I started reading about this topic when looking for a computationally cheap way of doing frequency shifting. This is distinct from pitch shifting:
There are a lot of introductory descriptions of the Fourier transforms on the web, so to do yet another demands some justification. Here’s the justification:
Convolution is, to me at least, a really inspirational subject. Why? Because it can initially seem like DSP magic, but it’s really not hard to understand at all. To understand the Fourier transforms for example, you first need to get to grips with imaginary numbers, Euler’s equation, rotation in the complex plane, and so on. This can make it a slightly daunting subject to learn. However, to study convolution you need little more than some high-shool level maths.
A delay effect is often thought of as an “echoing” sound. However digital delay lines are also used to make other effects such as comb filters. The main concept that these effects rely on is feedback.
Low-pass filters are some of the most fundamental tools for audio processing. You don’t need to understand loads of maths to have a feel for how they work.