Guitar tone stack modeling with a neural state-space filter

In this work, we present a data-driven approach to modeling tone stack circuits in guitar amplifiers and distortion pedals. To this aim, the proposed modeling approach uses a feedforward fully connected neural network to predict the parameters of a coupled-form state-space filter, ensuring the numerical stability of the resulting time-varying system. The neural network is conditioned on the tone controls of the target tone stack and is optimized jointly with the coupled-form state-space filter to match the target frequency response. To assess the proposed approach, we model three popular tone stack schematics with both matched-order and over-parameterized filters and conduct an objective comparison with well-established approaches that use cascaded biquad filters. Results from the conducted experiments demonstrate improved accuracy of the proposed modeling approach, especially in the case of
over-parameterized state-space filters while guaranteeing numerical stability. Our method can be deployed, after training, in real-time audio processors.