An improved virtual analog model of the Moog ladder filter

D’Angelo, Stefano; Välimäki, Vesa

doi:10.1109/icassp.2013.6637744

Cited by 5 publications

(15 citation statements)

References 8 publications

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“…Therefore, by the superposition principle, equating (9) and (11), imposing , and solving for leads to (12) which in turn implies that for the other input it must be (13) Finally, the proposed method overall consists in replacing a non-computable filter expressed in the form (8) with an analogous computable filter of form (10) such that the frequency response of the original implicitly-defined filter, linearized around a chosen operating point , is preserved in the analogous explicitly-defined filter, linearized around the same operating point. This substitution is possible if can be linearized around and is defined for all its input values in (10), and when , , , and satisfy (12) and (13).…”

Section: A Problem Statementmentioning

confidence: 99%

“…This particular linearization strategy allows to conveniently represent IIR-type approximations with a finite number of coefficients, a property which will prove to be useful later on. The linearized filter is therefore represented in the domain by (9) Applying the same approximation to the analogous filter described by (10) and depicted in Fig. 2(b), where denotes convolution, and , , and are the discrete-time-domain impulse responses of , , and , respectively, results in (11) with .…”

Section: A Problem Statementmentioning

confidence: 99%

“…Recent attempts to develop such a model [7], [10] add fictitious unit delays to resolve this problem, thus compromising the linear response of the resulting digital filter around its operating point and therefore requiring ad-hoc parameter compensation strategies. Furthermore, [25] discusses the possibility of obtaining different frequency response modes (e.g., high-pass, band-pass, notch) through simple mixing of the outputs of individual ladder stages, hence making it desirable for a digital model to be able to provide such outputs.…”

Section: Implementation Of Delay-free Loopsmentioning

confidence: 99%

“…Section IV derives the explicit digital model of the circuit. Section V evaluates the proposed implementation and compares it to those developed in [7] and [10], as well as with a SPICE simulation [21] of the circuit. The paper eventually concludes with Section VI.…”

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confidence: 99%

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Generalized Moog Ladder Filter: Part II–Explicit Nonlinear Model through a Novel Delay-Free Loop Implementation Method

D’Angelo

Välimäki

2014

IEEE/ACM Trans. Audio Speech Lang. Process.

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One of the most critical aspects of virtual analog simulation of circuits for music production consists in accurate reproduction of their nonlinear behavior, yet this goal is in many cases difficult to achieve due to the presence of implicit differential equations in circuit models, since they naturally map to delay-free loops in the digital domain. This paper presents a novel and general method for non-iteratively implementing these loops in such a way that the linear response around a chosen operating point is preserved, the topology is minimally affected, and transformation of nonlinearities is not required. This technique is then applied to a generalized model of the Moog ladder filter, resulting in an implementation that outperforms its predecessors with only a modest computational load penalty. This digital version of the filter is shown to offer strong stability guarantees w.r.t. parameter variation, allows the extraction of different frequency response modes by simple mixing of individual ladder stage outputs, and is suitable for real-time sound synthesis and audio effects processing.

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Section: A Problem Statementmentioning

confidence: 99%

Section: A Problem Statementmentioning

confidence: 99%

Section: Implementation Of Delay-free Loopsmentioning

confidence: 99%

mentioning

confidence: 99%

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Generalized Moog Ladder Filter: Part II–Explicit Nonlinear Model through a Novel Delay-Free Loop Implementation Method

D’Angelo

Välimäki

2014

IEEE/ACM Trans. Audio Speech Lang. Process.

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“…This filter has been subject to numerous studies since [1]. Most digitizations use the bilinear transform [31] or some similar procedure [32] to discretize the linear portion (small signal response) of the analog transfer function. As mentioned above, since there is feedback in the circuit, digitizations of this filter often include unit sample feedback (z −1 ).…”

Section: The Moog Ladder Filtermentioning

confidence: 99%

Dynamical Systems for Audio Synthesis: Embracing Nonlinearities and Delay-Free Loops

Medine

2016

Applied Sciences

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Many systems featuring nonlinearities and delay-free loops are of interest in digital audio, particularly in virtual analog and physical modeling applications. Many of these systems can be posed as systems of implicitly related ordinary differential equations. Provided each equation in the network is itself an explicit one, straightforward numerical solvers may be employed to compute the output of such systems without resorting to linearization or matrix inversions for every parameter change. This is a cheap and effective means for synthesizing delay-free, nonlinear systems without resorting to large lookup tables, iterative methods, or the insertion of fictitious delay and is therefor suitable for real-time applications. Several examples are shown to illustrate the efficacy of this approach.

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Modeling and measuring a Moog voltage-controlled filter

Paschou

Esqueda

Välimäki

et al. 2017

2017 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC)

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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.

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An improved virtual analog model of the Moog ladder filter

Cited by 5 publications

References 8 publications

Generalized Moog Ladder Filter: Part II–Explicit Nonlinear Model through a Novel Delay-Free Loop Implementation Method

Generalized Moog Ladder Filter: Part II–Explicit Nonlinear Model through a Novel Delay-Free Loop Implementation Method

Dynamical Systems for Audio Synthesis: Embracing Nonlinearities and Delay-Free Loops

Modeling and measuring a Moog voltage-controlled filter

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