9. Filters

So far, this book has mostly studied synthesis: techniques like additive and modulation synthesis that create sound from scratch. But computer music is as much about sculpting existing sound as it is about creating new sound. In this chapter we study filters, the tools we use to process a signal we already have, whether it came from a synthesizer, a microphone, or another filter.

This chapter was heavily inspired by the treatment of convolution in Digital Signals Theory [McF23], and we borrow much of its notation. Filter analysis and design is an extraordinarily deep subject, and we will only take a cursory look here. Readers who want to go further should consult Julius Smith’s Introduction to Digital Filters [Smi07b], a thorough and audio-focused treatment.