periodic-function

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

npm install periodic-function

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 | | | | sine(t, phase=0) | Sine wave. phase=0.25 gives cosine. | | | cosine(t, phase=0) | Cosine wave. Equivalent to sine(t, 0.25). | | | sawtooth(t) | Descending ramp: 1 at t=0, −1 approaching t=1. For ascending ramp use triangle(t, 0). | | | square(t, duty=0.5) | Square wave. duty = fraction of period spent high. | | | triangle(t, ratio=0.5) | Triangle wave. ratio = peak position (0 = ascending ramp, 1 = descending ramp). | | | 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. | | | pulse(t, width=0) | Dirac-like pulse: 1 at t=0, 0 elsewhere. width extends the high region. | | | clausen(t, harmonics=10) | Clausen function: Σ sin(kθ)/k². | | | noise(t) | Periodic noise — repeating random buffer. | | | Fourier / Wavetable | | | | 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. | | | wavetable(real, imag, {size=8192, normalize=true}) | Build a Float32Array wavetable from Fourier coefficients. Used for AudioContext.createPeriodicWave. | | | Lookup | | | | interpolate(t, samples) | Linearly interpolate between samples, treating them as one period. | | | step(t, samples) | Step lookup — nearest sample, no interpolation. |

Examples

// 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 — uses wavetable() for PeriodicWave
• MDN: createPeriodicWave
• List of periodic functions

License

MIT © Dmitry Iv