Antiderivative Antialiasing for Stateful Systems

Abstract

Nonlinear systems, such as guitar distortion effects, play an important role in musical signal processing. One major problem encountered in digital nonlinear systems is aliasing distortion. Consequently, various aliasing reduction methods have been proposed in the literature. One of these is based on using the antiderivative of the nonlinearity and has proven effective, but is limited to memoryless systems. In this work, it is extended to a class of stateful systems which includes but is not limited to systems with a single one-port nonlinearity. Two examples from the realm of virtual analog modeling show its applicability to and effectiveness for commonly encountered guitar distortion effect circuits.

Antiderivative Antialiasing Techniques in Nonlinear Wave Digital Structures

“…where a[k] and b[k] are the discrete-time wave signals and F 1 is the first-order antiderivative of f. Unfortunately as outlined in [29,33] the first-order ADAA filter introduces halfsample delay in the digital structure, altering the temporization of the system. At each time-step k the non-antialiased version of the same system would have a unitary delay that temporarily stores the state, to be used at time-step k + 1.…”

“…For this reason ADAA has been applied almost exclusively to memoryless systems [29,30,32]. An extension to stateful systems has been proposed by Holters in PAPERS ADAA IN NONLINEAR WAVE DIGITAL FILTERS [33] and consists of a global parameter modification to the coefficient matrices of the state-space formulation to compensate for the additional delay introduced in the system by the ADAA filter.…”

“…Inspired by the approach in [33], in a previous work [34] we introduced a different methodology for applying pth-order ADAA to stateful Wave Digital Filters (WDFs) with a single one-port nonlinearity. Such a methodology allows us to exploit the inherent modularity property of WDFs in the design of ADAA algorithms for VA modeling.…”

22nd International Conference on Digital Audio Effects DAFx 2019 (2–6 September 2019, Birmingham, United Kingdom)

“…Antiderivative Antialiasing for Stateful Systems [8] by Martin Holters addresses a specific problem in antialiasing, which is that an effective method proposed by Parker et al [9] using the antiderivative of the integrated amplitude of a time-step in a signal is limited to memoryless systems. The paper suggests modifications to the algorithm, which extend the method to stateful systems.…”

Special Issue on Digital Audio Effects

“…Anti-aliasing methods are sometimes brought to the foreground, as part of audio signal transformations, to increase the accuracy in nonlinear signal processing. The winner of the best paper award at the DAFx 2019 conference, Antiderivative Antialiasing for Stateful Systems by Martin Holters [11], extends the recent anti-derivative method to systems with memory, which are not limited to single one-port nonlinearities. The proposed method is applied successfully to the modeling of two guitar distortion effect circuits, which are popular subjects in the DAFx community.…”