#dsp #audio

fundsp

Audio processing and synthesis library

18 releases (7 breaking)

Uses new Rust 2021

new 0.8.0 Aug 13, 2022
0.6.6 Jul 31, 2022
0.5.1 Mar 29, 2022

#13 in Audio

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FunDSP

Audio Processing and Synthesis Library for Rust

FunDSP is an audio DSP (digital signal processing) library for audio processing and synthesis.

FunDSP features a powerful inline graph notation for describing audio processing networks. The notation taps into composable, zero-cost abstractions that express the structure of audio networks as Rust types.

Another innovative feature of FunDSP is its signal flow system, which can determine analytic frequency responses for any linear network.

FunDSP comes with a combinator environment containing a suite of audio components, math and utility functions and procedural generation tools.

Uses

  • Audio processing and synthesis for games and applications
  • Education
  • Music making
  • Sound hacking and audio golfing
  • Prototyping of DSP algorithms

Rust Audio Discord

To discuss FunDSP and other topics, come hang out with us at the Rust Audio Discord.

Graph Notation

FunDSP Composable Graph Notation expresses audio networks in algebraic form, using graph operators. It was developed together with the functional environment to minimize the number of typed characters needed to accomplish common audio tasks.

Many common algorithms can be expressed in a natural form conducive to understanding. For example, an FM oscillator can be written simply as:

sine_hz(f) * f * m + f >> sine()

The above expression defines an audio graph that is compiled into a stack allocated, inlined form using the powerful generic abstractions built into Rust. Connectivity errors are detected during compilation, saving development time.

Audio DSP Becomes a First-Class Citizen

With no macros needed, the FunDSP graph notation integrates audio DSP tightly into the Rust programming language as a first-class citizen. Native Rust operator precedences work in harmony with the notation, minimizing the number of parentheses needed.

FunDSP graph expressions offer even more economy in being generic over channel arities, which are encoded at the type level. A mono network can be expressed as a stereo network simply by replacing its mono generators and filters with stereo ones, the graph notation remaining the same.

FunDSP Composable Graph Notation was developed by Sami Perttu, with contributions from Benjamin Saunders.

Basics

Component Systems

There are two parallel component systems: the static AudioNode and the dynamic AudioUnit.

Both systems operate on audio signals synchronously as an infinite stream.


Trait Sample Type Dispatch Allocation Strategy Connectivity
AudioNode generic (f32 or f64) static, inlined stack input and output arity fixed at compile time
AudioUnit32 f32 dynamic, object safe heap input and output arity fixed after construction
AudioUnit64 f64 -..- -..- -..-

AudioNodes can be stack allocated for the most part. At the moment, block processing via AudioNode::process requires heap allocation. Some nodes may also use the heap for audio buffers and the like.

The purpose of the AudioUnit system is to grant more flexibility in dynamic situations: decisions about input and output arities and contents can be deferred to runtime.

Processing

Processing samples is easy in both AudioNode and AudioUnit systems. The tick method is for processing single sample frames, while the process method processes whole blocks.

Mono samples can be retrieved with get_mono and filter_mono methods. The get_mono method returns the next sample from a generator that has no inputs and one or two outputs, while the filter_mono method filters the next sample from a node that has one input and one output:

let out_sample = node.get_mono();
let out_sample = node.filter_mono(sample);

Stereo samples can be retrieved with get_stereo and filter_stereo methods. The get_stereo method returns the next stereo sample pair from a generator that has no inputs and one or two outputs, while the filter_stereo method filters the next sample from a node that has two inputs and two outputs.

let (out_left_sample, out_right_sample) = node.get_stereo();
let (out_left_sample, out_right_sample) = node.filter_stereo(left_sample, right_sample);

Sample Rate Independence

Of the signals flowing in graphs, some contain audio while others are controls of different kinds.

With control signals and parameters in general, we prefer to use natural units like Hz and seconds. It is useful to keep parameters independent of the sample rate, which we can then adjust as we like.

In addition to sample rate adjustments, natural units enable support for selective oversampling (the oversample component) in nested sections that are easy to configure and modify.

Some low-level components ignore the sample rate by design, such as the single sample delay tick.

The default sample rate is 44.1 kHz. In both systems, a component A can be reinitialized with a new sample rate: A.reset(Some(sample_rate)).

Audio Processing Environment

FunDSP preludes define convenient combinator environments for audio processing.

There are three name-level compatible versions of the prelude.

The default environment (fundsp::prelude) offers a generic interface. It is flexible and attempts to conform to Rust practices.

The 64-bit hacker environment (fundsp::hacker) for audio hacking is fully 64-bit to minimize type annotations and maximize audio quality. The hacker interface uses 1 floating point type (f64) and 1 integer type (i64) only.

The 32-bit hacker environment (fundsp::hacker32) aims to offer maximum processing speed.

An application interfacing fundsp can mix and match preludes as needed. The aims of the environments are:

  • Minimize the number of characters needed to type to express an idiom.
  • Keep the syntax clean so that a subset of the hacker environment can be parsed straightforwardly as a high-level DSL for quick prototyping.
  • Make the syntax usable even to people with no prior exposure to programming.
  • Exemplify an effective procedural style.

Deterministic Pseudorandom Phase

FunDSP uses a deterministic pseudorandom phase system for audio generators. Generator phases are seeded from network structure and node location.

Thus, two identical networks sound identical separately but different when combined. This means that noise() | noise() is a stereo noise source, for example.

Operators

Custom operators are available for combining audio components inline. In order of precedence, from highest to lowest:


Expression Meaning Inputs Outputs Notes
-A negate A a a Negates any number of outputs, even zero.
!A thru A a same as inputs Passes through extra inputs.
A * B multiply A with B a + b a = b Aka amplification, or ring modulation when both are audio signals. Number of outputs in A and B must match.
A * constant multiply A a a Broadcasts constant. Same applies to constant * A.
A + B sum A and B a + b a = b Aka mixing. Number of outputs in A and B must match.
A + constant add to A a a Broadcasts constant. Same applies to constant + A.
A - B difference of A and B a + b a = b Number of outputs in A and B must match.
A - constant subtract from A a a Broadcasts constant. Same applies to constant - A.
A >> B pipe A to B a b Aka chaining. Number of outputs in A must match number of inputs in B.
A & B bus A and B a = b a = b Sum A and B. A and B must have identical connectivity.
A ^ B branch input to A and B in parallel a = b a + b Number of inputs in A and B must match.
A | B stack A and B in parallel a + b a + b Concatenates A and B inputs and outputs.

In the table, constant denotes an f32 or f64 value.

All operators are associative, except the left associative -.

Operators Diagram

Broadcasting

Arithmetic operators are applied to outputs channel-wise.

Arithmetic between two components never broadcasts channels: channel arities have to match always.

Direct arithmetic with f32 and f64 values, however, broadcasts to an arbitrary number of channels.

The negation operator broadcasts also: -A is equivalent with (0.0 - A).

For example, A * constant(2.0) and A >> mul(2.0) are equivalent and expect A to have one output. On the other hand, A * 2.0 works with any A, even sinks.

Thru

The thru (!) operator is syntactic sugar for chaining filters with similar connectivity.

It adjusts output arity to match input arity and passes through any missing outputs to the next node. The missing outputs are parameters to the filter.

For example, while lowpass() is a 2nd order lowpass filter, !lowpass() >> lowpass() is a steeper 4th order lowpass filter with identical connectivity.

Generators, Filters and Sinks

Components can be broadly classified into generators, filters and sinks. Generators have only outputs, while filters have both inputs and outputs.

Sinks are components with no outputs. Direct arithmetic on a sink translates to a no-op. In the prelude, sink() returns a mono sink.

Graph Combinators

Of special interest among operators are the four custom combinators: pipe ( >> ), bus ( & ), branch ( ^ ), and stack ( | ).

The pipe is a serial operator where components appear in processing order. Branch, stack, and arithmetic operators are parallel operators where components appear in channel order.

Bus is a commutative operator where components may appear in any order. The other operators are not commutative in general.

All four are fully associative, and each come with their own connectivity rules.

Pipe

The pipe ( >> ) operator builds traditional processing chains akin to composition of functions. In A >> B, each output of A is piped to a matching input of B, so the output arity of A must match the input arity of B.

It is possible to pipe a sink to a generator. This is similar to stacking. Processing works as normal and the sink processes its inputs before the generator is run.

Branch

Where the arithmetic operators are reducing in nature, the branch ( ^ ) operator splits a signal into parallel branches.

In A ^ B, both components receive the same input but their outputs are disjoint. Because the components receive the same input, the number of inputs in A and B must match. In A ^ B, the outputs of A appear first, followed with outputs of B.

Branching is useful for building banks of components such as filters.

Bus

The bus ( & ) operator can be thought of as an inline audio bus with a fixed set of input and output channels. It builds signal buses from components with identical connectivity.

In A & B, the same input is sent to both A and B, and their outputs are mixed together. Components in a bus may appear in any order.

The bus is especially useful because it does not alter connectivity: we can always bus together any set of matching components without touching the rest of the expression.

Both A + B and A & B are mixing operators. The difference between the two is that A + B is reducing: A and B have their own, disjoint inputs, which are combined at the output. In A & B, both components source from the same inputs, and the number of inputs must match.

One application of the bus is controlling effect mix in conjunction with the pass opcode, which passes signal through unchanged. For example, to add 20% chorus to a mono signal, one might type pass() & 0.2 * chorus(0, 0.015, 0.005, 0.3).

Stack

The stack ( | ) operator builds composite components. It can be applied to any two components.

As a graph operator, the stack corresponds to the disjoint union. In A | B, the inputs and outputs of A and B are disjoint and they are processed independently, in parallel.

In stacks, components are written in channel order. In A | B | C, channels of A come first, followed by channels of B, then C.

Expressions Are Graphs

The expression A >> (B ^ C ^ D) defines a signal processing graph. It has whatever inputs A has, and outputs everything from B and C and D in parallel.

The whole structure is packed, monomorphized and inlined with the constituent nodes consumed. If you want to reuse components, define them as functions or closures. See the preludes for examples.

Connectivity is checked during compilation. Mismatched connectivity will result in a compilation error complaining about mismatched typenum types. The arrays Frame<T, Size> that connect components come from the generic-array and numeric-array crates.

Computational Structure

Graph combinators consume their arguments. This prevents cycles and imposes an overall tree shape on the resulting computation graph.

Implicit cycle prevention means that the built structures are always computationally efficient in the dataflow sense. All reuse of computed data takes place locally, inside combinators and components.

There are two main ways to structure the reuse of signals in FunDSP graph notation: branching and busing. Both are exposed as fundamental operators, guiding toward efficient structuring of computation. Dataflow concerns are thus explicated in the graph notation itself.

Net32 and Net64

The graph notation can get cumbersome for complex graphs. Also, sometimes the number of inputs and outputs is not known until runtime.

The Net32 and Net64 components offer an explicit graph interface for connecting AudioUnit32 and AudioUnit64 nodes, respectively.

For example, to build dc(220.0) >> sine() dynamically using Net64:

use fundsp::hacker::*;
// Instantiate network with 0 inputs and 1 output.
let mut net = Net64::new(0, 1);
// Add nodes, obtaining their IDs.
let dc_id = net.add(Box::new(dc(220.0)));
let sine_id = net.add(Box::new(sine()));
// Connect nodes.
net.pipe(dc_id, sine_id);
net.pipe_output(sine_id);

Input Modalities And Ranges

Some signals found flowing in audio networks.

Modality Preferred Units/Range Notes
frequency Hz
phase 0...1 The wavetable oscillator uses this range.
time s
audio data -1...1 Inner processing may use any range that is convenient. However, only special output formats can store audio data outside this range.
stereo pan -1...1 (left to right) For ergonomy, consider clamping any pan input to this range.
control amount 0...1 If there is no natural interpretation of the parameter.

Signal Flow Analysis

FunDSP features a comprehensive signal flow system that analyzes causal latencies and frequency responses in audio networks.

The system can calculate the frequency response of any linear network analytically by composing transfer functions and folding constants. Linear networks are constructed from linear filters, delays, and the operations of:

  • Mixing.
  • Chaining. Chaining of linear filters and delays maintains linearity.
  • Constant scaling. Signals may be scaled by constant factors.

Signal latencies are similarly analyzed from input to output in detail, facilitating automatic removal of pre-delay from effects chains.

For example, FIR filters can be composed inline from single sample delays (the tick opcode) and arithmetic. Signal flow analysis will readily reveal that a 2-point averaging filter has zero gain at the Nyquist frequency, while a 3-point averaging filter does not:

assert!((pass() & tick()).response(0, 22050.0).unwrap().norm() < 1.0e-9);
assert!((pass() & tick() & tick() >> tick()).response(0, 22050.0).unwrap().norm() > 0.1);

However, with appropriate scaling a 3-point FIR can vanish, too:

assert!((0.5 * pass() & tick() & 0.5 * tick() >> tick()).response(0, 22050.0).unwrap().norm() < 1.0e-9);

List of Linear Filters

Verified frequency responses are available for all linear filters.


Opcode Type Parameters Family Notes
allpass allpass (2nd order) frequency, Q Simper SVF
allpole allpass (1st order) delay 1st order Adjustable delay in samples.
bandpass bandpass (2nd order) frequency, Q Simper SVF
bell peaking (2nd order) frequency, Q, gain Simper SVF Adjustable amplitude gain.
butterpass lowpass (2nd order) frequency biquad Butterworth lowpass has a maximally flat passband and monotonic frequency response.
dcblock DC blocker (1st order) frequency 1st order Zero centers signal, countering any constant offset ("direct current").
fir FIR - FIR
follow lowpass (3rd order) response time nested 1st order Smoothing filter with adjustable edge response time.
highpass highpass (2nd order) frequency, Q Simper SVF
highpole highpass (1st order) frequency 1st order
highshelf high shelf (2nd order) frequency, Q, gain Simper SVF Adjustable amplitude gain.
lowpass lowpass (2nd order) frequency, Q Simper SVF
lowpole lowpass (1st order) frequency 1st order
lowshelf low shelf (2nd order) frequency, Q, gain Simper SVF Adjustable amplitude gain.
morph morphing (2nd order) frequency, Q, morph Simper SVF Morphs between lowpass, peaking and highpass modes.
notch notch (2nd order) frequency, Q Simper SVF
peak peaking (2nd order) frequency, Q Simper SVF
pinkpass lowpass (3 dB/octave) - mixed FIR / 1st order Turns white noise into pink noise.
resonator bandpass (2nd order) frequency, bandwidth biquad Gain stays constant as bandwidth is varied.

List of Nonlinear Filters

Unlike linear filters, nonlinear filters may be sensitive to incoming signal level. Due to nonlinearity, we do not attempt to calculate frequency responses for these filters.


Opcode Type Parameters Family Notes
moog lowpass (4th order) frequency, Q Moog ladder Sensitive to input level.

Parametric Equalizer Recipe

In this example we make a 12-band, double precision parametric equalizer using the peaking bell filter.

First, declare the processing pipeline. Here we space the bands at 1 kHz increments starting from 1 kHz, set Q values to 1.0 and set gains of all bands to 0 dB initially:

use fundsp::hacker::*;
let mut equalizer = pipe::<U12, _, _>(|i| bell_hz(1000.0 + 1000.0 * i as f64, 1.0, db_amp(0.0)));

The type of the equalizer is An<Chain<U12, f64, FixedSvf<f64, f64, BellMode<f64>>>>. The equalizer is ready to use immediately. Filter samples:

let output_sample = equalizer.filter_mono(input_sample);

We can access individual bands via equalizer.node(i) and equalizer.node_mut(i) where i ranges from 0 to 11. Set band 0 to amplify by 10 dB at 500 Hz with Q set to 2.0:

equalizer.node_mut(0).set_gain(db_amp(10.0));
equalizer.node_mut(0).set_center(500.0);
equalizer.node_mut(0).set_q(2.0);

For plotting the frequency response, we can query the equalizer. Query equalizer gain at 1 kHz:

let decibel_gain_at_1k = equalizer.response_db(0, 1000.0).unwrap();

The default sample rate is 44.1 kHz. Set sample rate to 48 kHz:

equalizer.reset(Some(48_000.0));

evcxr

The Debug output of audio filters contains information about the node and an ASCII chart of the frequency response of channel 0.

Here is an example of using evcxr to examine frequency responses interactively:

C:\rust>evcxr
Welcome to evcxr. For help, type :help
>> :dep fundsp "0.6.3"
>> use fundsp::hacker::*;
>> bell_hz(1000.0, 1.0, db_amp(50.0))
 60 dB -----------------------------------------------  60 dB
 
 50 dB -------------------------.---------------------  50 dB
                                *
 40 dB -------------------------*---------------------  40 dB
                               ** 
 30 dB -----------------------.***--------------------  30 dB
                             ******.
 20 dB -------------------..*********.----------------  20 dB
                       ..**************.
 10 dB -------------..********************..----------  10 dB
               ..*****************************...
  0 dB ....***************************************....   0 dB
       |   |    |    |     |    |    |    |    |    |
       10  50   100  200   500  1k   2k   5k   10k  20k Hz

Peak Magnitude : 50.00 dB (1000 Hz)
Inputs         : 1
Outputs        : 1
Latency        : 0.0 samples
Footprint      : 96 bytes

>>

Free Functions

These free functions are available in the environment.


Component Opcodes

The type parameters in the table refer to the hacker prelude.

M, N, U are type-level integers. They are U0, U1, U2...


Function Inputs Outputs Explanation
add(x) x x Add constant x to signal.
allpass() 3 (audio, frequency, Q) 1 Allpass filter (2nd order).
allpass_hz(f, q) 1 1 Allpass filter (2nd order) centered at f Hz with Q q.
allpass_q(q) 2 (audio, frequency) 1 Allpass filter (2nd order) with Q q.
allpole 2 (audio, delay) 1 Allpass filter (1st order). 2nd input is delay in samples (delay > 0).
allpole_delay(delay) 1 1 Allpass filter (1st order) with delay in samples (delay > 0).
bandpass() 3 (audio, frequency, Q) 1 Bandpass filter (2nd order).
bandpass_hz(f, q) 1 1 Bandpass filter (2nd order) centered at f Hz with Q q.
bandpass_q(q) 2 (audio, frequency) 1 Bandpass filter (2nd order) with Q q.
bell() 4 (audio, frequency, Q, gain) 1 Peaking filter (2nd order) with adjustable amplitude gain.
bell_hz(f, q, gain) 1 1 Peaking filter (2nd order) centered at f Hz with Q q and amplitude gain gain.
bell_q(q, gain) 2 (audio, frequency) 1 Peaking filter (2nd order) with Q q and amplitude gain gain.
brown() - 1 Brown noise.
branch::<U, _, _>(f) f U * f Branch into U nodes from indexed generator f.
branchf::<U, _, _>(f) f U * f Branch into U nodes from fractional generator f, e.g., | x | resonator_hz(xerp(20.0, 20_000.0, x), xerp(5.0, 5_000.0, x)).
bus::<U, _, _>(f) f f Bus together U nodes from indexed generator f, e.g., | i | mul(i as f64 + 1.0) >> sine().
busf::<U, _, _>(f) f f Bus together U nodes from fractional generator f.
butterpass() 2 (audio, frequency) 1 Butterworth lowpass filter (2nd order).
butterpass_hz(f) 1 1 Butterworth lowpass filter (2nd order) with cutoff frequency f Hz.
chorus(seed, sep, var, mod) 1 1 Chorus effect with LFO seed seed, voice separation sep seconds, delay variation var seconds and LFO modulation frequency mod Hz.
clip() 1 1 Clip signal to -1...1.
clip_to(min, max) 1 1 Clip signal to min...max.
constant(x) - x Constant signal x. Synonymous with dc.
dc(x) - x Constant signal x. Synonymous with constant.
dcblock() 1 1 Zero center signal with cutoff frequency 10 Hz.
dcblock_hz(f) 1 1 Zero center signal with cutoff frequency f.
declick() 1 1 Apply 10 ms of fade-in to signal.
declick_s(t) 1 1 Apply t seconds of fade-in to signal.
delay(t) 1 1 Delay of t seconds. Delay time is rounded to the nearest sample.
detector() 2 (audio, frequency) 1 (power) Frequency detector.
detector_hz(f) 1 (audio) 1 (power) Frequency detector of DFT component f Hz.
dsf_saw() 2 (frequency, roughness) 1 Saw-like discrete summation formula oscillator.
dsf_saw_r(roughness) 1 (frequency) 1 Saw-like discrete summation formula oscillator with roughness in 0...1.
dsf_square() 2 (frequency, roughness) 1 Square-like discrete summation formula oscillator.
dsf_square_r(roughness) 1 (frequency) 1 Square-like discrete summation formula oscillator with roughness in 0...1.
envelope(f) - f Time-varying control f with scalar or tuple output, e.g., |t| exp(-t). Synonymous with lfo.
envelope2(f) 1 (x) f Time-varying, input dependent control f with scalar or tuple output, e.g., |t, x| exp(-t * x). Synonymous with lfo2.
envelope3(f) 2 (x, y) f Time-varying, input dependent control f with scalar or tuple output, e.g., |t, x, y| y * exp(-t * x). Synonymous with lfo3.
fdn(x) x x Enclose feedback circuit x (with equal number of inputs and outputs) using diffusive Hadamard feedback.
fdn2(x, y) x, y x, y Enclose feedback circuit x (with equal number of inputs and outputs) using diffusive Hadamard feedback, with extra feedback loop processing y. The feedforward path does not include y.
feedback(x) x x Enclose feedback circuit x (with equal number of inputs and outputs).
feedback2(x, y) x, y x, y Enclose feedback circuit x (with equal number of inputs and outputs) with extra feedback loop processing y. The feedforward path does not include y.
fir(weights) 1 1 FIR filter with the specified weights, for example, fir((0.5, 0.5)).
flanger(fb, min_d, max_d, f) 1 1 Flanger effect with feedback amount fb, minimum delay min_d seconds, maximum delay max_d seconds and delay function f, e.g., |t| lerp11(0.01, 0.02, sin_hz(0.1, t)).
follow(t) 1 1 Smoothing filter with halfway response time t seconds.
follow((a, r)) 1 1 Asymmetric smoothing filter with halfway attack time a seconds and halfway release time r seconds.
highpass() 3 (audio, frequency, Q) 1 Highpass filter (2nd order).
highpass_hz(f, q) 1 1 Highpass filter (2nd order) with cutoff frequency f Hz and Q q.
highpass_q(q) 2 (audio, frequency) 1 Highpass filter (2nd order) with Q q.
highpole() 2 (audio, frequency) 1 Highpass filter (1st order).
highpole_hz(f) 1 1 Highpass filter (1st order) with cutoff frequency f Hz.
highshelf() 4 (audio, frequency, Q, gain) 1 High shelf filter (2nd order) with adjustable amplitude gain.
highshelf_hz(f, q, gain) 1 1 High shelf filter (2nd order) centered at f Hz with Q q and amplitude gain gain.
highshelf_q(q, gain) 2 (audio, frequency) 1 High shelf filter (2nd order) with Q q and amplitude gain gain.
join::<U>() U 1 Average together U channels. Inverse of split.
lfo(f) - f Time-varying control f with scalar or tuple output, e.g., |t| exp(-t). Synonymous with envelope.
lfo2(f) 1 (x) f Time-varying, input dependent control f with scalar or tuple output, e.g., |t, x| exp(-t * x). Synonymous with envelope2.
lfo3(f) 2 (x, y) f Time-varying, input dependent control f with scalar or tuple output, e.g., |t, x, y| y * exp(-t * x). Synonymous with envelope3.
limiter((a, r)) 1 1 Look-ahead limiter with attack time a seconds and release time r seconds.
limiter_stereo((a, r)) 2 2 Stereo look-ahead limiter with attack time a seconds and release time r seconds.
lowpass() 3 (audio, frequency, Q) 1 Lowpass filter (2nd order).
lowpass_hz(f, q) 1 1 Lowpass filter (2nd order) with cutoff frequency f Hz and Q q.
lowpass_q(q) 2 (audio, frequency) 1 Lowpass filter (2nd order) with Q q.
lowpole() 2 (audio, frequency) 1 1-pole lowpass filter (1st order).
lowpole_hz(f) 1 1 1-pole lowpass filter (1st order) with cutoff frequency f Hz.
lowshelf() 4 (audio, frequency, Q, gain) 1 Low shelf filter (2nd order) with adjustable amplitude gain.
lowshelf_hz(f, q, gain) 1 1 Low shelf filter (2nd order) centered at f Hz with Q q and amplitude gain gain.
lowshelf_q(q, gain) 2 (audio, frequency) 1 Low shelf filter (2nd order) with Q q and amplitude gain gain.
map(f) f f Map channels freely, e.g., map(|i: &Frame<f64, U2>| max(i[0], i[1])).
meter(mode) 1 1 (meter) Analyze input and output a summary according to the metering mode.
mls() - 1 White MLS noise source.
mls_bits(n) - 1 White MLS noise source from n-bit MLS sequence (1 <= n <= 31).
monitor(mode, id) 1 1 Pass-through node that analyzes data passed through as a parameter that can be queried.
moog() 3 (audio, frequency, Q) 1 Moog resonant lowpass filter (4th order).
moog_hz(f, q) 1 1 Moog resonant lowpass filter (4th order) with cutoff frequency f and resonance q.
moog_q(q) 2 (audio, frequency) 1 Moog resonant lowpass filter (4th order) with resonance q.
morph 4 (audio, frequency, Q, morph) 1 Morphing filter with morph input in -1...1 (-1 = lowpass, 0 = peaking, 1 = highpass)
morph_hz(f, q, morph) 1 1 Morphing filter with center frequency f, Q q and morph morph in -1...1 (-1 = lowpass, 0 = peaking, 1 = highpass)
mul(x) x x Multiply signal with constant x.
multijoin::<M, N>() M * N M Average N branches of M channels into one. Inverse of multisplit.
multipass::<U>() U U Pass multichannel signal through.
multisink::<U>() U - Consumes multichannel signal.
multisplit::<M, N>() M M * N Split M channels into N branches.
multitap::<N>(min_delay, max_delay) N + 1 (audio, delay...) 1 Tapped delay line with cubic interpolation. Number of taps is N.
multitick::<U>() U U Multichannel single sample delay.
multizero::<U>() - U Multichannel zero signal.
noise() - 1 White noise source. Synonymous with white.
notch() 3 (audio, frequency, Q) 1 Notch filter (2nd order).
notch_hz(f, q) 1 1 Notch filter (2nd order) centered at f Hz with Q q.
notch_q(q) 2 (audio, frequency) 1 Notch filter (2nd order) with Q q.
oversample(x) x x 2x oversample enclosed node x.
pan(pan) 1 2 Fixed mono-to-stereo equal power panner with pan in -1...1.
panner() 2 (audio, pan) 2 Mono-to-stereo equal power panner with pan in -1...1.
pass() 1 1 Pass signal through.
peak() 3 (audio, frequency, Q) 1 Peaking filter (2nd order).
peak_hz(f, q) 1 1 Peaking filter (2nd order) centered at f Hz with Q q.
peak_q(q) 2 (audio, frequency) 1 Peaking filter (2nd order) with Q q.
phaser(fb, f) 1 1 Phaser effect with feedback amount fb and modulation function f, e.g., |t| sin_hz(0.1, t) * 0.5 + 0.5.
pink() - 1 Pink noise source.
pinkpass() 1 1 Pinking filter (3 dB/octave).
pipe::<U, _, _>(f) f f Chain U nodes from indexed generator f.
pipef::<U, _, _>(f) f f Chain U nodes from fractional generator f.
pluck(f, gain, damping) 1 (excitation) 1 Karplus-Strong plucked string oscillator with frequency f Hz, gain per second (gain <= 1) and high frequency damping in 0...1.
pulse() 2 (frequency, duty cycle) 1 Bandlimited pulse wave with duty cycle in 0...1.
resonator() 3 (audio, frequency, bandwidth) 1 Constant-gain bandpass resonator (2nd order).
resonator_hz(f, bw) 1 1 Constant-gain bandpass resonator (2nd order) with center frequency f Hz and bandwidth bw Hz.
reverb_stereo(r, t) 2 2 Stereo reverb with room size r meters (10 is average) and reverberation time t seconds.
saw() 1 (frequency) 1 Bandlimited saw wave oscillator.
saw_hz(f) - 1 Bandlimited saw wave oscillator at f Hz.
shape(mode) 1 1 Shape signal with waveshaper mode mode.
shape_fn(f) 1 1 Shape signal with waveshaper function f, e.g., tanh.
sine() 1 (frequency) 1 Sine oscillator.
sine_hz(f) - 1 Sine oscillator at f Hz.
sink() 1 - Consume signal.
split::<U>() 1 U Split signal into U channels.
square() 1 (frequency) 1 Bandlimited square wave oscillator.
square_hz(f) - 1 Bandlimited square wave oscillator at frequency f Hz.
stack::<U, _, _>(f) U * f U * f Stack U nodes from indexed generator f.
stackf::<U, _, _>(f) U * f U * f Stack U nodes from fractional generator f, e.g., | x | delay(xerp(0.1, 0.2, x)).
sub(x) x x Subtract constant x from signal.
sum::<U, _, _>(f) U * f f Sum U nodes from indexed generator f.
sumf::<U, _, _>(f) U * f f Sum U nodes from fractional generator f, e.g., | x | delay(xerp(0.1, 0.2, x)).
system(x, dt, f) x x Dynamical system that controls node x with update interval dt seconds and update function f(t, dt, x).
swap() 2 2 Swap stereo channels.
tag(id, value) - 1 Tagged constant with tag id (i64) and initial value value (f64).
tap(min_delay, max_delay) 2 (audio, delay) 1 Tapped delay line with cubic interpolation. All times are in seconds.
tick() 1 1 Single sample delay.
timer(id) - - Timer node that presents time as a parameter that can be queried.
triangle() 1 (frequency) 1 Bandlimited triangle wave oscillator.
triangle_hz(f) - 1 Bandlimited triangle wave oscillator at f Hz.
wave32(wave, channel, loop_point) - 1 Play back a channel of Wave32. Optional loop point is the index to jump to at the end of the wave.
wave64(wave, channel, loop_point) - 1 Play back a channel of Wave64. Optional loop point is the index to jump to at the end of the wave.
white() - 1 White noise source. Synonymous with noise.
zero() - 1 Zero signal.

Subsampled Controls

envelope(f) is a node that samples a time varying control function f. For example, envelope(|t| exp(-t)) is an exponentially decaying envelope. A control function is something that is expected to change relatively slowly. Therefore, we can save time by not calling it at every sample.

The argument to the function is time in seconds. Whenever the node is reset, time resets to zero.

envelope is generic over channel arity: The return type of the function - scalar or tuple - determines the number of outputs.

The samples are spaced at an average of 2 ms apart, jittered by noise derived from pseudorandom phase. The values in between are linearly interpolated.

lfo (Low Frequency Oscillator) is another name for envelope.

Indexed And Fractional Generator Functions

branch, bus, pipe, sum and stack are opcodes that combine multiple nodes, according to their first generic argument. They accept a generator function that is issued i64 integers starting from 0. The nodes are stack allocated.

For example, to create 20 pseudorandom noise bands in 1 kHz...2 kHz:

use fundsp::hacker::*;
let partials = bus::<U20, _, _>(|i| noise() >> resonator_hz(xerp(1_000.0, 2_000.0, rnd(i)), 20.0));

Similarly, branchf, busf, pipef, sumf and stackf accept a generator function that is issued values evenly distributed in the unit interval 0...1. The first node is issued the value 0 and the last node the value 1. If there is only one node, then it receives the value 0.5.

For example, to distribute 20 noise bands evenly in 1 kHz...2 kHz:

use fundsp::hacker::*;
let partials = busf::<U20, _, _>(|f| noise() >> resonator_hz(xerp(1_000.0, 2_000.0, f), 20.0));

Waveshaping Modes

These are arguments to the shape opcode.

  • Shape::Clip: Clip signal to -1...1.
  • Shape::ClipTo(minimum, maximum): Clip signal between the two arguments.
  • Shape::Tanh(hardness): Apply tanh distortion with configurable hardness. Argument to tanh is multiplied by the hardness value.
  • Shape::Softsign(hardness): Apply softsign distortion with configurable hardness. Argument to softsign is multiplied by the hardness value.
  • Shape::Crush(levels): Apply a staircase function with configurable number of levels per unit.
  • Shape::SoftCrush(levels): Apply a smooth staircase function with configurable number of levels per unit.

Tagged Constants As Parameters

Tagged single channel constants can be instantiated with tag(id, value), where id is i64 and the initial value value is f64.

Tagged constants enable a simple parameter system where a parameter can be set (recursively) with set(id, value) and queried (recursively) with get(id). set sets all matching parameters contained under the node to the value, while get retrieves the first matching parameter, if any.

The timer(id) opcode instantiates current time in seconds as a parameter that can be queried. It has no inputs or outputs; it can be added to any node by stacking.

Metering Modes

The monitor(mode, id) opcode is a pass-through node that presents some aspect of data passed through as parameter id. Metering modes are:

  • Meter::Sample: Retains the latest value passed through.
  • Meter::Peak(smoothing): Peak amplitude meter with smoothing as per-sample smoothing factor in 0...1.
  • Meter::Rms(smoothing): Root mean square meter with smoothing as per-sample smoothing factor in 0...1.
  • Meter::Detect(frequency): Detects presence of a single frequency. Outputs detected power.

The same modes are used in the meter opcode.


Math And Utility Functions


Function Explanation
abs(x) absolute value of x
a_weight(f) A-weighted amplitude response at f Hz (normalized to 1.0 at 1 kHz)
bpm_hz(bpm) convert bpm BPM (beats per minute) to Hz
ceil(x) ceiling function
clamp(min, max, x) clamp x between min and max
clamp01(x) clamp x between 0 and 1
clamp11(x) clamp x between -1 and 1
cos(x) cos
cos_hz(f, t) cosine that oscillates at f Hz at time t seconds
cubed(x) cube of x
db_amp(x) convert x dB to amplitude (or gain) with 0 dB = 1.0
delerp(x0, x1, x) recover linear interpolation amount t in 0...1 from interpolated value
delerp11(x0, x1, x) recover linear interpolation amount t in -1...1 from interpolated value
dexerp(x0, x1, x) recover exponential interpolation amount t in 0...1 from interpolated value (x0, x1, x > 0)
dexerp11(x0, x1, x) recover exponential interpolation amount t in -1...1 from interpolated value (x0, x1, x > 0)
dissonance(f0, f1) dissonance amount in 0...1 between pure tones at f0 and f1 Hz
dissonance_max(f) maximally dissonant pure frequency above f Hz
downarc(x) concave quarter circle easing curve (inverse function of uparc in 0...1)
ease_noise(ease, seed, x) value noise in -1...1 interpolated with easing function ease, e.g., smooth3
ease_noise((rise, fall), seed, x) value noise in -1...1 interpolated with easing function rise in rising segments and fall in falling segments, e.g., (uparc, downarc)
exp(x) exp
exp10(x) 10 to the power of x
exp2(x) 2 to the power of x
floor(x) floor function
fract(x) fract function
fractal_noise(seed, octaves, roughness, x) fractal spline noise (octaves > 0, roughness > 0)
fractal_ease_noise(ease, seed, octaves, roughness, x) fractal ease noise (octaves > 0, roughness > 0) interpolated with easing function ease
id(x) identity function (linear easing function)
lerp(x0, x1, t) linear interpolation between x0 and x1 with t in 0...1
lerp11(x0, x1, t) linear interpolation between x0 and x1 with t in -1...1
log(x) natural logarithm
log10(x) base 10 logarithm
log2(x) binary logarithm
midi_hz(x) convert MIDI note number x to Hz (69.0 = A4 = 440 Hz)
min(x, y) minimum of x and y
max(x, y) maximum of x and y
m_weight(f) M-weighted amplitude response at f Hz (normalized to 1.0 at 1 kHz)
pow(x, y) x raised to the power y
rnd(i) pseudorandom number in 0...1 from integer i
round(x) round x to nearest integer
semitone_ratio(x) convert interval x semitones to frequency ratio
signum(x) sign of x
sin(x) sin
sin_hz(f, t) sine that oscillates at f Hz at time t seconds
smooth3(x) smooth cubic easing polynomial
smooth5(x) smooth 5th degree easing polynomial (commonly used in computer graphics)
smooth7(x) smooth 7th degree easing polynomial
smooth9(x) smooth 9th degree easing polynomial
softexp(x) polynomial alternative to exp
softmix(x, y, bias) weighted average of x and y according to bias: polynomial softmin when bias < 0, average when bias = 0, polynomial softmax when bias > 0
softsign(x) softsign function, a polynomial alternative to tanh
squared(x) square of x
sqrt(x) square root of x
spline(x0, x1, x2, x3, t) Catmull-Rom cubic interpolation between x1 and x2, taking x0 and x3 into account
spline_mono(x0, x1, x2, x3, t) monotonic cubic interpolation between x1 and x2, taking x0 and x3 into account
spline_noise(seed, x) value noise in -1...1 interpolated with a cubic spline, with one interpolation point per integer cell
tan(x) tan
tanh(x) hyperbolic tangent
uparc(x) convex quarter circle easing curve (inverse function of downarc in 0...1)
xerp(x0, x1, t) exponential interpolation between x0 and x1 (x0, x1 > 0) with t in 0...1
xerp11(x0, x1, t) exponential interpolation between x0 and x1 (x0, x1 > 0) with t in -1...1

Easing Functions

Easing functions are interpolation curves that remap the range 0...1. These math functions have the shape of an easing function.

Function Explanation
cubed(x) cube of x
downarc(x) concave quarter circle easing curve (inverse function of uparc in 0...1)
id(x) identity function (linear easing function)
smooth3(x) smooth cubic easing polynomial
smooth5(x) smooth 5th degree easing polynomial (commonly used in computer graphics)
smooth7(x) smooth 7th degree easing polynomial
smooth9(x) smooth 9th degree easing polynomial
squared(x) square of x
sqrt(x) square root of x
uparc(x) convex quarter circle easing curve (inverse function of downarc in 0...1)

Noise Functions


Examples

Some examples of graph expressions.


Expression Inputs Outputs Meaning
pass() ^ pass() 1 2 mono-to-stereo splitter
split::<U2>() 1 2 -..-
mul(0.5) + mul(0.5) 2 1 stereo-to-mono mixdown (inverse of mono-to-stereo splitter)
join::<U2>() 2 1 -..-
pass() ^ pass() ^ pass() 1 3 mono-to-trio splitter
split::<U3>() 1 3 -..-
sink() | zero() 1 1 replace signal with silence
mul(0.0) 1 1 -..-
mul(db_amp(3.0)) 1 1 amplify signal by 3 dB
sink() | pass() 2 1 extract right channel
pass() | sink() 2 1 extract left channel
sink() | zero() | pass() 2 2 replace left channel with silence
mul(0.0) | pass() 2 2 -..-
mul((0.0, 1.0)) 2 2 -..-
pass() | sink() | zero() 2 2 replace right channel with silence
pass() | mul(0.0) 2 2 -..-
mul((1.0, 0.0)) 2 2 -..-
(pass() & tick()) * 0.5 1 1 2-point averaging FIR filter
fir((0.5, 0.5)) 1 1 -..-
fir(Frame::from([0.5, 0.5])) 1 1 -..-
!butterpass() >> lowpole() 2 1 2nd order and 1-pole lowpass filters in series (3rd order)
!butterpass() >> !butterpass() >> butterpass() 2 1 triple lowpass filter in series (6th order)
!resonator() >> resonator() 3 1 double resonator in series (4th order)
oversample(sine_hz(f) * f * m + f >> sine()) - 1 Oversampled FM (frequency modulation) oscillator at f Hz with modulation index m
sine() & mul(2.0) >> sine() 1 1 frequency doubled dual sine oscillator
envelope(|t| exp(-t)) * noise() - 1 exponentially decaying white noise
feedback(delay(1.0) * db_amp(-3.0)) 1 1 1 second feedback delay with 3 dB attenuation
feedback((delay(1.0) | delay(1.0)) >> swap() * db_amp(-6.0)) 2 2 1 second ping-pong delay with 6 dB attenuation.
tag(0, 0.1) * delay(1.0) & (1.0 - tag(0, 0.1)) * pass() 1 1 1 second delay with wet/dry mix controlled by parameter 0.
sine() & mul(semitone_ratio(4.0)) >> sine() & mul(semitone_ratio(7.0)) >> sine() 1 1 major chord
dc(midi_hz(72.0)) >> sine() & dc(midi_hz(76.0)) >> sine() & dc(midi_hz(79.0)) >> sine() 0 1 C major chord generator
!zero() 0 0 A null node. Stacking it with another node modifies its sound subtly, as the hash is altered.
!-!!!--!!!-!!--!zero() 0 0 Hot-rodded null node outfitted with a custom hash. Uses more electricity.

Examples From The Prelude

Many functions in the prelude itself are defined as graph expressions.


Function Inputs Outputs Definition
brown() - 1 white() >> lowpole_hz(10.0) * constant(13.7)
detector_hz(f) 1 1 (pass() | constant(f)) >> detector()
mls() - 1 mls_bits(29)
pink() - 1 white() >> pinkpass()
saw_hz(f) - 1 constant(f) >> saw()
sine_hz(f) - 1 constant(f) >> sine()
square_hz(f) - 1 constant(f) >> square()
triangle_hz(f) - 1 constant(f) >> triangle()
zero() - 1 constant(0.0)

Equivalent Expressions

There are usually many ways to express a particular graph. The following expression pairs are identical.


Expression Is The Same As Notes
(pass() ^ mul(2.0)) >> sine() + sine() sine() & mul(2.0) >> sine() Busing is often more convenient than explicit branching followed with summing.
--sink()-42.0^sink()&---sink()*3.14 sink() Branching, busing and arithmetic on sinks are no-ops.
constant(0.0) | dc(1.0) constant((0.0, 1.0)) Stacking concatenates channels.
sink() | zero() zero() | sink() The order does not matter because sink() only adds an input, while zero() only adds an output.
(butterpass() ^ (sink() | pass())) >> butterpass() !butterpass() >> butterpass() Running a manual bypass.
!sink() pass() The attempt of the sink to consume signal is foiled by the thru operator, which passes the missing output through.
!(noise() | noise()) !noise() The thru operator nullifies any generator.

Audio Graph Types

The AudioNode component system represents audio network structure at the type level.

The representation contains input and output arities, which are encoded as types U0, U1, ..., by the typenum crate. The associated types are AudioNode::Inputs and AudioNode::Outputs.

The representation contains sample and inner processing types when applicable, encoded in that order. These are chosen statically. The associated sample type, which is used to transport data between nodes, is AudioNode::Sample.

The preludes employ the wrapper type An<X: AudioNode> containing operator overloads and other trait implementations. The wrapper also implements either of AudioUnit32 or AudioUnit64 traits.

The type encoding is straightforward. As an example, in the hacker prelude

noise() & constant(440.0) >> sine()

is represented as

An<Bus<f64, Noise<f64>, Pipe<f64, Constant<U1, f64>, Sine<f64>>>>

The compiler reports these types in an opaque form. An attached utility, examples/type.rs, can unscramble such opaque types. This invocation prints the above type:

cargo run --example type -- "fundsp::combinator::An<Bus<f64, Noise<f64>, Pipe<f64, Constant<typenum::uint::UInt<typenum::uint::UTerm, typenum::bit::B1>, f64>, Sine<f64>>>>"

It is also possible to declare the return type as an impl AudioNode. However, this type is also opaque and cannot be stored as an AudioNode; conversion to AudioUnit32 or AudioUnit64 may be necessary in this case.

Declaring the full arity in the signature does enable use of the node in further combinations. For example:

fn split_quad() -> An<impl AudioNode<Sample = f64, Inputs = U1, Outputs = U4>> {
    pass() ^ pass() ^ pass() ^ pass()
}

License

Licensed under either of Apache License, Version 2.0 or MIT license at your option.

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in FunDSP by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.

Dependencies

~2.5MB
~52K SLoC