!@thi.ng/dsp

!npm downloads

> [!NOTE]
> This is one of 214 standalone projects, maintained as part
> of the @thi.ng/umbrella monorepo
> and anti-framework.
>
> 🚀 Please help me to work full-time on these projects by sponsoring me on
> GitHub. Thank you! ❤️

- About
- Status
- Support packages
- Related packages
- Installation
- Dependencies
- Usage examples
- API
- IGen
- Higher order generators
- Oscillators
- IProc
- Filters
- Filter responses
- Delay
- Feedback delay
- Filtered feedback delay
- Wave shaping
- Foldback distortion
- FFT
- Window functions
- Utilities
- Authors
- License

About

Composable signal generators, oscillators, filters, FFT, spectrum, windowing & related DSP utils.

Partially ported from other thi.ng projects (e.g.
thi.ng/synstack,
thi.ng/vexed-generation,
toxiclibs).

Status

STABLE - used in production

Search or submit any issues for this package

Even though this library is now at v2.0.0 and still retains most of the features
from earlier versions, all recently added features (IGen's, IProc's, composition
ops etc.) should be considered "beta" and are likely to undergo further
(hopefully not too drastic) changes in the near future. Also, pending outcomes
of ongoing experiments, some aspects might be ported to WASM.

Support packages

- @thi.ng/dsp-io-wav - WAV file format generation

Related packages

- @thi.ng/math - Assorted common math functions & utilities

Installation

``bash
yarn add @thi.ng/dsp
`

ESM import:

`ts
import * as dsp from "@thi.ng/dsp";
`

Browser ESM import:

`html

`

JSDelivr documentation

For Node.js REPL:

`js
const dsp = await import("@thi.ng/dsp");
`

Package sizes (brotli'd, pre-treeshake): ESM: 7.56 KB

Dependencies

- @thi.ng/api
- @thi.ng/checks
- @thi.ng/errors
- @thi.ng/math
- @thi.ng/random
- @thi.ng/transducers

Note: @thi.ng/api is in _most_ cases a type-only import (not used at runtime)

Usage examples

Nine projects in this repo's
/examples
directory are using this package:

| Screenshot | Description | Live demo | Source |
|:---------------------------------------------------------------------------------------------------------------------------|:-------------------------------------------------------------------------|:----------------------------------------------------------|:---------------------------------------------------------------------------------------|
| | Interactive inverse FFT toy synth | Demo | Source |
| | Fiber-based cooperative multitasking basics | Demo | Source |
| | Polygon to cubic curve conversion & visualization | Demo | Source |
| | Steering behavior drawing with alpha-blended shapes | Demo | Source |
| | Minimal rdom-canvas animation | Demo | Source |
| | Generative audio synth offline renderer and WAV file export | Demo | Source |
| | WebGL cube maps with async texture loading | Demo | Source |
| | WebGL screenspace ambient occlusion | Demo | Source |
| | Interactively drawing to & reading from a WebGL offscreen render texture | Demo | Source |

API

Generated API docs

$3

The following unit generators are infinite data sources based on the IGen
interface
with most being resettable too. The interface is similar to ES6 iterators in
that the next value can be obtained by calling .next(), however since IGens
are always infinite, there's no need to wrap the result
value
as is done with ES6 iterables. Furthermore, all gens defined in this package do
implement Symbol.iterator and so can actually be used as standard iterables as
well.

IGen also implements the
IDeref
interface to obtain the gen's current (last generated) value.

`ts
import { curve } from "@thi.ng/dsp";

// create exponential curve from 0 - 10 over 5 steps
const c = curve(0, 10, 5);

// get next value
c.next()
// 0
c.next()
// 6.087111442696312
c.next()
// 8.505616378877338
c.next()
// 9.46652635750935
c.next()
// 9.848310977098592
c.next()
// 9.999999999999998

// get current value
c.deref()
// 9.999999999999998

// reset gen
c.reset()

// produce an array (can also write into existing buffer)
c.take(6)
// [
// 0,
// 6.087111442696312,
// 8.505616378877338,
// 9.46652635750935,
// 9.848310977098592,
// 9.999999999999998
// ]

// use as ES6 iterable, here w/ transducers
import { take } from "@thi.ng/transducers";

[...take(6, c.reset())]
// [
// 0,
// 6.087111442696312,
// 8.505616378877338,
// 9.46652635750935,
// 9.848310977098592,
// 9.999999999999998
// ]
`

- add - adder
- adsr - timebased ADSR / AD envelope generator
- alt - alternating values
- constant - constant value
- cosine - trig-free cosine osc
- curve - timebased exponential gain/decay (factory for madd)
- impulse - impulse gen
- impulseTrain - timebased cyclic impulse
- line - timebased line gen (factory for add)
- madd - multiply-adder
- mul - multiplier (exponential gain/decay)
- pinkNoise - configurable pink noise (1/f power spectrum)
- reciprocal - fractional sequence (1, 1/2, 1/3, 1/4 etc.)
- sincos - trig-free sin/cos LFO
- sweep - freq sweep gen w/ phase accumulation for oscillators
- whiteNoise - white noise

#### Higher order generators

- mapG - IGen composition / transformation (1-4 inputs)
- addG - higher-order adder
- product - product of input gens
- sum - sum of input gens

#### Oscillators

##### IGen wrappers

- osc - arbitrary function oscillator w/ modulation support
- modOsc - FM / FMAM oscillator builder

`ts
import { osc, modOsc, saw, sin } from "@thi.ng/dsp";

const FS = 44100;

// simple 100Hz sine oscillator
const o = osc(sin, 100 / FS, 0.5);

// get next sample
o.next();
...

// frequency & amplitude modulated saw osc
const fmam = modOsc(
// carrier waveform
saw,
// carrier freq
1000 / FS,
// fmod
osc(saw, 5000 / FS, 0.3),
// amod
osc(saw, 500 / FS)
);

// compute 1sec of signal
fmam.take(FS)
`

Diagram of the FM/AM osc with some low pass filters applied:

!FM/AM waveform

##### Stateless oscillator functions

- additive
- dsf
- mix
- parabolic
- rect
- saw
- sawAdditive
- squareAdditive
- squareSin
- sin
- tri
- wavetable

$3

The second fundamental interface in this package, similar to IGen and used to
implement processors & transformers of input values (e.g those generated by the
various IGens available). IProc implementations have a .next(x) method,
where x is the next input to be processed.

The package also provides several approaches to compose multi-step processing
pipelines (see section further below). Furthermore, all implementations in this
package implement the @thi.ng/transducers IXform
interface
and so can be directly used in transducer pipelines too.

Additional higher order IProc implementations:

- bounce - sum multiple inputs
- mix - linear interpolation of 2 inputs
- multiplex - process 1 input into multiple outs
- pipe - IGen & multiple IProc pipeline setup
- serial - serial processing of multiple IProc

`ts
import { comp, push, take, transduce } from "@thi.ng/transducers";

const FS = 48000; // sample rate
const F1 = 1 / FS; // start freq
const F2 = 10000 / FS; // end freq

// generate oscillator sweep with some effects applied
const sig = new Float32Array(
transduce(
comp(
// consume 8 secs worth of samples
take(8 * FS),
// lowpass filter (state variable filter)
svfLP(F2),
// soft clip
waveShaper(4),
// 0.5sec delay w/ 60% feedback
feedbackDelay(0.5 * FS, 0.6)
),
// reducer: collect as array
push(),
// oscillator (consumed as ES6 iterable)
osc(
// osc function (use only 3 harmonics)
sawAdditive(3),
// freq sweep F1 -> F2 over 6 sec
sweep(F1, F2, 6 * FS),
// envelope (using attack & decay phase only)
adsr({ a: 0.05 FS, d: 5.95 FS, s: 0 })
)
)
);

fs.writeFileSync("sig.raw", Buffer.from(sig.buffer));
`

Use the @thi.ng/dsp-io-wav
package
to export as WAV, or alternatively use ffmpeg for conversion:

`bash
ffmpeg -f f32le -ar 48k -ac 1 -i sig.raw sig.wav -y
`

#### Filters

The following diagrams show various combinations of oscillator signals and their
filtered responses (with different cutoff/center frequencies).

All diagrams were generated with this
script.

The following filter types / functions are available:

##### 1-pole

- onepoleLP - low pass, 6dB/oct falloff
- dcBlock - high pass, 6dB/oct falloff
- allpass - allpass (-90° phase shift @ center freq)

Low pass:

!LPF response

DC blocker:

!DC block response

Allpass:

!Allpass response

##### Biquad

Source

- biquadLP - low pass, 12dB/oct falloff, resonance
- biquadHP - high pass, 12dB/oct falloff, resonance
- biquadBP - band pass, 12dB/oct falloff, resonance
- biquadNotch - notch / band-stop, resonance/bandwidth
- biquadPeak - peak EQ, customizable +/- gain, bandwidth
- biquadLoShelf - low shelf, customizable +/- gain
- biquadHiShelf - low shelf, customizable +/- gain

(Q = 0.707 for all versions)

Low pass:

!LPF response

High pass:

!HPF response

Band pass:

!BPF response

Notch:

!Notch response

Peak (gain = 6dB):

!Peak response

Low shelf (gain = -6dB):

!Lo-shelf response

High shelf (gain = -6dB):

!Hi-shelf response

##### State variable filter

Source

- svfLP - low pass, resonance
- svfHP - high pass, resonance
- svfBP - band pass, resonance
- svfNotch - notch / band-stop, resonance/bandwidth
- svfPeak - peak EQ, customizable +/- gain, bandwidth
- svfAllpass - allpass, bandwidth

(Q = 0.5 for all versions)

Low pass:

!LPF response

High pass:

!HPF response

Band pass:

!BPF response

Notch:

!Notch response

Peak (gain = 6dB):

!Peak response

Allpass:

!Allpass response

#### Filter responses

Using the Filter response
utils,
the following filter types can be evaluated for analyzing their impact on
specific frequencies (or frequency bands). Any type implementing
IFilter can
be used, currently:

- 1-pole
- DC-block
- Biquad

`ts
import { biquadPeak, freqRange, filterResponse } from "@thi.ng/dsp";

// peak biquad @ 5kHz w/ -60dB gain
const coeffs = biquadPeak(5000 / FS, 10, -60).filterCoeffs();
// {
// zeroes: [ 0.030659922512760035, -0.04493872132576855, 0.028719301737009807 ],
// poles: [ 1, -0.04493872132576855, -0.94062077575023 ]
// }

// compute 256 filter responses between 0 - nyquist
// (magnitude in dBFS by default, phase shift in radians)
const resp = freqRange(0, 0.5, 256).map((f) => filterResponse(coeffs, f));
// [
// { freq: 0, phase: 0, mag: -9.836140158843584e-14 },
// {
// freq: 0.00196078431372549,
// phase: -1.025916720326544,
// mag: -5.731888923801755
// },
// {
// freq: 0.00392156862745098,
// phase: -1.27451127560192,
// mag: -10.788101434823263
// },
// ...
// ]
`

Basic filter response plot:

!Filter response

#### Delay

Source

Ringbuffer / delay line for arbitrary values and support for single & multi-taps
at any relative positions. Useful fundamental building block for various other
effects, filters etc.

#### Feedback delay

Source

Variation of delay() which adds a portion of the delayed value to each new
input and stores result in delay line.

#### Filtered feedback delay

Source

Variation of feedbackDelay() which processes feedback via given filter /
IProc, e.g. to create dub style filter delays.

#### Wave shaping

Source

This operator remaps inputs via a user provided function. The following shaping
functions are provided:

- waveshapeTan - arctan based (soft-clip/distortion)
- waveshapeSigmoid - sigmoid based, similar to above
- waveshapeSin - depending on coefficient, can produce entirely new waveforms

Use the interactive calculator @
Desmos to experiment.

Acrtan:

!Tan response

Sigmoid:

!Sigmoid response

Sine:

!Sine response

#### Foldback distortion

Source

Recursively folds input into [-thresh .. +thresh] interval and amplifies it
with amp (default: 1/thresh).

Use the interactive calculator @
Desmos to experiment.

!Foldback response

$3

Source

- fft()
- ifft()
- normalizeFFT()
- denormalizeFFT()
- scaleFFT()
- complexArray()
- conjugate()
- powerSumSquared()
- powerMeanSquared()
- powerTimeIntegral()
- spectrumMag()
- spectrumPow() (optionally as dBFS)
- spectrumPhase()
- binFreq()
- freqBin()
- fftFreq()
- integralT() / integralTSquared()
- integralF() / integralFSquared()

#### Window functions

Source

- window()
- applyWindow()
- windowRect()
- windowBartlett()
- windowWelch()
- windowSin()
- windowSinPow()
- windowLanczos()
- windowHann()
- windowHamming()
- windowBlackman()
- windowBlackmanHarris()
- windowNuttal()
- windowBlackmanNuttal()
- windowGauss()

$3

- Unit conversions
- Filter response

Authors

- Karsten Schmidt

If this project contributes to an academic publication, please cite it as:

`bibtex
@misc{thing-dsp,
title = "@thi.ng/dsp",
author = "Karsten Schmidt",
note = "https://thi.ng/dsp",
year = 2015
}
``

License

© 2015 - 2026 Karsten Schmidt // Apache License 2.0