# periodic-function

> Periodic waveform functions — phase normalized to [0,1]

Latest version **2.1.2** (published 2026-07-11) · MIT license · 0 weekly downloads

## Install

```sh
npm install periodic-function
pnpm add periodic-function
yarn add periodic-function
bun add periodic-function
```

## Health

**Score 60/100 (C)** — status: active.

Positive: esm support; no vulnerabilities; recently updated; high maintenance score.

Warnings: low downloads; no types.

## Facts

| | |
|---|---|
| Version | 2.1.2 |
| Published | 2026-07-11 |
| First published | 2017-06-22 |
| Weekly downloads | 0 |
| License | MIT |
| TypeScript types | none |
| Module format | ESM + CommonJS |
| Dependencies | 0 |
| Unpacked size | 9.3 KB |
| Known vulnerabilities | 0 |
| Install scripts | no |
| GitHub stars | 58 |
| Author | Dmitry Iv |
| Maintainers | dfcreative, dy |
| Keywords | periodic, waveform, sine, sawtooth, square, triangle, fourier, wavetable, dsp, audio |

## Links

- npm: https://www.npmjs.com/package/periodic-function
- Repository: https://github.com/audiojs/periodic-function
- Homepage: https://github.com/audiojs/periodic-function#readme
- Issues: https://github.com/audiojs/periodic-function/issues
- Funding: https://github.com/sponsors/audiojs
- npm.io page: https://npm.io/package/periodic-function

## Alternatives

- [mobx-react](https://npm.io/package/mobx-react.md) — 2.8M weekly downloads
- [rc-tree](https://npm.io/package/rc-tree.md) — 2.6M weekly downloads
- [@react-oauth/google](https://npm.io/package/@react-oauth/google.md) — 1.3M weekly downloads
- [@wagmi/connectors](https://npm.io/package/@wagmi/connectors.md) — 877.0K weekly downloads
- [vee-validate](https://npm.io/package/vee-validate.md) — 836.4K weekly downloads

## Recent versions

- 2.1.2 (latest) — 2026-07-11
- 2.1.1 — 2026-07-09
- 2.1.0 — 2026-03-31
- 2.0.0 — 2026-03-31
- 1.1.4 — 2017-06-30
- 1.1.3 — 2017-06-29
- 1.1.2 — 2017-06-29
- 1.1.1 — 2017-06-29
- 1.1.0 — 2017-06-22
- 1.0.0 — 2017-06-22

## README

# periodic-function

Periodic waveform functions. Phase `t` is normalized to `[0, 1]` — one full turn.

```
npm install periodic-function
```

```js
import { sine, square, wavetable } from 'periodic-function'

sine(0.25)          // 1  (peak)
square(0.75)        // -1 (low)
wavetable(null, [0, 1, 0, 0.5])  // Float32Array wavetable from Fourier coefficients
```

## API

All functions take phase `t ∈ [0, 1]` as first argument. Values outside `[0, 1]` wrap correctly.

| | Function | Description |
|:---:|---|---|
| | **Waveforms** | |
| <img src="img/sine.svg" width="200" height="60" alt="sine"> | `sine(t, phase=0)` | Sine wave. `phase=0.25` gives cosine. |
| <img src="img/cosine.svg" width="200" height="60" alt="cosine"> | `cosine(t, phase=0)` | Cosine wave. Equivalent to `sine(t, 0.25)`. |
| <img src="img/sawtooth.svg" width="200" height="60" alt="sawtooth"> | `sawtooth(t)` | Descending ramp: 1 at t=0, −1 approaching t=1. For ascending ramp use `triangle(t, 0)`. |
| <img src="img/square.svg" width="200" height="60" alt="square"> | `square(t, duty=0.5)` | Square wave. `duty` = fraction of period spent high. |
| <img src="img/triangle.svg" width="200" height="60" alt="triangle"> | `triangle(t, ratio=0.5)` | Triangle wave. `ratio` = peak position (0 = ascending ramp, 1 = descending ramp). |
| <img src="img/trapezoid.svg" width="200" height="60" alt="trapezoid"> | `trapezoid(t, p1=0.25, p2=0.5, p3=0.75)` | Trapezoid wave. Rise ends at `p1`, fall starts at `p2`, fall ends at `p3`. Generalizes square and triangle. |
| <img src="img/pulse.svg" width="200" height="60" alt="pulse"> | `pulse(t, width=0)` | Dirac-like pulse: 1 at t=0, 0 elsewhere. `width` extends the high region. |
| <img src="img/clausen.svg" width="200" height="60" alt="clausen"> | `clausen(t, harmonics=10)` | [Clausen function](https://en.wikipedia.org/wiki/Clausen_function): Σ sin(kθ)/k². |
| <img src="img/noise.svg" width="200" height="60" alt="noise"> | `noise(t)` | Periodic noise — repeating random buffer. |
| | **Fourier / Wavetable** | |
| <img src="img/fourier.svg" width="200" height="60" alt="fourier"> | `fourier(t, real, imag)` | Evaluate one sample from Fourier coefficients. `real[k]` and `imag[k]` are cosine/sine amplitudes for harmonic `k`. Index 0 is DC, 1 is fundamental. |
| <img src="img/wavetable.svg" width="200" height="60" alt="wavetable"> | `wavetable(real, imag, {size=8192, normalize=true})` | Build a `Float32Array` wavetable from Fourier coefficients. Used for `AudioContext.createPeriodicWave`. |
| | **Lookup** | |
| <img src="img/interpolate.svg" width="200" height="60" alt="interpolate"> | `interpolate(t, samples)` | Linearly interpolate between samples, treating them as one period. |
| <img src="img/step.svg" width="200" height="60" alt="step"> | `step(t, samples)` | Step lookup — nearest sample, no interpolation. |

## Examples

```js
// Cosine as a phase-shifted sine
sine(0, 0.25)     // 1  (same as cosine(0))

// Square wave with 10% duty cycle
square(0.05, 0.1) // 1
square(0.15, 0.1) // -1

// Triangle with peak at 0.25 (asymmetric)
triangle(0.25, 0.25) // -1  (valley, since peak is at t=0)

// Trapezoid as a square with soft edges
trapezoid(t, 0.05, 0.5, 0.55)

// Fourier series: pure sine
fourier(0.25, null, [0, 1])  // 1

// Wavetable for Web Audio API PeriodicWave
const real = new Float32Array(64)
const imag = new Float32Array(64)
for (let k = 1; k < 64; k += 2) imag[k] = 4 / (Math.PI * k)  // square wave
const table = wavetable(real, imag)  // Float32Array[8192], normalized to ±1
```

## Related

- [web-audio-api](https://github.com/audiojs/web-audio-api) — uses `wavetable()` for `PeriodicWave`
- [MDN: createPeriodicWave](https://developer.mozilla.org/en-US/docs/Web/API/AudioContext/createPeriodicWave)
- [List of periodic functions](https://en.wikipedia.org/wiki/List_of_periodic_functions)

## License

MIT © Dmitry Iv

<p align=center><a href="https://github.com/krishnized/license/">ॐ</a></p>

---
_Source: https://npm.io/package/periodic-function · Machine-readable twin of the npm.io package page. Health data is recomputed on every publish._