Mathematics, signal processing and sound synthesis

To give students the maximum possible understanding and mastery of the principles of signal processing and sound synthesis, so that they can apply these principles in their future work as sound engineers. This also includes the ability to create their own versions of existing sound synthesis and sound processing tools and any missing tools that may be needed.

The signal processing course is divided into three successive phases:

Phase 1:

Introduction to the principles of signal processing, limiting mathematical developments as much as possible.

In this first phase the following elements are covered: introduction to the concepts of signals (analogue and digital), convolution and filtering of signals, problems of digitising signals, introduction to signal analysis.

Phase 2:

Filtering problems, introducing mathematical developments wherever appropriate.

This second phase covers the following elements: the case of analogue filters and digital filters (useful transforms, stability, causality, implementation, linear filtering, alterations to dynamics in digital), transforms and their properties, analogue/digital transitions and vice versa for filter templates, filter phase problems (linear phase filters, minimum phase filters, all-pass filters, phase distortion).

Phase 3:

Audio effects and practical applications of signal processing to audio.

In this final phase, students will apply the concepts introduced in the first two phases to audio signals. This application begins with the use of complementary computer tools, scilab and pure data, free clones of Matlab and Max/MSP respectively, as part of a study of the basic elements found in audio signal processing tools. This means that, depending on their progress, students will be required to program the following elements: elementary signal generator, mini audio player, mini analyser, potentiometers, pan-pot laws, crossfade, mixing of several channels, level meters, convolvers, RIF and RII filters, usual classical filters, various implementations of a variable equaliser, compression/expansion, basic digital reverberation, creation of simple psycho-acoustic test tools.

At the end of this third phase, the student should be able to independently produce prototypes of the relevant tools that they will come across in the course of their work as a sound engineer, or to develop a prototype of any tools they come across.

A good command of the following elements of mathematics is required: fractions and expansion into simple elements, differential equations, analysis of functions, complex numbers, integral calculus.

The sound synthesis course aims to :

- impart a detailed knowledge of the historical development of sound synthesis tools in the world of musical creation. (analogue and digital synthesis).

- provide an in-depth knowledge of the different sound synthesis methods.

- master the fundamental theoretical concepts of all the synthesis models used in past and present musical production (subtractive, additive, FM, wavetable, granular, sample-based, physical model, procedural, formantic, phase modulation, waveshaping, etc.).

- know how to choose the best synthesis method for a music creation project

- know how to model, prototype, programme, build and use your own sound synthesis tools.

- be able to guide composers, arrangers and instrumentalists in electroacoustic/electronic/pop productions.

Suggested bibliography :

- St. W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing (www.dspguide.com), California Technical Publishing, San Diego, California, 1999

- M. H. Hayes, Schaum's Outline of Theory and Problems of Digital Signal Processing, Schaum's Outlines, MacGraw-Hill, New York, 1999

- U. Zölzer, Digital Audio Signal Processing, John Wiley & sons, New York, 1997

- U. Zölzer, Digital Audio Effects, John Wiley & sons, New York, 2002

- L. Millot, Some clues to build a sound analysis relevant to hearing (convention paper 6041), in 116th AES Convention, Audio Engineering Society, Berlin 2004

- L. Millot, Bases de Traitement du Signal : Introduction aux principes, volume I (65 pages)

- L. Millot, Bases de Traitement du Signal : Problèmes de filtrage, volume II (74 pages)

FSMS 1-2

- Continuous assessment and completion of a pure data programming mini-project dealing with a theme borrowed from the fields of signal processing, digital audio, acoustics, psycho-acoustics and applied electroacoustics and/or their interaction.

- Design of a sound synthesis module and production of its prototype (virtual synthesiser, plug-in, Max-MSP object, VCV patch), sound production (composition and/or recreation of a work from the electroacoustic/electronic/synthesised pop repertoire).