@audio/lpc

Linear predictive coding — model a signal as an autoregressive process, then predict, extrapolate, or fill gaps from it.

The Levinson-Durbin solution to the Yule-Walker equations, plus the AR-prediction tools that classical audio restoration is built on. Pure math, no dependencies.

import { lpc, arExtrapolate, arInterpolate } from '@audio/lpc'

let { a, e } = lpc(window, 16)          // AR(16) coefficients a[], residual variance e
let filled = arExtrapolate(context, a, 32)   // project 32 samples forward (de-clip)

lpc(x, p) / arFit(x, p)

LPC analysis of order p over window x (lpc is the conventional alias). Returns { a: Float64Array(p+1), e } — a[0] === 1, e is the residual variance. Internally levinson(autocorr(x, p), p).

autocorr(x, p) · levinson(R, p)

The two stages, exposed separately: biased autocorrelation R[0..p], and the Levinson-Durbin Toeplitz solve. Call directly when you already have an autocorrelation, or want the reflection-coefficient path.

arPredict(a, hist)

One-step prediction x̂[n] = -∑ a[k]·x[n−k] from a history buffer.

arExtrapolate(context, a, m)

Project m samples forward from context under model a. Used to reconstruct clipped regions from their un-clipped neighbourhood.

arInterpolate(x, gap, a)

Least-squares fill of missing indices gap (sorted) inside x, in place, under model a — the interpolator behind de-click / de-crackle. Gauss-Seidel, converges well past audible accuracy for short bursts.

Notes

Foundation for LPC vocoders and formant tracking (Markel & Gray 1976); restoration methods follow Godsill & Rayner (1998). Used by @audio/denoise's declick/decrackle/declip. MIT.