Audio Effects : Theory, Implementation and Application book cover
1st Edition

Audio Effects
Theory, Implementation and Application

ISBN 9780429097232
Published October 23, 2014 by CRC Press
367 Pages

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Book Description

Audio Effects: Theory, Implementation and Application explores digital audio effects relevant to audio signal processing and music informatics. It supplies fundamental background information on digital signal processing, focusing on audio-specific aspects that constitute the building block on which audio effects are developed. The text integrates theory and practice, relating technical implementation to musical implications. It can be used to gain an understanding of the operation of existing audio effects or to create new ones. In addition to delivering detailed coverage of common (and unusual) audio effects, the book discusses current digital audio standards, most notably VST and AudioUnit. Source code is provided in C/C++ and implemented as audio effect plug-ins with accompanying sound samples. Each section of the book includes study questions, anecdotes from the history of music technology, and examples that offer valuable real-world insight, making this an ideal resource for researchers and for students moving directly into industry.

Table of Contents


About the Authors

Aim and Scope of Book

Introduction and Fundamentals

Understanding Sound and Digital Audio

Working with Decibels

Level Measurements

Representing and Understanding Digital Signals

Representing Complex Numbers

Frequency and Time-Frequency Representations


Modifying and Processing Digital Signals

The Z Transform and Filter Representation

Digital Filter Example

Nonlinear and Time-Varying Effects

Delay Line Effects



Basic Delay

Delay with Feedback

Other Delay Types

Slapback Delay

Multitap Delay

Ping-Pong Delay


Basic Delay


Delay Line Interpolation

Code Example


Vibrato Simulation




Low-Frequency Oscillator


Code Example




Principle of Operation

Basic Flanger

Low-Frequency Oscillator

Flanger with Feedback

Stereo Flanging


Common Parameters

Depth (or Mix)

Delay and Sweep Width

Speed and Waveform

Feedback (or Regeneration)

Inverted Mode (or Phase)


Buffer Allocation


Code Example


Resonant Pitches

Avoiding Disappearing Instruments

Flanging versus Chorus



Basic Chorus

Low-Frequency Oscillator

Pitch-Shifting in the Chorus

Multivoice Chorus

Stereo Chorus


Common Parameters

Depth (or Mix)

Delay and Sweep Width

Speed and Waveform

Number of Voices

Other Variations

Summary: Flanger and Chorus Compared

Filter Design

Filter Construction and Transformation

Simple, Prototype Low-Pass Filter

High-Order Prototype Low-Pass Filter

Changing the Gain at the Cutoff Frequency

Shifting the Cutoff Frequency

Creating a Shelving Filter

Inverting the Magnitude Response

Simple Low-Pass to Band Pass Transformation

Popular IIR Filter Design

Low Pass

High Pass

Low Shelf

High Shelf

Gain at Bandwidth

Band Pass Filters

Band Stop Filters

Peaking and Notch Filters

The Allpass Filter

Applications of Filter Fundamentals

Exponential Moving Average Filter

Loudspeaker Crossovers

Filter Effects



Two-Knob Tone Controls

Three-Knob Tone Controls

Presence Control

Loudness Control

Graphic Equalizers

Bands in a Graphic Equalizer

Parametric Equalizers



General Notes

Tone Control Architecture

Calculating Filter Coefficients

Presence and Loudness Architecture

Graphic Equalizer Architecture

Parametric Equalizer Architecture

Code Example


Graphic Equalizer Application

Parametric Equalizer Application



Basis in Speech

Basic Wah-Wah



Other Variations


Filter Design

Low-Frequency Oscillator

Envelope Follower

Analog Emulation



Basic Phaser

Low-Frequency Oscillator

Phaser with Feedback

Stereo Phaser


Allpass Filter Calculation

Alternate Implementation

LFO Waveform

Analog and Digital Implementations

Common Parameters

Code Example

Amplitude Modulation







Audio Rate and Control Rate

Code Example

Ring Modulation


Modulation in the Frequency Domain


w-Frequency Oscillator



Code Example


Dynamics Processing

Dynamic Range Compression


Compressor Controls

Signal Paths

The Gain Stage

The Gain Computer

Level Detection

RMS Detector

Peak Detector

Level-Corrected Peak Detectors


Feedback and Feedforward Design

An Alternate Digital Feedback Compressor

Detector Placement

Code Example




Noise Gates and Expanders

Theory and Implementation


Overdrive, Distortion, and Fuzz


Characteristic Curve

Hard and Soft Clipping

Input Gain

Symmetry and Rectification

Harmonic Distortion

Intermodulation Distortion

Analog Emulation


Basic Implementation

Aliasing and Oversampling


Common Parameters

Tube Sound Distortion

Code Example


Expressivity and Spectral Content


Comparison with Compression

The Phase Vocoder

Phase Vocoder Theory



Analysis: Fast Fourier Transform

Interpreting Frequency Domain Data

Target Phase, Phase Deviation, and Instantaneous Frequency

Synthesis: Inverse Fast Fourier Transform


Filterbank Analysis Variant

Oscillator Bank Reconstruction Variant

Phase Vocoder Effects


Robotization Code Example


Whisperization Code Example

Time Scaling

Time-Scaling Resynthesis

Pitch Shifting

Code Example

Phase Vocoder Artifacts

Spatial Audio




Vector Base Amplitude Panning


Wave Field Synthesis

The Head-Related Transfer Function

ITD Model

ILD Model


Joint Panorama and Precedence

Ambisonics and Its Relationship to VBAP

Implementation of WFS

HRTF Calculation


Transparent Amplification

Surround Sound

Sound Reproduction Using HRTFs

The Doppler Effect

A Familiar Example

Derivation of the Doppler Effect

Simple Derivation of the Basic Doppler Effect

General Derivation of the Doppler Effect

Simplifications and Approximations


Time-Varying Delay Line Reads

Multiple Write Pointers

Code Example




Sabine and Norris–Eyring Equations

Direct and Reverberant Sound Fields


Algorithmic Reverb

Schroeder’s Reverberator

Moorer’s Reverberator

Generating Reverberation with the Image Source Method


The Image Source Model

Modeling Reflections as Virtual Sources

Locating the Virtual Sources

The Impulse Response for a Virtual Source

Convolutional Reverb

Convolution and Fast Convolution

Block-Based Convolution

Physical Meaning

Other Approaches


Why Use Reverb?

Stereo Reverb

Gated Reverb

Reverse Reverb

Common Parameters

Audio Production

The Mixing Console

The Channel Section

The Master Section

Metering and Monitoring

Basic Mixing Console

Signal Flow and Routing

Inserts for Processors, Auxiliary Sends for Effects

Subgroup and Grouping

Digital versus Analog


Digital User Interface Design

Sound Quality

Do You Need to Decide?

Software Mixers

Digital Audio Workstations

Common Functionality of Computer-Based DAWs

MIDI and Sequencers

Audio Effect Ordering

Noise Gates

Compressors and Noise Gates

Compression and EQ

Reverb and Flanger

Reverb and Vibrato

Delay Line Effects


Order Summary

Combinations of Audio Effects

Parallel Effects and Parallel Compression



De-Esser Sidechain Compression for Mastering

Multiband Compression

Dynamic Equalization

Combining LFOs with Other Effects


Building Audio Effect Plug-Ins

Plug-In Basics

Programming Language

Plug-In Properties

The JUCE Framework

Theory of Operation

Callback Function

Managing Parameters

Initialization and Cleanup

Preserving State

Example: Building a Delay Effect in JUCE

Required Software

Creating a New Plug-In in JUCE

Opening Example Plug-Ins

File Overview


Declaration and Methods



Audio Callback


Managing Parameters





Managing Parameters




Advanced Topics

Efficiency Considerations

Thread Safety




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Joshua D. Reiss, Ph.D, is a senior lecturer with the Centre for Digital Music in the School of Electronic Engineering and Computer Science at Queen Mary University of London. He has bachelor’s degrees in both physics and mathematics, and earned his Ph.D in physics from the Georgia Institute of Technology. He is a member of the Board of Governors of the Audio Engineering Society, and co-founder of the company MixGenius. Dr. Reiss has published more than 100 scientific papers and serves on several steering and technical committees. He has investigated music retrieval systems, time scaling and pitch shifting techniques, polyphonic music transcription, loudspeaker design, automatic mixing for live sound, and digital audio effects. His primary focus of research, which ties together many of the above topics, is on the use of state-of-the-art signal processing techniques for professional sound engineering.

Andrew P. McPherson, Ph.D, joined Queen Mary University of London as a lecturer in the Centre for Digital Music in September 2011. He holds a Ph.D in music composition from the University of Pennsylvania and an M.Eng in electrical engineering from the Massachusetts Institute of Technology. Prior to joining Queen Mary, he was a postdoc in the Music Entertainment Technology Laboratory at Drexel University, supported by a Computing Innovation Fellowship from the Computing Research Association and the National Science Foundation (NSF). Dr. McPherson’s current research topics include electronic augmentation of the acoustic piano, new musical applications of multi-touch sensing, quantitative studies of expressive performance technique, and embedded audio processing systems. He remains active as a composer of orchestral, chamber, and electronic music, with performances across the United States, Canada, and the UK at venues including the Tanglewood and Aspen music festivals.


"This book strikes a great balance between theory and get-your-hands-dirty applications. You get the essential math that deepens your understanding, but not so much that it discourages the motivated reader. The book is rich with actual examples—working code—so that you can build and hear functioning effects right away. The strong orientation to families of effects found in every recording studio means that readers of this book can look forward to making a full set of useful, relevant, real-world effects. The theory is just enough to arm you with the power to innovate and create, so you learn how to do what is shown in the book and, more importantly, to make your own extensions, variations, and inventions."
—Alex U. Case, University of Massachusetts Lowell, USA

"Audio Effects: Theory, Implementation and Application is a fascinating new book on audio processing algorithms. It starts from basics of digital audio engineering and signal processing, and then continues to explain in detail the most important audio effects algorithms. I very much like the chapter on delay-line effects, which gives a great overview of all the well-known methods, such as slapback and ping-pong delay effects, and flanging and chorus algorithms. This book not only explains the basic idea and applications of each method, but also briefly shows the mathematics in the background of all techniques. I much enjoyed reading the historical anecdotes about the origins of some audio effect techniques. Every chapter ends with a compact set of problems, which makes this book very useful as a textbook. Both easy and challenging problems are included."
—Vesa Välimäki, Aalto University, Esbo, Finland

"This is a clear and concise guide to the details and applications of audio signal processing. The mathematical treatment of the subject is rigorous yet accessible, and problems to test understanding are included at the end of each chapter. Code examples in C++ are provided."
—Jez Wells, University of York, UK

"Audio Effects: Theory, Implementation, and Applications is a great book for those who are excited about the technical side of audio effects. Newcomers can gain a basic understanding of each of the topics and advanced students can take their understanding to the next level. The diagrams and formulae are in-depth and also function as a great one-stop reference on the subject."
—Craig Abaya, San Francisco State University, California, USA

"In the book, audio signal processing is explained in a very nice and smart way. Mentioning and explaining system theoretic aspects of basic processing structures helps readers to understand them in detail. Besides that, the application of these structures in music and audio in general is described in great detail, and in a very motivating manner. The authors start with simple structures (e.g., with constant parameters), allowing for a simple entry. Afterward, variants (e.g., by allowing the parameters to be changed in a periodic fashion) are described that show how structures are used in practice. Additional C-code examples help if readers really want to get hands-on experience when implementing audio processing schemes."
—Gerhard Schmidt, Kiel University, Germany

"... one of the best-written, best-structured, and most complete books on the topic of audio processing. ... The book uses dedicated chapters for a wide range of effects that take place in the time-domain (delay, reverberation, phase vocoder), the frequency domain (filters, Doppler effects, equalizers) or the realm of dynamics (overdrive, modulation, compression, etc.) and in each instance provides the theory of mathematical foundation using sophomore-level engineering math, clear and effective figures, excellent examples and exercises, as well as a short paragraph akin to a “did you know?” entry that lightens the reading. Whenever appropriate, the authors also include programming examples. From the excellent introduction to the final chapter (dedicated to building software plug-ins for some of the popular digital audio workstations environments), the book exalts clarity of thought and of presentation. ... What this book offers is an in-depth guide to how audio effects can be designed, calculated, and implemented in software. It is an effective text for college-level students in electrical engineering (or computer science) who have a passion for audio. ... Every reference book should have a good bibliography and reference section, and in this regards the readers will not be disappointed either. The references are both broad and deep, and they are extremely current. ... Personally I would not hesitate to spend the money on this work, as I can see annotating a lot of the pages (especially the code portions). ... a book of this quality should have a spot on an engineer's bookshelf."
—Dominique J. Chéenne, Columbia College Chicago, Illinois, USA, from Noise Control Engineering Journal, November-December 2014

"... presents the application and implementation, from a technical approach, of the gamut of audio effects with a balanced focus on the math and science involved. ... There are a large number of well-placed references throughout the book for further reading or expanded research into filters and DSP effects. ... I would recommend this book to anyone interested in a behind-the-scenes look at how our modern DSP-based effects do their magic. The book also will help with understanding the math and concepts related to modern DSP-based effects."
—David Brown, Santa Ana, California, USA, from the Journal of the Audio Engineering Society, Vol. 63, No. 9, September 2015