinear function; aliasing suppression may be understood, intuitively, in terms of operation over increasingly smoothed forms of the nonlinearity. The proposed idea of differentiating antiderivatives is related to previous antialiasing synthesis methods called the differential polynomial waveform [23], [24], [25], [26], [27], and integrated wavetable/sampling synthesis [28], [29], [30]. ...
Article
Aliasing is a commonly-encountered problem in audio signal processing, particularly when memoryless nonlinearities are simulated in discrete time. A conventional remedy is to operate at an oversampled rate. A new aliasing reduction method is proposed here for discrete-time memoryless nonlinearities, which is suitable for operation at reduced oversampling rates. The method employs higher order antiderivatives of the nonlinear function used. The first order form of the new method is equivalent to a technique proposed recently by Parker et al. Higher order extensions offer considerable improvement over the first antiderivative method, in terms of the signal-to-noise ratio. The proposed methods can be implemented with fewer operations than oversampling and are applicable to discrete-time modeling of a wide range of nonlinear analog systems.
... The BLEP signal is a pre-integrated bandlimited impulse. Subtracting out a unit-step function produces a BLEP residual that may be used to alter the points AES 141st Convention, Los Angeles, USA, 2016 September 29-October 2 Page 2 of 10 around the discontinuity [1]. Figure 1.1 shows the impulse response of an ideal low-pass filter -the familiar sinc function -along with the result of integrating it and converting the result to bipolar form. ...
Thesis
Full-text available
This work addresses the real-time simulation of nonlinear audio circuits. In this thesis, we use the port-Hamiltonian (pH) formalism to guarantee power balance and passivity. Moreover, we adopt a continuous-time functional framework to represent "virtual analog" signals and propose to approximate solutions by projection over time frames. As a main result, we establish a sufficient condition on projectors to obtain time-continuous power-balanced trajectories. Our goal is twofold: first, to manage frequency-bandwidth expansion due to nonlinearities, we consider numerical engines processing signals that are not bandlimited but, instead, have a "finite rate of innovation"; second, to get back to the bandlimited domain, we design "virtual analog-to-digital converters". Several numerical methods are built to be power-balanced, high-order accurate, with a controllable regularity order. Their properties are studied: existence and uniqueness, accuracy order and dispersion, but also, frequency resolution beyond the Nyquist frequency, aliasing rejection, reproducing and Peano kernels. This approach reveals bridges between numerical analysis, signal processing and generalised sampling theory, by relating accuracy, polynomial reproduction, bandwidth, Legendre filterbanks, etc. A systematic framework to transform schematics into equations and simulations is detailed. It is applied to representative audio circuits (for the UVI company), featuring both ordinary and differential-algebraic equations. Special work is devoted to pH modelling of operational amplifiers. Finally, we revisit pH modelling within the framework of Geometric Algebra, opening perspectives for structure encoding.
Thesis
Full-text available
Digital systems gain more and more popularity in todays music industry. Musicians and producers are using digital systems because of their advantages over analog electronics. They require less physical space, are cheaper to produce and are not prone to aging circuit components or temperature variations. Furthermore, they always produce the same output signal for a defined input sequence. However, musicians like vintage equipment. Old guitar amplifiers or legendary recording equipment are sold at very high prices. Therefore, it is desirable to create digital models of analog music electronics which can be used in modern digital environments. This work presents an approach for recreating nonlinear audio circuits using system identification techniques. Measurements of the input- and output-signals from the analog reference devices are used to adjust a digital model treating the reference device as a ‘black-box’. With this technique the schematic of the reference device does not need to be known and no circuit elements have to be measured to recreate the analog device. An appropriate block-based model is chosen, depending on the type of reference system. Then the parameters of the digital model are adjusted with an optimization method according to the measured input- and output-signals. The performance of the optimized digital model is evaluated with objective scores and listening tests. Two types of nonlinear reference systems are examined in this work. The first type of reference systems are dynamic range compressors like the ‘MXR Dynacomp’, the ‘Aguilar TLC’, or the ‘UREI 1176LN’. A block-based model describing a generic dynamic range compression system is chosen and an automated routine is developed to adjust it. The adapted digital models are evaluated with objective scores and a listening test is performed for the UREI 1176LN studio compressor. The second type of nonlinear systems are distortion systems like e.g. amplifiers for electric guitars. This work presents novel modeling approaches for different kinds of distortion systems from basic distortion circuits which can be found in distortion pedals for guitars to (vintage) guitar amplifiers like the ‘Marshall JCM900’, or the ‘Fender Bassman’. The linear blocks of the digital model are measured and used in the model while the nonlinear blocks are adapted with parameter optimization methods like the Levenberg–Marquardt method. The quality of the adjusted models is evaluated with objective scores and listening tests. The adjusted digital models give convincing results and can be implemented as real-time digital versions of their analog counterparts. This enables the musician to safe a snapshot of a certain sound and recall it anytime with a digital system like a VST plug-in or as a program on a dedicated hardware.
Conference Paper
Full-text available
Early analog synthesizer designs are very popular nowadays, and the discrete-time emulation of voltage-controlled oscillator (VCO) circuits is covered by a large number of virtual analog (VA) textbooks, papers and tutorials. One of the issues of well-known VCOs is their tuning instability and sensitivity to environmental conditions. For this reason, digitally-controlled oscillators were later introduce to provide stable tuning. Up to now, such designs have gained much less attention in the music processing literature. In this paper, we examine one of such designs, which is based on the Walsh-Hadamard transform. The concept was employed in the ARP Pro Soloist and in the Welson Syntex, among others. Some historical background is provided, along with a discussion on the principle, the actual implementation and a band-limited virtual analog derivation.
Article
Full-text available
A fast method is described for generating a periodic discrete‐time signal with harmonics of equal amplitude and a fundamental frequency which is not necessarily an integral fraction of the sampling frequency (as with ordinary pulse generators). Such a signal can be used as input to digital filters for the synthesis of speech and music.
Conference Paper
The bandlimited digital synthesis model of Stilson and Smith is extended with a single feed-forward comb filter. Time-varying comb filter techniques are shown to produce a variety of classic analog waveform effects, including waveform morphing, pulse-width modulation, harmonization, and frequency modulation. The techniques discussed are not guaranteed to maintain perfect bandlimiting; however, they are generally applicable to other synthesis models.
Book
This is a general introduction to the theory of computer music, giving details on sound, digital signal processing, math, and C programming. It assumes a strong knowledge of music.
Article
Various alternatives are explored for converting the Moog f our-pole Voltage Controlled Filter (VCF) to discrete-time form for digital implementation in such a way as to preserve the usefulness of its control signals. The well known bilinear transform method yields a delay-free loop and cannot be used without introducing an ad-hoc delay. Related methods from digital control theory yield realizable forms. New forms motivated by root locus studies give good results.
Article
The application of voltage-controlled oscillators, amplifiers, and filters in the composition of electronic music is discussed, and circuits for each of these instruments are described. The voltage-controlled oscillator incorporates an exponential control voltage/frequency relationship and supplies sawtooth, triangular, and pulse waveforms simultaneously. The voltage-controlled amplifier is completely balanced and direct-coupled, and has a gain range in excess of 80 db. The voltage-controlled bandpass filter employs a voltage-controlled amplifier and passive components in a closed loop to form an equivalent parallel tuned circuit with variable resonant frequency.
Technical Report
A comprehensive review of FIR (Finite Impulse Response) and allpass filter design techniques for bandlimited approximation of a fractional digital delay is presented. Emphasis is on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value. Several new approaches are proposed and numerous examples are provided that illustrate the performance of the methods.