In this paper we present an approach to using traditional digital IIR filter structures inside deep-learning networks trained using backpropagation. We establish the link between such structures and recurrent neural networks. Three different differentiable IIR filter topologies are presented and compared against each other and an established baseline. Additionally, a simple Wiener-Hammerstein model using differentiable IIRs as its filtering component is presented and trained on a guitar signal played through a Boss DS-1 guitar pedal.

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Component-wise circuit modeling, also known as “white-box” modeling, is a well established and much discussed technique in virtual analog modeling. This approach is generally limited in accuracy by lack of access to the exact component values present in a real example of the circuit. In this paper we show how this problem can be addressed by implementing the white-box model in a differentiable form, and allowing approximate component values to be learned from raw input–output audio measured from a real device.

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