Constant-Q transform using Goertzel algorithm

cqt.js

/**
 * Constant-Q Transform (CQT) calculated using Goertzel algorithm
 *
 * This by itself doesn't need Web Audio API in order to work but it is necessary for real-time visualizations
 *
 * Real-time usage:
 * analyserNode.getFloatTimeDomainData(dataArray);
 * const spectrum = cqt(dataArray, freqBands, audioCtx.sampleRate, bandwidthOffset, windowFunction);
 *
 * Note: the implementation of this CQT is slow compared to FFT
 */

function cqt(waveform, hzArray = generateOctaveBands(), sampleRate = 44100, bandwidthOffset = 1, windowFunction = applyWindow) {
  return hzArray.map(x => {
    const coeff = 2 * Math.cos(2*Math.PI*x.ctr/sampleRate),
          bandwidth = Math.abs(x.hi - x.lo) + (sampleRate/waveform.length) * bandwidthOffset,
          tlen = Math.min(1/bandwidth, waveform.length/sampleRate);
    let f1 = 0,
        f2 = 0,
        sine,
        lowerIdx = Math.trunc(waveform.length-tlen*sampleRate),
        higherIdx = waveform.length-1,
        norm = 0;
    for (let i = lowerIdx; i <= higherIdx; i++) {
      let posX = (i - lowerIdx) / (higherIdx - lowerIdx) * 2 - 1;
      let w = windowFunction(posX);
      norm += w;
      
      // Goertzel transform
      sine = waveform[i]*w + coeff * f1 - f2;
      f2 = f1;
      f1 = sine;
    }
    return Math.sqrt(f1 ** 2 + f2 ** 2 - coeff * f1 * f2) / norm;
  });
}

// Generate octave bands, default is 1/12 octave spanning 20Hz-20kHz (note index 4 to 123, which corresponds to E0 to D#10 respectively)
function generateOctaveBands(bandsPerOctave = 12, lowerNote = 4, higherNote = 123, detune = 0, bandwidth = 0.5) {
  const root24 = 2 ** ( 1 / 24 );
  const c0 = 440 * root24 ** -114; // ~16.35 Hz
  const groupNotes = 24/bandsPerOctave;
  let bands = [];
  for (let i = Math.round(lowerNote*2/groupNotes); i <= Math.round(higherNote*2/groupNotes); i++) {
    bands.push({
      lo: c0 * root24 ** ((i-bandwidth)*groupNotes+detune),
      ctr: c0 * root24 ** (i*groupNotes+detune),
      hi: c0 * root24 ** ((i+bandwidth)*groupNotes+detune)
    });
  }
  return bands;
}

function applyWindow(x) {
  return 0.42 + 0.5 * Math.cos(x*Math.PI) + 0.08 * Math.cos(x*Math.PI*2); // Blackman window to match AnalyserNode's windowing function
}