@audio/eq-fit

Fit an N-band parametric EQ to a target magnitude curve

import fit from '@audio/eq-fit'

The missing math between curve producers (@audio/spectral-target, @audio/measure-response, or a plain list of {f, gain} points) and band consumers (@audio/eq-parametric). Two stages: greedy residual-peak-picking places an initial band at each remaining error's largest excursion (in the spirit of AutoEQ's — jaakkopasanen/AutoEq — initial-guess heuristic, reimplemented here rather than ported); then Levenberg–Marquardt (Marquardt 1963) jointly refines every band's frequency, gain, and Q against the whole curve at once. Coefficients and |H(f)| come from @audio/biquad's RBJ Audio-EQ-Cookbook implementation — this module only searches for good {fc, Q, gain}, it never derives filter math of its own.

// from control points
let r = fit([{ f: 100, gain: 4 }, { f: 3000, gain: -3 }, { f: 8000, gain: 2 }], { bands: 6 })
r.bands     // [{ type: 'peak', fc, Q, gain }, ...] — ready for @audio/eq-parametric's params.bands
r.preamp    // dB, ≤ 0 — suggested frequency-response headroom
r.error     // weighted RMS dB error of the fit
r.response  // f => dB, the fitted cascade's response incl. preamp

// from a function
fit(f => (f > 5000 ? -6 : 0), { bands: 4, shelves: true })

// from a @audio/measure-response result
import measureResponse from '@audio/measure-response'
fit(measureResponse(impulseResponse, { fs }), { fs })

// apply it
import parametricEq from '@audio/eq-parametric'
parametricEq(data, { bands: r.bands, fs: 44100 })
const preampGain = 10 ** (r.preamp / 20)
for (let i = 0; i < data.length; i++) data[i] *= preampGain

// interchange with AutoEQ / Equalizer APO
import { toEqualizerApo, fromEqualizerApo } from '@audio/eq-fit'
toEqualizerApo(r)             // "Preamp: -2.1 dB\nFilter 1: ON PK Fc 100 Hz Gain 4.0 dB Q 1.41\n…"
fromEqualizerApo(apoText)     // { bands, preamp } — reads AutoEQ's own ParametricEQ.txt files too

target accepts any of: {f, gain}[] control points (log-frequency interpolation), an f => dB function, a Float32Array of dB-per-bin over [0, fs/2] (the @audio/spectral-target bin-grid convention), or {freqs, db} (the @audio/measure-response shape). Deterministic — no randomness anywhere in either stage, so the same input always returns the same bands.

preamp is -max(0, peak of the fitted cascade) estimated over the evaluation grid. It supplies frequency-response headroom; parametricEq does not apply it automatically. This estimate does not guarantee a time-domain sample or true-peak ceiling. Measure the processed signal and use peak control when required.

Use when: turning a measured or target curve — a headphone correction target, a room-EQ deviation curve, a captured reference spectrum — into a small parametric band list a real-time EQ (or a hardware unit that only understands PK/LSC/HSC text) can use, instead of the full-resolution FIR alternative (@audio/eq-fir).

Algorithm

1. Init — for each side (shelves on): if the target's own value at fMin/fMax exceeds ±0.1 dB, place a shelf there (Q 0.707, corner where the (⅓-octave smoothed) curve crosses half that edge value). Remaining slots: repeatedly smooth the current residual (⅓-octave), place a peaking band at its largest excursion (gain = residual there, Q from the −3 dB-of-gain half-power width of the local lobe), subtract, repeat until bands is used or weighted RMS ≤ tolerance.
2. Refine — joint nonlinear least squares over every band's (ln fc, gain, ln Q) at once: Levenberg–Marquardt (Marquardt 1963, the diag(JᵀJ)-scaled damping, not Levenberg's plain identity; initial damping τ·max(diag(JᵀJ)) per Marquardt's own §4) with a numeric Jacobian (central differences) and box constraints enforced by clamp-and-reproject. Stops on relative cost improvement < 1e-6 or iterations (Nocedal & Wright, Numerical Optimization 2nd ed., §10.3).
3. Bands with |gain| < 0.1 dB are dropped, the rest sorted by fc.

Measured on this package's own test suite: exact recovery (fc within 2%, gain within 0.2 dB, Q within 10%, RMS < 0.05 dB) of a synthetic 3-band target; RMS < 0.3 dB fitting a 10-band target with deliberately overlapping bands using bands: 10; RMS ≤ 0.5 dB / max ≤ 1.5 dB on a synthetic Harman-tilt headphone curve; the fitted bands run through @audio/eq-parametric and measured back via FFT of the impulse response match response(f) within 0.1 dB; fitting 10 bands on the default 256-point grid takes ~90 ms.

References

• Bristow-Johnson, R. (2005). "Audio EQ Cookbook." — biquad coefficients, via @audio/biquad.
• Marquardt, D.W. (1963). "An Algorithm for Least-Squares Estimation of Nonlinear Parameters." J. Soc. Indust. Appl. Math. 11(2):431–441.
• Nocedal, J. & Wright, S. (2006). Numerical Optimization (2nd ed.), §10.3 — Levenberg–Marquardt as damped Gauss–Newton.
• jaakkopasanen/AutoEq — the ParametricEQ.txt text format and the headphone-correction use case this module targets; test.js parses a real result file from AutoEQ's own archive.
• Equalizer APO — the ParametricEQ.txt config syntax toEqualizerApo/fromEqualizerApo read and write.

Part of @audio/eq — the eq family umbrella.

MIT © audiojs