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// MQ Extraction Algorithm
// McAulay-Quatieri sinusoidal analysis
// Extract partials from audio buffer
function extractPartials(params, stftCache) {
const {fftSize, threshold, sampleRate} = params;
const numFrames = stftCache.getNumFrames();
const frames = [];
for (let i = 0; i < numFrames; ++i) {
const cachedFrame = stftCache.getFrameAtIndex(i);
const squaredAmp = stftCache.getSquaredAmplitude(cachedFrame.time);
const peaks = detectPeaks(squaredAmp, fftSize, sampleRate, threshold);
frames.push({time: cachedFrame.time, peaks});
}
const partials = trackPartials(frames);
for (const partial of partials) {
partial.freqCurve = fitBezier(partial.times, partial.freqs);
partial.ampCurve = fitBezier(partial.times, partial.amps);
}
return {partials, frames};
}
// Detect spectral peaks via local maxima + parabolic interpolation
// squaredAmp: pre-computed re*re+im*im per bin
function detectPeaks(squaredAmp, fftSize, sampleRate, thresholdDB) {
const mag = new Float32Array(fftSize / 2);
for (let i = 0; i < fftSize / 2; ++i) {
mag[i] = 10 * Math.log10(Math.max(squaredAmp[i], 1e-20));
}
const peaks = [];
for (let i = 2; i < mag.length - 2; ++i) {
if (mag[i] > thresholdDB &&
mag[i] > mag[i-1] && mag[i] > mag[i-2] &&
mag[i] > mag[i+1] && mag[i] > mag[i+2]) {
// Parabolic interpolation for sub-bin accuracy
const alpha = mag[i-1];
const beta = mag[i];
const gamma = mag[i+1];
const p = 0.5 * (alpha - gamma) / (alpha - 2*beta + gamma);
const freq = (i + p) * sampleRate / fftSize;
const ampDB = beta - 0.25 * (alpha - gamma) * p;
peaks.push({freq, amp: Math.pow(10, ampDB / 20)});
}
}
return peaks;
}
// Track partials across frames (birth/death/continuation)
function trackPartials(frames) {
const partials = [];
const activePartials = [];
const candidates = []; // pre-birth
const trackingRatio = 0.05; // 5% frequency tolerance
const minTrackingHz = 20;
const birthPersistence = 3; // frames before partial is born
const deathAge = 5; // frames without match before death
const minLength = 10; // frames required to keep partial
for (const frame of frames) {
const matched = new Set();
// Continue active partials
for (const partial of activePartials) {
const lastFreq = partial.freqs[partial.freqs.length - 1];
const tol = Math.max(lastFreq * trackingRatio, minTrackingHz);
let bestIdx = -1, bestDist = Infinity;
for (let i = 0; i < frame.peaks.length; ++i) {
if (matched.has(i)) continue;
const dist = Math.abs(frame.peaks[i].freq - lastFreq);
if (dist < tol && dist < bestDist) { bestDist = dist; bestIdx = i; }
}
if (bestIdx >= 0) {
const pk = frame.peaks[bestIdx];
partial.times.push(frame.time);
partial.freqs.push(pk.freq);
partial.amps.push(pk.amp);
partial.age = 0;
matched.add(bestIdx);
} else {
partial.age++;
}
}
// Advance candidates
for (let i = candidates.length - 1; i >= 0; --i) {
const cand = candidates[i];
const lastFreq = cand.freqs[cand.freqs.length - 1];
const tol = Math.max(lastFreq * trackingRatio, minTrackingHz);
let bestIdx = -1, bestDist = Infinity;
for (let j = 0; j < frame.peaks.length; ++j) {
if (matched.has(j)) continue;
const dist = Math.abs(frame.peaks[j].freq - lastFreq);
if (dist < tol && dist < bestDist) { bestDist = dist; bestIdx = j; }
}
if (bestIdx >= 0) {
const pk = frame.peaks[bestIdx];
cand.times.push(frame.time);
cand.freqs.push(pk.freq);
cand.amps.push(pk.amp);
matched.add(bestIdx);
if (cand.times.length >= birthPersistence) {
activePartials.push(cand);
candidates.splice(i, 1);
}
} else {
candidates.splice(i, 1);
}
}
// Spawn candidates from unmatched peaks
for (let i = 0; i < frame.peaks.length; ++i) {
if (matched.has(i)) continue;
const pk = frame.peaks[i];
candidates.push({times: [frame.time], freqs: [pk.freq], amps: [pk.amp], age: 0});
}
// Kill aged-out partials
for (let i = activePartials.length - 1; i >= 0; --i) {
if (activePartials[i].age > deathAge) {
if (activePartials[i].times.length >= minLength) partials.push(activePartials[i]);
activePartials.splice(i, 1);
}
}
}
// Collect remaining active partials
for (const partial of activePartials) {
if (partial.times.length >= minLength) partials.push(partial);
}
return partials;
}
// Fit cubic bezier to trajectory using samples at ~1/3 and ~2/3 as control points
function fitBezier(times, values) {
const n = times.length - 1;
const t0 = times[0], v0 = values[0];
const t3 = times[n], v3 = values[n];
const dt = t3 - t0;
if (dt <= 0 || n === 0) {
return {t0, v0, t1: t0, v1: v0, t2: t3, v2: v3, t3, v3};
}
const v1 = values[Math.round(n / 3)];
const v2 = values[Math.round(2 * n / 3)];
return {t0, v0, t1: t0 + dt / 3, v1, t2: t0 + 2 * dt / 3, v2, t3, v3};
}
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