Download Distortion and Pitch Processing Using a Modal Reverberator Architecture 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.
Download Digitizing the Ibanez Weeping Demon Wah Pedal 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.
Download Design principles for lumped model discretisation using Möbius transforms 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.
Download Wave Digital Filter Adaptors for Arbitrary Topologies and Multiport Linear Elements 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.
Download Resolving Wave Digital Filters with Multiple/Multiport Nonlinearities 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.