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

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