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Phase `t` is normalized to `[0, 1]` — one full turn.\n\n```\nnpm install periodic-function\n```\n\n```js\nimport { sine, square, wavetable } from 'periodic-function'\n\nsine(0.25) // 1 (peak)\nsquare(0.75) // -1 (low)\nwavetable(null, [0, 1, 0, 0.5]) // Float32Array wavetable from Fourier coefficients\n```\n\n## API\n\nAll functions take phase `t ∈ [0, 1]` as first argument. Values outside `[0, 1]` wrap correctly.\n\n| | Function | Description |\n|:---:|---|---|\n| | **Waveforms** | |\n| \"sine\" | `sine(t, phase=0)` | Sine wave. `phase=0.25` gives cosine. |\n| \"cosine\" | `cosine(t, phase=0)` | Cosine wave. Equivalent to `sine(t, 0.25)`. |\n| \"sawtooth\" | `sawtooth(t)` | Descending ramp: 1 at t=0, −1 approaching t=1. For ascending ramp use `triangle(t, 0)`. |\n| \"square\" | `square(t, duty=0.5)` | Square wave. `duty` = fraction of period spent high. |\n| \"triangle\" | `triangle(t, ratio=0.5)` | Triangle wave. `ratio` = peak position (0 = ascending ramp, 1 = descending ramp). |\n| \"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. |\n| \"pulse\" | `pulse(t, width=0)` | Dirac-like pulse: 1 at t=0, 0 elsewhere. `width` extends the high region. |\n| \"clausen\" | `clausen(t, harmonics=10)` | [Clausen function](https://en.wikipedia.org/wiki/Clausen_function): Σ sin(kθ)/k². |\n| \"noise\" | `noise(t)` | Periodic noise — repeating random buffer. |\n| | **Fourier / Wavetable** | |\n| \"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. |\n| \"wavetable\" | `wavetable(real, imag, {size=8192, normalize=true})` | Build a `Float32Array` wavetable from Fourier coefficients. Used for `AudioContext.createPeriodicWave`. |\n| | **Lookup** | |\n| \"interpolate\" | `interpolate(t, samples)` | Linearly interpolate between samples, treating them as one period. |\n| \"step\" | `step(t, samples)` | Step lookup — nearest sample, no interpolation. |\n\n## Examples\n\n```js\n// Cosine as a phase-shifted sine\nsine(0, 0.25) // 1 (same as cosine(0))\n\n// Square wave with 10% duty cycle\nsquare(0.05, 0.1) // 1\nsquare(0.15, 0.1) // -1\n\n// Triangle with peak at 0.25 (asymmetric)\ntriangle(0.25, 0.25) // -1 (valley, since peak is at t=0)\n\n// Trapezoid as a square with soft edges\ntrapezoid(t, 0.05, 0.5, 0.55)\n\n// Fourier series: pure sine\nfourier(0.25, null, [0, 1]) // 1\n\n// Wavetable for Web Audio API PeriodicWave\nconst real = new Float32Array(64)\nconst imag = new Float32Array(64)\nfor (let k = 1; k < 64; k += 2) imag[k] = 4 / (Math.PI * k) // square wave\nconst table = wavetable(real, imag) // Float32Array[8192], normalized to ±1\n```\n\n## Related\n\n- [web-audio-api](https://github.com/audiojs/web-audio-api) — uses `wavetable()` for `PeriodicWave`\n- [MDN: createPeriodicWave](https://developer.mozilla.org/en-US/docs/Web/API/AudioContext/createPeriodicWave)\n- [List of periodic functions](https://en.wikipedia.org/wiki/List_of_periodic_functions)\n\n## License\n\nMIT © Dmitry Iv\n\n

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