Signal processing for acoustics and audio applications

Introduction

This section covers a selection of foundational signal processing topics, along with a summary of mathematical tools that I’ve found helpful over the years. Simple coding examples, mainly in Matlab, are included throughout.

The focus is on concepts that are useful in practical applications, such as data processing, but perhaps not 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 external resources are also available.

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

The Discrete Fourier Transform

Useful maths	An overview of mathematics useful for signal processing concepts and applications (especially the DFT)
Definition of the DFT as an inner product	Definition of the DFT as an inner product operation
Frequency axes	Understanding frequency axes for the DFT
Even- vs. odd-length DFT transforms	The DFT structure for even- vs. odd-length (real valued disctete time signals)
Amplitude scaling between the time and frequency domains	An important issue to take into account when working with real world, physical signals in the discrete frequency domain
Useful properties to keep in mind	A few of the most useful DFT properties to keep in mind when doing signal analysis tasks