Direct design of biquad filter cascades with deep learning by sampling random polynomials
This work addresses the limitations of slow and sensitive iterative optimization methods for filter design, offering a more efficient and accurate solution for audio and signal processing applications.
The paper tackles the problem of designing infinite impulse response filters to match arbitrary magnitude responses by learning a direct mapping from target responses to filter coefficients using a neural network trained on random filters. The result is a method that is, on average, both faster and more accurate than existing techniques like modified Yule-Walker and gradient descent, as demonstrated in case studies with head-related transfer functions and guitar cabinets.
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.