  In this work, we propose using differentiable cascaded biquads to model an
audio distortion effect. We extend trainable infinite impulse response (IIR)
filters to the hyperconditioned case, in which a transformation is learned to
directly map external parameters of the distortion effect to its internal
filter and gain parameters, along with activations necessary to ensure filter
stability. We propose a novel, efficient training scheme of IIR filters by
means of a Fourier transform. Our models have significantly fewer parameters
and reduced complexity relative to more traditional black-box neural audio
effect modeling methodologies using finite impulse response filters. Our
smallest, best-performing model adequately models a BOSS MT-2 pedal at 44.1
kHz, using a total of 40 biquads and only 210 parameters. Its model parameters
are interpretable, can be related back to the original analog audio circuit,
and can even be intuitively altered by machine learning non-specialists after
model training. Quantitative and qualitative results illustrate the
effectiveness of the proposed method.
