Digital Filter Modelling

Linear time-invariant (LTI) digital filters are the workhorses of audio signal processing. They are an indispensable component in algorithms from audio coding to artificial reverberation and, of course, audio synthesisers of many kinds.

In this section, we assume familiarity with the basics of digital filters. For example, terms like impulse response, z-transform, and frequency response should be familiar to you. We refer readers who would like to improve their knowledge on the subject to Julius O. Smith III’s excellent online textbook [Smi07].

The section starts by introducing differentiable formulations of finite impulse response (FIR) filters, and uses these to create a time-varying filtered noise synthesiser. Then, we turn our attention to infinite impulse response filters, discussing their advantages and drawbacks, and presenting two approaches to differentiable implementation.