Signals and signal processing in acoustics and audio applications


This section covers a selection of foundational signal processing principles, along with a summary of select mathematical tools that I’ve found helpful in developing an intuitive understanding of the subject. Simple coding examples, mainly in Matlab, are included throughout.

The objective is to focus on concepts that are useful in practice, and perhaps not always obvious to those learning for the first time. In short, it’s a summary of things I find useful to remember (but sometimes forget).

Links to a few of my favourite further resources in this area are available elsewhere.

Acoustic and electrical signals

Acoustic signals: Basic principles – Overview of basic principles, terminology, and concepts that we use when talking about acoustic and audio signals

Electrical signals: Levels and power – Overview of basic principles, terminology, and concepts used for electrical signals (particularly where they are transduced from acoustic signals)

The Discrete Fourier Transform

The Discrete Fourier Transform: Useful maths – An overview of mathematics useful for signal processing concepts and applications (the Discrete Fourier Transform, in particular)

The Discrete Fourier Transform: Definition as an inner product – Definition of the DFT as an inner product operation

The Discrete Fourier Transform: Frequency axes – How to conceptualise and use frequency axes for the DFT

The Discrete Fourier Transform: Even and odd transform sizes N (real signals) – Examining the DFT structure for odd/even N and real valued discrete time signals

The Discrete Fourier Transform: Signal length (Euclidian norm) considerations – An important issue to take into account when working with real world, physical signals in the discrete frequency domain

The Discrete Fourier Transform: Useful properties to keep in mind – A few of the most useful DFT properties to keep in mind when doing signal analysis tasks