1.1 Digital Audio Effects DAFX with MATLAB®

Audio effects are used by all individuals involved in the generation of musical signals and start with special playing techniques by musicians, merge to the use of special microphone techniques and migrate to effect processors for synthesizing, recording, production and broadcasting of musical signals. This book will cover several categories of sound or audio effects and their impact on sound modifications. Digital audio effects—as an acronym we use DAFX—are boxes or software tools with input audio signals or sounds which are modified according to some sound control parameters and deliver output signals or sounds (see Figure 1.1). The input and output signals are monitored by loudspeakers or headphones and some kind of visual representation of the signal, such as the time signal, the signal level and its spectrum. According to acoustical criteria the sound engineer or musician sets his control parameters for the sound effect he would like to achieve. Both input and output signals are in digital format and represent analog audio signals. Modification of the sound characteristic of the input signal is the main goal of digital audio effects. The settings of the control parameters are often done by sound engineers, musicians (performers, composers, or digital instrument makers) or simply the music listener, but can also be part of one specific level in the signal processing chain of the digital audio effect.

Figure 1.1 Digital audio effect and its control [Arf99].

The aim of this book is the description of digital audio effects with regard to:

• Physical and acoustical effect: we take a short look at the physical background and explanation. We describe analog means or devices which generate the sound effect.
• Digital signal processing: we give a formal description of the underlying algorithm and show some implementation examples.
• Musical applications: we point out some applications and give references to sound examples available on CD or on the web.

The physical and acoustical phenomena of digital audio effects will be presented at the beginning of each effect description, followed by an explanation of the signal processing techniques to achieve the effect, some musical applications and the control of effect parameters.

In this introductory chapter we next introduce some vocabulary clarifications, and then present an overview of classifications of digital audio effects. We then explain some simple basics of digital signal processing and show how to write simulation software for audio effects processing with the MATLAB1 simulation tool or freeware simulation tools2. MATLAB implementations of digital audio effects are a long way from running in real time on a personal computer or allowing real-time control of its parameters. Nevertheless the programming of signal processing algorithms and in particular sound-effect algorithms with MATLAB is very easy and can be learned very quickly.

Sound Effect, Audio Effect and Sound Transformation

As soon as the word “effect” is used, the viewpoint that stands behind is the one of the subject who is observing a phenomenon. Indeed, “effect” denotes an impression produced in the mind of a person, a change in perception resulting from a cause. Two uses of this word denote related, but slightly different aspects: “sound effects” and “audio effects.” Note that in this book, we discuss the latter exclusively. The expression—“sound effects”—is often used to depict sorts of earcones (icons for the ear), special sounds which in production mode have a strong signature and which therefore are very easily identifiable. Databases of sound effects provide natural (recorded) and processed sounds (resulting from sound synthesis and from audio effects) that produce specific effects on perception used to simulate actions, interaction or emotions in various contexts. They are, for instance, used for movie soundtracks, for cartoons and for music pieces. On the other hand, the expression “audio effects” corresponds to the tool that is used to apply transformations to sounds in order to modify how they affect us. We can understand those two meanings as a shift of the meaning of “effect”: from the perception of a change itself to the signal processing technique that is used to achieve this change of perception. This shift reflects a semantic confusion between the object (what is perceived) and the tool to make the object (the signal processing technique). “Sound effect” really deals with the subjective viewpoint, whereas “audio effect” uses a subject-related term (effect) to talk about an objective reality: the tool to produce the sound transformation.

Historically, it can arguably be said that audio effects appeared first, and sound transformations later, when this expression was tagged on refined sound models. Indeed, techniques that made use of an analysis/transformation/synthesis scheme embedded a transformation step performed on a refined model of the sound. This is the technical aspect that clearly distinguishes “audio effects” and “sound transformations,” the former using a simple representation of the sound (samples) to perform signal processing, whereas the latter uses complex techniques to perform enhanced signal processing. Audio effects originally denoted simple processing systems based on simple operations, e.g. chorus by random control of delay line modulation; echo by a delay line; distortion by non-linear processing. It was assumed that audio effects process sound at its surface, since sound is represented by the wave form samples (which is not a high-level sound model) and simply processed by delay lines, filters, gains, etc. By surface we do not mean how strongly the sound is modified (it in fact can be deeply modified; just think of distortion), but we mean how far we go in unfolding the sound representations to be accurate and refined in the data and model parameters we manipulate. Sound transformations, on the other hand, denoted complex processing systems based on analysis/transformation/synthesis models. We, for instance, think of the phase vocoder with fundamental frequency tracking, the source-filter model, or the sinusoidal plus residual additive model. They were considered to offer deeper modifications, such as high-quality pitch-shifting with formant preservation, timbre morphing, and time-scaling with attack, pitch and panning preservation. Such deep manipulation of control parameters allows in turn the sound modifications to be heard as very subtle.

Over time, however, practice blurred the boundaries between audio effects and sound transformations. Indeed, several analysis/transformation/synthesis schemes can simply perform various processing that we consider to be audio effects. On the other hand, usual audio effects such as filters have undergone tremendous development in terms of design, in order to achieve the ability to control the frequency range and the amplitude gain, while taking care to limit the phase modulation. Also, some usual audio effects considered as simple processing actually require complex processing. For instance, reverberation systems are usually considered as simple audio effects because they were originally developed using simple operations with delay lines, even though they apply complex sound transformations. For all those reasons, one may consider that the terms “audio effects,” “sound transformations” and “musical sound processing” are all refering to the same idea, which is to apply signal processing techniques to sounds in order to modify how they will be perceived, or in other words, to transform a sound into another sound with a perceptually different quality. While the different terms are often used interchangeably, we use “audio effects” throughout the book for the sake of consistency.