function createGraph(options) {
  let context = new OfflineAudioContext(1, renderFrames, sampleRate);

  // Use a default sawtooth wave for the test signal.  We want something is a
  // bit more harmonic content than a sine wave, but otherwise it doesn't
  // really matter.
  let src = context.createOscillator();
  src.type = 'sawtooth';

  let analyser = context.createAnalyser();
  analyser.fftSize = Math.pow(2, options.order);
  analyser.smoothingTimeConstant = options.smoothing || 0;
  analyser.minDecibels = options.minDecibels || analyser.minDecibels;

  // Connect the nodes together and start the source.
  src.connect(analyser);
  analyser.connect(context.destination);

  src.start();

  return {
    context: context,
    analyser: analyser,
  };
}

// Apply the windowing function, in place.
function applyWindow(timeData) {
  let length = timeData.length;
  let alpha = 0.16;
  let a0 = (1 - alpha) / 2;
  let a1 = 0.5;
  let a2 = alpha / 2;
  let omega = 2 * Math.PI / length;

  for (let k = 0; k < length; ++k) {
    let w = a0 - a1 * Math.cos(omega * k) + a2 * Math.cos(2 * omega * k);
    timeData[k] *= w;
  }
}

// Compute the FFT magnitude of |timeData|.
function computeFFTMagnitude(timeData, order) {
  // Compute the expected frequency response.  First, apply the window.
  // Compute the forward FFT.
  applyWindow(timeData);

  let fft = new FFT(order);
  let fftSize = Math.pow(2, order);
  let fftr = new Float32Array(fftSize);
  let ffti = new Float32Array(fftSize);
  fft.rfft(timeData, fftr, ffti);

  // Compute the magnitude of the expected result.
  let expected = new Float32Array(fftSize / 2);
  for (let k = 0; k < expected.length; ++k)
    expected[k] = Math.hypot(fftr[k], ffti[k]) / fftSize;

  return expected;
}

// Convert dB value to linear value.
function dbToLinear(x) {
  return Math.pow(10, x / 20);
}

// Convert linear value to dB.
function linearToDb(x) {
  return 20 * Math.log10(x);
}

// Clip the FFT magnitude so that values below |limit| are set to |limit|.  The
// FFT must be in dB.  The input array is clipped in place.
function clipMagnitude(limit, x) {
  for (let k = 0; k < x.length; ++k)
    x[k] = Math.max(limit, x[k])
}

// Compare the float frequency data in dB, |freqData|, against the expected
// value, |expectedFreq|. |options| is a dictionary with the property
// |floatRelError| for setting the comparison threshold and |precision| for
// setting the printed precision.  Setting |precision| to |undefined| means
// printing all digits.  If |options.precision} doesn't exist, use a default
// precision.
function compareFloatFreq(message, freqData, expectedFreq, should, options) {
  // Any dB values below -100 is pretty much in the noise due to round-off in
  // the (single-precisiion) FFT, so just clip those values to -100.
  let lowerLimit = -100;
  clipMagnitude(lowerLimit, expectedFreq);

  let actual = freqData;
  clipMagnitude(lowerLimit, actual);

  let success = should(actual, message).beCloseToArray(expectedFreq, {
    relativeThreshold: options.floatRelError || 0,
  });

  return {success: success, expected: expectedFreq};
}

// Apply FFT smoothing, accumulating the result in |oldFreqData| with the new
// data in |newFreqData|.  The smoothing time constant is |smoothingTime|
function smoothFFT(oldFreqData, newFreqData, smoothingTime) {
  for (let k = 0; k < oldFreqData.length; ++k) {
    let value =
        smoothingTime * oldFreqData[k] + (1 - smoothingTime) * newFreqData[k];
    oldFreqData[k] = value;
  }
}

// Convert the float frequency data, |floatFreqData|, to byte values using the
// dB limits |minDecibels| and |maxDecibels|.  The new byte array is returned.
function convertFloatToByte(floatFreqData, minDecibels, maxDecibels) {
  let scale = 255 / (maxDecibels - minDecibels);

  return floatFreqData.map(function(x) {
    let value = Math.floor(scale * (x - minDecibels));
    return Math.min(255, Math.max(0, value));
  });
}