  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.
