Module code: TON1023

Module Overview

This module lays the mathematical foundation that you will need for analyising, manipulating, or synthesising audio signals. It is the mathematical backbone of the programme and the concepts that you learn in this module will be encountered and applied not only in a wide range of modules across all years, but also in your professional practice. An understanding of audio from a mathematical perspective will give you a deeper insight into the behaviour of sound and will equip you with the vocabulary you need to communicate about specific features of audio. This module starts from the foundations of what is a complex number and slowly builds its way up toward to audio signal analysis using Fourier transforms and spectrograms. 

Module provider

Music and Media

Module Leader

DE SENA Enzo (Music & Med)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

Module cap (Maximum number of students): N/A

Overall student workload

Workshop Hours: 12

Independent Learning Hours: 92

Lecture Hours: 18

Seminar Hours: 3

Guided Learning: 5

Captured Content: 20

Module Availability

Year long

Prerequisites / Co-requisites

TON1024 Computer Systems or FVP1013 Computer Systems

Module content

Indicative content includes:

  • Signals

  • Complex numbers

  • Phasors

  • Fourier series

  • Fourier transform

  • Sampling

  • Frequency analysis of discrete-time signals.

  • Spectrograms

Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test Computer-based in-class test (3 hours) 35
School-timetabled exam/test In-class test (3 hours) 35
Coursework Coursework 30

Alternative Assessment


Assessment Strategy

The assessment strategy is designed to provide you with the opportunity to demonstrate and develop your knowledge and understanding of audio signal processing.

Thus, the summative assessment for this module consists of:

  • one computer-based in-class test (addresses learning outcomes 1-2);

  • one in-class test (addesses learning outcomes 1-3); and

  • Coursework – consisting of mathematical problems and programming tasks (addresses learning outcomes 4-8).

Formative assessment

Formative assessment and feedback will be provided in tutorials as required, during in-class exercises, and in the form of regular revision questions in lectures.


You will receive written feedback on your coursework. You will also receive verbal feedback in lectures via revision questions and in-class discussions.

Module aims

  • To develop your understanding of audio signals from a mathematical point of view and advance your mathematical skills so that you are fully equipped to tackle several modules throughout the programme such as Acoustics, Electroacoustics, Computer Systems, Audio Signal Processing & Synthesis, and Audio Engineering.

Learning outcomes

Attributes Developed
001 Recognise different types of signals and perform simple operations on signals in order to manipulate them with respect to time and amplitude. KC
002 Understand and develop mathematical skills in working with complex numbers. These include performing basic arithmetic operations, plotting them in the complex plane, recognising and converting between Cartesian, polar, and exponential forms. KC
003 Explain and illustrate how simple harmonic signals can be represented as complex phasors. Perform addition of sinusoids using phasors. KC
004 Explain how a continuous-time signal is sampled to obtain a discrete-time signal. Explain the concept of aliasing and how it relates to the Nyquist-Shannon sampling theorem. KCT
005 Use the Fourier series and the Fourier transform to represent a signal in both the time domain and the frequency domain. KC
006 Use the discrete-time Fourier transform and the short-time Fourier transform to analyse a discrete-time signal. KCT
007 Use computer programming code to analyse a discrete-time signal in the frequency domain and/or time-frequency domain. KCPT
008 Apply computer programming and problem-solving skills successfully to audio-related tasks PT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to: develop your skills and knowledge in mathematics and audio signal analysis, allowing modules in later semesters to build on this.

The learning and teaching methods include:

  • Lectures

  • Seminar

  • Workshops

  • Captured content and guided learning

  • Coursework assignments and feedback

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list
Upon accessing the reading list, please search for the module using the module code: TON1023

Other information

Digital capabilities: This module will enable you to develop digital capabilities such as being able to do basic audio signal analysis using Python, i.e. implementation of mathematical concepts using computer code.

Employability: You will develop professional skills in by becoming more familiar with the mathematical/technical aspects of audio that you record, mix, and/or produce in your professional career. You will also develop some of the mathematical vocabulary used to describe audio and use this to communicate problems effectively and work toward solutions in a professional environment such as a recording/production studio.

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Music and Sound Recording (Tonmeister) BSc (Hons)(CORE) Year-long Core Each unit of assessment must be passed at 40% to pass the module
Music and Sound Recording (Tonmeister) BMus (Hons)(CORE) Year-long Core Each unit of assessment must be passed at 40% to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.