Digital models of analog circuits for musical audio production: A review of techniques and library for automated circuit solving

Abstract

In music production, many recording and mixing engineers prefer to use analog equipment as a matter of perceptual preference. Digital models of analog circuits have the potential to achieve similar perceptual qualities as hardware without the drawbacks of cost, maintenance, and availability. Many different techniques of system modeling are used in music production software, ranging on a spectrum from “black-box modeling” to “white-box modeling.” In black-box modeling, the analog system is modeled as a processing block which maps an input signal to an output signal. Examples include the linear impulse response, adaptive filters, Volterra series, and Weiner-Hammerstein models. In white-box modeling, each individual component of the analog circuit is modeled as part of the overall system. Examples include wave digital filters, state-space modeling, and modified nodal analysis. Various other techniques exist on the spectrum between these two types, using some combination of each. One example is Virtual Analog Filtering based on the Topology Preserving Transform. Machine Learning techniques have also had an important role in advancing the accuracy of digital modeling. Lastly, the “Point to Point Library,” developed by the author, will be demonstrated. This MATLAB and C + + library performs automated circuit solving for modeling audio effects.