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

TL;DR

This paper introduces a neural network-based method for directly designing biquad filter cascades by sampling random polynomials, achieving faster and more accurate filter coefficient estimation compared to traditional techniques.

Contribution

It presents a novel deep learning approach that maps target responses to filter coefficients, trained on diverse random filters for improved generalization and efficiency.

Findings

Faster filter design compared to traditional methods.

More accurate filter coefficient estimation.

Better generalization to real-world filters.

Abstract

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.