# Direct design of biquad filter cascades with deep learning by sampling random polynomials

arXiv: https://arxiv.org/abs/2110.03691 · HTML: https://mlsanity.com/paper/2110.03691/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 40 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Lightweight and interpretable neural modeling of an audio distortion effect using hyperconditioned differentiable biquads](https://mlsanity.com/paper/2103.08709/) (2021)

## Built on by (most cited first, 8 of 8)

- [Differentiable All-pole Filters for Time-varying Audio Systems](https://mlsanity.com/paper/2404.07970/) (2024)
- [Rigid-Body Sound Synthesis with Differentiable Modal Resonators](https://mlsanity.com/paper/2210.15306/) (2022)
- [Adoption of AI Technology in the Music Mixing Workflow: An Investigation](https://mlsanity.com/paper/2304.03407/) (2023)
- [Real-time Percussive Technique Recognition and Embedding Learning for the Acoustic Guitar](https://mlsanity.com/paper/2307.07426/) (2023)
- [Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods](https://mlsanity.com/paper/2408.16650/) (2024)
- [Automatic Equalization for Individual Instrument Tracks Using Convolutional Neural Networks](https://mlsanity.com/paper/2407.16691/) (2024)
- [An Interpretable, Controllable Time-Varying IIR Denoiser for On-Device Assistive Hearing](https://mlsanity.com/paper/2603.02794/) (2026)
- [Diff2Mix: Controllable Music Mixing via Diffusion Models and Differentiable Audio Effects](https://mlsanity.com/paper/2608.05442/) (2026)

## Abstract (arXiv)

Designing infinite impulse response filters to match an arbitrary magnitude response requires specialized techniques. Methods like modified Yule-Walker are relatively efficient, but may not be sufficiently accurate in matching high order responses. On the other hand, iterative optimization techniques often enable superior performance, but come at the cost of longer run-times and are sensitive to initial conditions, requiring manual tuning. In this work, we address some of these limitations by learning a direct mapping from the target magnitude response to the filter coefficient space with a neural network trained on millions of random filters. We demonstrate our approach enables both fast and accurate estimation of filter coefficients given a desired response. We investigate training with different families of random filters, and find training with a variety of filter families enables better generalization when estimating real-world filters, using head-related transfer functions and guitar cabinets as case studies. We compare our method against existing methods including modified Yule-Walker and gradient descent and show our approach is, on average, both faster and more accurate.