Antiderivative Antialiasing for Stateful Systems

Martin Holters

doi:10.3390/app10010020

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.

Highlights

Nonlinear systems play an important role in musical signal processing
One major problem encountered in digital nonlinear systems, whether designed from scratch or derived by virtual analog modeling is aliasing distortion
The half-sample delay introduced by the method of [10] becomes problematic if the nonlinearity is embedded in the feedback loop of a stateful system

Summary

Introduction

Nonlinear systems play an important role in musical signal processing. In particular, there are many effects categorized as overdrive, distortion, or fuzz, whose primary objective is to introduce harmonic distortion to enrich the signal. The nonlinear behavior is combined with (linear) filtering to spectrally shape the output signal or to make the amount of introduced distortion frequency-dependent. While many of these systems were originally designed in the analog domain, naturally, there is interest in deriving digital models for them, e.g., [1,2,3,4]. Various alternatives have been proposed, e.g., [5,6,7,8,9,10,11] These methods, usually come with certain limitations, most commonly the restriction to memoryless systems. The main differences are the generalization of the method to the case of multiple parallel nonlinear functions and an added discussion of nonlinearities with vector-valued input

Antiderivative-Based Aliasing Reduction for Memoryless Nonlinear Systems

Extension to Stateful Systems

Computational Cost

Diode Clipper

Tube Screamer-Like Distortion Circuit

Conclusions and Outlook