A reverberator based on a room response modal analysis is adapted to produce distortion, pitch and time manipulation effects, as well as gated and iterated reverberation. The so-called “modal reverberator” is a parallel collection of resonant filters, with resonance frequencies and dampings tuned to the modal frequencies and decay times of the space or object being simulated. Here, the resonant filters are implemented as cascades of heterodyning, smoothing, and modulation steps, forming a type of analysis/synthesis architecture. By applying memoryless nonlinearities to the modulating sinusoids, distortion effects are produced, including distortion without intermodulation products. By using different frequencies for the heterodyning and associated modulation operations, pitch manipulation effects are generated, including pitch shifting and spectral “inversion.” By resampling the smoothing filter output, the signal time axis is stretched without introducing pitch changes. As these effects are integrated into a reverberator architecture, reverberation controls such as decay time can be used produce novel effects having some of the sonic characteristics of reverberation.

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Being able to transform an analog audio circuit into a digital model is a big deal for musicians, producers, and circuit benders alike. In this paper, we address some of the issues that arise when attempting to make such a digital model. Using the canonical state variable filter as the main point of interest in our schematic, we will walk through the process of making a signal flow graph, obtaining a transfer function, and making a usable digital filter. Additionally, we will address an issue that is common throughout virtual analog literature; reducing the very large expressions for each of the filter coefficients. Using a novel factoring algorithm, we show that these expressions can be reduced from thousands of operations down to tens of operations.

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Computational modelling of audio systems commonly involves discretising lumped models. The properties of common discretisation schemes are typically derived through analysis of how the imaginary axis on the Laplace-transform s-plane maps onto the Ztransform z-plane and the implied stability regions. This analysis ignores some important considerations regarding the mapping of individual poles, in particular the case of highly-damped poles. In this paper, we analyse the properties of an extended class of discretisations based on Möbius transforms, both as mappings and discretisation schemes. We analyse and extend the concept of frequency warping, well-known in the context of the bilinear transform, and we characterise the relationship between the damping and frequencies of poles in the s- and z-planes. We present and analyse several design criteria (damping monotonicity, stability) corresponding to desirable properties of the discretised system. Satisfying these criteria involves selecting appropriate transforms based on the pole structure of the system on the s-plane. These theoretical developments are finally illustrated on a diode clipper nonlinear model.

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We present a Modified-Nodal-Analysis-derived method for developing Wave Digital Filter (WDF) adaptors corresponding to complicated (non-series/parallel) topologies that may include multiport linear elements (e.g. controlled sources and transformers). A second method resolves noncomputable (non-tree-like) arrangements of series/parallel adaptors. As with the familiar 3-port series and parallel adaptors, one port of each derived adaptor may be rendered reflection-free, making it acceptable for inclusion in a standard WDF tree. With these techniques, the class of acceptable reference circuits for WDF modeling is greatly expanded. This is demonstrated by case studies on circuits which were previously intractable with WDF methods: the Bassman tone stack and Tube Screamer tone/volume stage.

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We present a novel framework for developing Wave Digital Filter (WDF) models from reference circuits with multiple/multiport nonlinearities. Collecting all nonlinearities into a vector at the root of a WDF tree bypasses the traditional WDF limitation to a single nonlinearity. The resulting system has a complicated scattering relationship between the nonlinearity ports and the ports of the rest of the (linear) circuit, which can be solved by a Modified-NodalAnalysis-derived method. For computability reasons, the scattering and vector nonlinearity must be solved jointly; we suggest a derivative of the K-method. This novel framework significantly expands the class of appropriate WDF reference circuits. A case study on a clipping stage from the Big Muff Pi distortion pedal involves both a transistor and a diode pair. Since it is intractable with standard WDF methods, its successful simulation demonstrates the usefulness of the novel framework.

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Wave Digital Filters were developed to discretize linear time invariant lumped systems, particularly electronic circuits. The timeinvariant assumption is baked into the underlying theory and becomes problematic when simulating audio circuits that are by nature time-varying. We present extensions to WDF theory that incorporate proper numerical schemes, allowing for the accurate simulation of time-varying systems. We present generalized continuous-time models of reactive components that encapsulate the time-varying lossless models presented by Fettweis, the circuit-theoretic time-varying models, as well as traditional LTI models as special cases. Models of timevarying reactive components are valuable tools to have when modeling circuits containing variable capacitors or inductors or electrical devices such as condenser microphones. A power metric is derived and the model is discretized using the alpha-transform numerical scheme and parametric wave definition. Case studies of circuits containing time-varying resistance and capacitance are presented and help to validate the proposed generalized continuous-time model and discretization.

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A family of spectrally-flat noise sequences called “Velvet Noise” have found use in reverb modeling, decorrelation, speech synthesis, and abstract sound synthesis. These noise sequences are ternary—they consist of only the values −1, 0, and +1. They are also sparse in time, with pulse density being their main design parameter, and at typical audio sampling rates need only several thousand non-zero samples per second to sound “smooth.” This paper proposes “Crushed Velvet Noise” (CVN) generalizations to the classic family of Velvet Noise sequences including “Original Velvet Noise” (OVN), “Additive Random Noise” (ARN), and “Totally Random Noise” (TRN). In these generalizations, the probability of getting a positive or negative impulse is a free parameter. Manipulating this probability gives Crushed OVN and ARN low-shelf spectra rather than the flat spectra of standard Velvet Noise, while the spectrum of Crushed TRN is still flat. This new family of noise sequences is still ternary and sparse in time. However, pulse density now controls the shelf cutoff frequency, and the distribution of polarities controls the shelf depth. Crushed Velvet Noise sequences with pulses of only a single polarity are particularly useful in a niche style of music called “1- bit music”: music with a binary waveform consisting of only 0s and 1s. We propose Crushed Velvet Noise as a valuable tool in 1- bit music composition, where its sparsity allows for good approximations to operations, such as addition, which are impossible for signals in general in the 1-bit domain.

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Memoryless waveshapers are commonly used in audio signal processing. In discrete time, they suffer from well-known aliasing artifacts. We present a method for applying antiderivative antialising (ADAA), which mitigates aliasing, to any waveshaping function that can be represented as a piecewise polynomial. Specifically, we treat the special case of a piecewise linear waveshaper. Furthermore, we introduce a method for for replacing the sharp corners and jump discontinuities in any piecewise linear waveshaper with smoothed polynomial approximations, whose derivatives match the adjacent line segments up to a specified order. This piecewise polynomial can again be antialiased as a special case of the general piecewise polynomial. Especially when combined with light oversampling, these techniques are effective at reducing aliasing and the proposed method for rounding corners in piecewise linear waveshapers can also create more “realistic” analog-style waveshapers than standard piecewise linear functions.

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