Fundamentals

In digital audio signal processing and digital audio effects, we are primarily concerned with systems that take a discrete, uniformly sampled audio signal, process it, and produce a discrete, uniformly sampled output audio signal. Therefore, we start by introducing some fundamental properties of sound that are frequently used, then how we represent it as a digital signal, and then we move on to how we describe the systems that act on and modify such signals. This is not meant to give a detailed overview of digital signal processing, which would involve discussion of continuous time signals, infinite signals, and mathematical relationships. Rather, we intend to focus on just the type of signals and systems that are encountered in audio effects, and on the most useful properties and representations. Having said that, this is also intended to be self-contained. Little prior knowledge is assumed, and it should not be necessary to refer to more detailed discussions in other texts in order to understand these concepts.