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.
Wavefolders are a particular class of nonlinear waveshaping circuits, and a staple of the "West Coast" tradition of analog sound synthesis. In this paper, we present analyses of two popular wavefolding circuits-the Lockhart and Serge wavefolders-and show that they achieve a very similar audio effect. We digitally model the input-output relationship of both circuits using the Lambert-W function, and examine their time-and frequency-domain behavior. To ameliorate the issue of aliasing distortion introduced by the nonlinear nature of wavefolding, we propose the use of the first-order antiderivative method. This method allows us to implement the proposed digital models in real-time without having to resort to high oversampling factors. The practical synthesis usage of both circuits is discussed by considering the case of multiple wavefolder stages arranged in series.
Spring reverberation is a sonically unique form of artificial reverberation, desirable as an effect distinct from that of more conventional reverberation. Recent work has introduced a parametric model of spring reverberation based on long chains of allpass filters. Such chains can be computationally expensive. In this paper, we propose a number of modifications to these structures, via the application of multirate and multiband methods. These changes reduce the computational complexity of the structure to one third of its original cost and make the effect more suitable for real-time applications.
The digital emulation of analog audio effects and synthesis components, through the simulation of lumped circuit components has seen a large amount of activity in recent years; electromechanical effects have seen rather less, primarily because they employ distributed mechanical components, which are not easily dealt with in a rigorous manner using typical audio processing constructs such as delay lines and digital filters. Spring reverberation is an example of such a system-a spring exhibits complex, highly dispersive behavior, including coupling between different types of wave propagation (longitudinal and transverse). Standard numerical techniques, such as finite difference schemes are a good match to such a problem, but require specialized design and analysis techniques in the context of audio processing. A model of helical spring vibration is introduced, along with a family of finite difference schemes suitable for time domain simulation. Various topics are covered, including numerical stability conditions, tuning of the scheme to the response of the model system, numerical boundary conditions and connection to an excitation and readout, implementation details, as well as computational requirements. Simulation results are presented, and full energy-based stability analysis appears in an Appendix.
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