FunDSP

Audio Processing and Synthesis Library for Rust

FunDSP is an audio DSP (digital signal processing) library with a focus on usability.

FunDSP features a powerful inline graph notation that empowers users to accomplish diverse audio processing tasks with ease and elegance.

The custom notation taps into composable, zero-cost abstractions that express audio processing 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

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.

Processing

Processing samples is easy in the AudioNode system. 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 output, 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 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(sr)).

Audio Processing Environment

FunDSP prelude defines a convenient combinator environment for audio processing.

There are two 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 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.

An application interfacing fundsp will likely pick the default environment for maximum flexibility, while experimenters will be drawn to the succinctness of the hacker prelude.

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` together	`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.

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.

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 filters, delays, and the operations of:

Mixing.
Chaining. Chaining of 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 Filters

All filters in the list are linear. Verified frequency responses are available for all filters.

Opcode	Type	Parameters	Family	Notes
`allpass`	allpass (2nd order)	frequency, Q	Simper SVF
`allpole`	allpass (1st order)	frequency, 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.
`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.

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<f64, U12, 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));

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`	Adds 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.
`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 centers signal with cutoff frequency 10 Hz.
`dcblock_hz(f)`	1	1	Zero centers 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.
`envelope(f)`	-	`f`	Time-varying control `f` with scalar or tuple output, e.g., `\|t\| exp(-t)`. Synonymous with `lfo`.
`envelope2(f)`	1	`f`	Time-varying, input dependent control `f` with scalar or tuple output, e.g., `\|t, x\| exp(-t * x)`. Synonymous with `lfo2`.
`fdn(x)`	`x`	`x`	Encloses feedback circuit `x` (with equal number of inputs and outputs) using diffusive Hadamard feedback.
`feedback(x)`	`x`	`x`	Encloses feedback circuit `x` (with equal number of inputs and outputs).
`fir(weights)`	1	1	FIR filter with the specified weights, for example, `fir((0.5, 0.5))`
`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.
`goertzel()`	2 (audio, frequency)	1 (power)	Frequency detector.
`goertzel_hz(f)`	1 (audio)	1 (power)	Frequency detector of DFT component `f` Hz.
`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	`f`	Time-varying, input dependent control `f` with scalar or tuple output, e.g., `\|t, x\| exp(-t * x)`. Synonymous with `envelope2`.
`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`.
`mls()`	-	1	White MLS noise source.
`mls_bits(n)`	-	1	White MLS noise source from `n`-bit MLS sequence.
`monitor(id)`	1	1	Pass-through node that retains the latest value passed through as a parameter that can be queried.
`mul(x)`	`x`	`x`	Multiplies 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`	Passes multichannel signal through.
`multisink::<U>()`	`U`	-	Consumes multichannel signal.
`multisplit::<M, N>()`	`M`	`M * N`	Splits `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	Passes 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`.
`pink()`	-	1	Pink noise.
`pinkpass()`	1	1	Pinking filter (3 dB/octave).
`pipe::<U, _, _>(f)`	`f`	`f`	Chain together `U` nodes from indexed generator `f`.
`pipef::<U, _, _>(f)`	`f`	`f`	Chain together `U` nodes from fractional generator `f`.
`pulse()`	2 (pitch, 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(wet, t)`	2	2	Stereo reverb with `wet` signal balance in 0...1 and reverberation time `t` in seconds.
`saw()`	1 (pitch)	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 (pitch)	1	Sine oscillator.
`sine_hz(f)`	-	1	Sine oscillator at `f` Hz.
`sink()`	1	-	Consumes signal.
`split::<U>()`	1	`U`	Split signal into `U` channels.
`square()`	1 (pitch)	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`	Subtracts 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))`.
`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 set and queried.
`triangle()`	1 (pitch)	1	Bandlimited triangle wave oscillator.
`triangle_hz(f)`	-	1	Bandlimited triangle wave oscillator at `f` Hz.
`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.

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

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 value can be set (recursively) with set(tag, value) and queried (recursively) with get(tag). set sets all matching parameters to the value, while get retrieves the first matching parameter, if any.

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, id)`
`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
`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(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)

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)
`sine_hz(f) * f * m + f >> sine()`	-	1	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.
`sine() & mul(semitone(4.0)) >> sine() & mul(semitone(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)`
`goertzel_hz(f)`	1	1	`(pass() \| constant(f)) >> goertzel()`
`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.
`!(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 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<f64, typenum::uint::UInt<typenum::uint::UTerm, typenum::bit::B1>>, Sine<f64>>>>"

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.

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