dsp

Note

This is one of 199 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

yarn add @thi.ng/dsp

ESM import:

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

Browser ESM import:

<script type="module" src="https://esm.run/@thi.ng/dsp"></script>

JSDelivr documentation

For Node.js REPL:

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

IGen

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.

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

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:

Stateless oscillator functions

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

IProc

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

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:

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:

DC blocker:

Allpass:

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:

High pass:

Band pass:

Notch:

Peak (gain = 6dB):

Low shelf (gain = -6dB):

High shelf (gain = -6dB):

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:

High pass:

Band pass:

Notch:

Peak (gain = 6dB):

Allpass:

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

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:

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:

Sigmoid:

Sine:

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.

FFT

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()

Utilities

• Unit conversions
• Filter response

Authors

• Karsten Schmidt

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

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

License

© 2015 - 2024 Karsten Schmidt // Apache License 2.0