A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
while offering a high level of performance. FAUST aims at being complementary to existing audio languages by offering a viable and efficient alternative to C
C
Ĉ or ĉ is a consonant in Esperanto orthography, representing the sound .Esperanto orthography uses a diacritic for all four of its postalveolar consonants, as do the Latin-based Slavic alphabets...
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
to develop signal processing libraries, audio plug-ins or standalone applications.
The language is based on a simple and well defined formal semantics. A FAUST program denotes a signal processor, a mathematical function that transforms input signals into output signals.
Overview
As said in the introduction, the FAUST programming model combines a functional programming approach with a block-diagram syntax:
The functional programming approach provides a natural framework for signal processing. Digital signals are modeled as discrete functions of time, signal processors as second order functions that operate on them, and FAUST’s block-diagram composition operators, used to combine signal processors together, as third order functions, etc. .
Block-diagrams, even if purely textual like in FAUST, promote a modular approach of signal processing that suits very well the sound engineers’ and audio developers’ habits, while providing a powerful and expressive syntax.
A FAUST program doesn’t describe a sound or a group of sounds, but a signal processor, something that transforms input signals and produces output signals. The program source is organized as a set of definitions with at least the definition of the keyword process (the equivalent of main in C):
process = ...;
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
programs taking care of generating the most efficient code. The result can generally compete with, and sometimes even outperform, C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
code written by seasoned programmers.
The generated code works at the sample level. It is therefore suited to implement low-level DSP
DSP
- Computing :* Digital signal processing, the study and implementation of signals in digital computing and their processing methods* Digital signal processor, a specialized microprocessor designed specifically for digital signal processing...
functions like recursive filters. Moreover the code can be easily embedded. It is self-contained and doesn’t depend of any DSP
DSP
- Computing :* Digital signal processing, the study and implementation of signals in digital computing and their processing methods* Digital signal processor, a specialized microprocessor designed specifically for digital signal processing...
library or runtime system. It has a very deterministic behaviour and a constant memory footprint.
The semantic of FAUST is simple and well defined. This is not just of academic interest. It allows the FAUST compiler to be semantically driven. Instead of compiling a program literally, it compiles the mathematical function it denotes. This feature is useful for example to promote components reuse while preserving optimal perfomance. Moreover having access to the exact semantics of a FAUST program can simplify preservation issues
FAUST is a textual language but nevertheless block-diagram oriented. It actually combines two approaches: functional programming and algebraic block-diagrams. The key idea is to view block-diagram construction as function composition. For that, FAUST relies on a block-diagram algebra of five composition operations.
Simple Examples
Let’s start with some really simple one-line examples of FAUST program. Here is a first example that produces silence:
process = 0;
The second example is a little bit more sophisticated and copies the input signal to the output signal. It involves the _ (underscore) primitive that denotes the identity function on signals (that is a simple audio cable for a sound engineer):
process = _;
Another very simple example is the conversion of a two-channel stereo signal into a one-channel mono signal using the + primitive that adds two signals together:
process = +;
Most FAUST primitives are analogue to their C counterpart on numbers, but lifted to signals. For example the FAUST primitive sin operates on a signal X by applying the C function sin to each sample X(t) of X. In other words sin transforms an input signal X into an output signal Y such that Y (t) = sin(X(t)). All C numerical functions have their counterpart in FAUST.
Some signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
primitives are specific to FAUST. For example the delay operator @ takes two input signals: X (the signal to be delayed) and D (the delay to be applied), and produces an output signal Y such that Y (t) = X(t − D(t)).
Block-Diagram Composition
Contrary to Max-like visual programming languages where the user does manual connections, FAUST primitives are assembled in block diagrams by using a set of high-level block diagram composition operations. You can think of these composition operators as a generalization of the mathematical function composition operator.
The block-diagram composition operators used in FAUST
f~g
Recursive composition (precedence 4)
f,g
Parallel composition (precedence 3)
f:g
Sequential composition (precedence 2)
f<:g
Split composition (precedence 1)
f:>g
Merge composition (precedence 1)
Let’s say that we want to connect the output of + to the input of abs in order to compute the absolute value of the output signal. This connection can be done using the sequential composition operator ':' (colon):
process = + : abs;
Here is an example of parallel composition (a stereo cable) using the operator ',' that puts in parallel its left and right expressions:
process = _,_;
These operators can be arbitrarily combined. For example to multiply the input signal by 0.5 one can write:
process = _,0.5 : *;
Taking advantage of some syntactic sugar the above example can be rewritten (using what functional programmmers know as curryfication):
process = *(0.5);
The recursive composition operator '~' can be used to create block-diagrams with cycles (that include an implicit one-sample delay). Here is the example of an integrator that takes an input signal X and computes an output signal Y such that Y (t) = X(t) + Y(t−1):
process = + ~ _;
Full Applications Generation
Thanks to specific architecture files, a single FAUST program can be used to produce code for a variety of platforms and plug-in formats. These architecture files act as wrappers and describe the interactions with the host audio and GUI system. Currently more than 10 architectures are supported and new ones can be easily added.
Some architecture files available for FAUST
alsa-gtk.cpp
ALSA application + GTK
alsa-qt.cpp
ALSA application + QT4
jack-gtk.cpp
JACK application + GTK
jack-qt.cpp
JACK application + QT4
ca-qt.cpp
CoreAudio application + QT4
ladspa.cpp
LADSPA plug-in
max-msp.cpp
Max MSP plug-in
pd.cpp
Puredata plug-in
q.cpp
Q language plug-in
supercollider.cpp
Supercollider plug-in
vst.cpp
VST plug-in
Block-Diagram Generation
A useful option makes it possible to generates the block diagram representation of the program as one or more SVG graphic files.
It is interesting to note the difference between the block diagram and the generated C++ code.
As already said, the key idea here is not to compile the block diagram literally, but the mathematical function it denotes. Modern C/C++ compilers too don’t compile programs literally. But because of the complex semantic of C/C++ (due to side effects, pointer aliasing, etc.) they can’t go very far in that direction. This is a distinctive advantage of a purely functional language: it allows compilers to do very advanced optimisations.
External links
FAUST home page: Online compiler, support, documentation, news, etc.
