DXR is a code search and navigation tool aimed at making sense of large projects. It supports full-text and regex searches as well as structural queries.

Mercurial (c68fe15a81fc)

VCS Links

Line Code
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467
<!DOCTYPE HTML>
<html>
<head>
  <title>Test IIRFilterNode GetFrequencyResponse</title>
  <script src="/tests/SimpleTest/SimpleTest.js"></script>
  <script type="text/javascript" src="webaudio.js"></script>
  <script type="text/javascript" src="biquad-filters.js"></script>
  <link rel="stylesheet" type="text/css" href="/tests/SimpleTest/test.css" />
</head>
<body>
<pre id="test">
<script class="testbody" type="text/javascript">

SimpleTest.waitForExplicitFinish();

addLoadEvent(function() {
  var sampleRate = 48000;
  var testDurationSec = 1;
  var testFrames = testDurationSec * sampleRate;

  var testPromises = []
  testPromises.push(function () {
    // Test that the feedback coefficients are normalized.  Do this be creating two
    // IIRFilterNodes.  One has normalized coefficients, and one doesn't.  Compute the
    // difference and make sure they're the same.
    var context = new OfflineAudioContext(2, testFrames, sampleRate);

    // Use a simple impulse as the source.
    var buffer = context.createBuffer(1, 1, sampleRate);
    buffer.getChannelData(0)[0] = 1;
    var source = context.createBufferSource();
    source.buffer = buffer;

    // Gain node for computing the difference between the filters.
    var gain = context.createGain();
    gain.gain.value = -1;

    // The IIR filters.  Use a common feedforward array.
    var ff = [1];

    var fb1 = [1, .9];

    var fb2 = new Float64Array(2);
    // Scale the feedback coefficients by an arbitrary factor.
    var coefScaleFactor = 2;
    for (var k = 0; k < fb2.length; ++k) {
      fb2[k] = coefScaleFactor * fb1[k];
    }

    var iir1 = context.createIIRFilter(ff, fb1);
    var iir2 = context.createIIRFilter(ff, fb2);

    // Create the graph.  The output of iir1 (normalized coefficients) is channel 0, and the
    // output of iir2 (unnormalized coefficients), with appropriate scaling, is channel 1.
    var merger = context.createChannelMerger(2);
    source.connect(iir1);
    source.connect(iir2);
    iir1.connect(merger, 0, 0);
    iir2.connect(gain);

    // The gain for the gain node should be set to compensate for the scaling of the
    // coefficients.  Since iir2 has scaled the coefficients by coefScaleFactor, the output is
    // reduced by the same factor, so adjust the gain to scale the output of iir2 back up.
    gain.gain.value = coefScaleFactor;
    gain.connect(merger, 0, 1);

    merger.connect(context.destination);

    source.start();

    // Rock and roll!

    return context.startRendering().then(function (result) {
      // Find the max amplitude of the result, which should be near zero.
      var iir1Data = result.getChannelData(0);
      var iir2Data = result.getChannelData(1);

      // Threshold isn't exactly zero because the arithmetic is done differently between the
      // IIRFilterNode and the BiquadFilterNode.
      compareChannels(iir1Data, iir2Data);
    });
  }());

  testPromises.push(function () {
    // Create a simple 1-zero filter and compare with the expected output.
    var context = new OfflineAudioContext(1, testFrames, sampleRate);

    // Use a simple impulse as the source
    var buffer = context.createBuffer(1, 1, sampleRate);
    buffer.getChannelData(0)[0] = 1;
    var source = context.createBufferSource();
    source.buffer = buffer;

    // The filter is y(n) = 0.5*(x(n) + x(n-1)), a simple 2-point moving average.  This is
    // rather arbitrary; keep it simple.

    var iir = context.createIIRFilter([0.5, 0.5], [1]);

    // Create the graph
    source.connect(iir);
    iir.connect(context.destination);

    // Rock and roll!
    source.start();

    return context.startRendering().then(function (result) {
      var actual = result.getChannelData(0);
      var expected = new Float64Array(testFrames);
      // The filter is a simple 2-point moving average of an impulse, so the first two values
      // are non-zero and the rest are zero.
      expected[0] = 0.5;
      expected[1] = 0.5;
      compareChannels(actual, expected);
    });
  }());

  testPromises.push(function () {
    // Create a simple 1-pole filter and compare with the expected output.

    // The filter is y(n) + c*y(n-1)= x(n).  The analytical response is (-c)^n, so choose a
    // suitable number of frames to run the test for where the output isn't flushed to zero.
    var c = 0.9;
    var eps = 1e-20;
    var duration = Math.floor(Math.log(eps) / Math.log(Math.abs(c)));
    var context = new OfflineAudioContext(1, duration, sampleRate);

    // Use a simple impulse as the source
    var buffer = context.createBuffer(1, 1, sampleRate);
    buffer.getChannelData(0)[0] = 1;
    var source = context.createBufferSource();
    source.buffer = buffer;

    var iir = context.createIIRFilter([1], [1, c]);

    // Create the graph
    source.connect(iir);
    iir.connect(context.destination);

    // Rock and roll!
    source.start();

    return context.startRendering().then(function (result) {
      var actual = result.getChannelData(0);
      var expected = new Float64Array(actual.length);

      // The filter is a simple 1-pole filter: y(n) = -c*y(n-k)+x(n), with an impulse as the
      // input.
      expected[0] = 1;
      for (k = 1; k < testFrames; ++k) {
        expected[k] = -c * expected[k-1];
      }

      compareChannels(actual, expected);
    });
  }());

  // This function creates an IIRFilterNode equivalent to the specified
  // BiquadFilterNode and compares the outputs.  The
  // outputs from the two filters should be virtually identical.
  function testWithBiquadFilter(filterType) {
    var context = new OfflineAudioContext(2, testFrames, sampleRate);

    // Use a constant (step function) as the source
    var buffer = context.createBuffer(1, testFrames, context.sampleRate);
    for (var i = 0; i < testFrames; ++i) {
      buffer.getChannelData(0)[i] = 1;
    }
    var source = context.createBufferSource();
    source.buffer = buffer;

    // Create the biquad.  Choose some rather arbitrary values for Q and gain for the biquad
    // so that the shelf filters aren't identical.
    var biquad = context.createBiquadFilter();
    biquad.type = filterType;
    biquad.Q.value = 10;
    biquad.gain.value = 10;

    // Create the equivalent IIR Filter node by computing the coefficients of the given biquad
    // filter type.
    var nyquist = sampleRate / 2;
    var coef = createFilter(filterType,
                            biquad.frequency.value / nyquist,
                            biquad.Q.value,
                            biquad.gain.value);

    var iir = context.createIIRFilter([coef.b0, coef.b1, coef.b2], [1, coef.a1, coef.a2]);

    var merger = context.createChannelMerger(2);
    // Create the graph
    source.connect(biquad);
    source.connect(iir);

    biquad.connect(merger, 0, 0);
    iir.connect(merger, 0, 1);

    merger.connect(context.destination);

    // Rock and roll!
    source.start();

    return context.startRendering().then(function (result) {
      // Find the max amplitude of the result, which should be near zero.
      var expected = result.getChannelData(0);
      var actual = result.getChannelData(1);
      compareChannels(actual, expected);
    });
  }

  biquadFilterTypes = ["lowpass", "highpass", "bandpass", "notch",
                       "allpass", "lowshelf", "highshelf", "peaking"];

  // Create a set of tasks based on biquadTestConfigs.
  for (var i = 0; i < biquadFilterTypes.length; ++i) {
    testPromises.push(testWithBiquadFilter(biquadFilterTypes[i]));
  }

  testPromises.push(function () {
    // Multi-channel test.  Create a biquad filter and the equivalent IIR filter.  Filter the
    // same multichannel signal and compare the results.
    var nChannels = 3;
    var context = new OfflineAudioContext(nChannels, testFrames, sampleRate);

    // Create a set of oscillators as the multi-channel source.
    var source = [];

    for (k = 0; k < nChannels; ++k) {
      source[k] = context.createOscillator();
      source[k].type = "sawtooth";
      // The frequency of the oscillator is pretty arbitrary, but each oscillator should have a
      // different frequency.
      source[k].frequency.value = 100 + k * 100;
    }

    var merger = context.createChannelMerger(3);

    var biquad = context.createBiquadFilter();

    // Create the equivalent IIR Filter node.
    var nyquist = sampleRate / 2;
    var coef = createFilter(biquad.type,
      biquad.frequency.value / nyquist,
      biquad.Q.value,
      biquad.gain.value);
    var fb = [1, coef.a1, coef.a2];
    var ff = [coef.b0, coef.b1, coef.b2];

    var iir = context.createIIRFilter(ff, fb);
    // Gain node to compute the difference between the IIR and biquad filter.
    var gain = context.createGain();
    gain.gain.value = -1;

    // Create the graph.
    for (k = 0; k < nChannels; ++k)
      source[k].connect(merger, 0, k);

    merger.connect(biquad);
    merger.connect(iir);
    iir.connect(gain);
    biquad.connect(context.destination);
    gain.connect(context.destination);

    for (k = 0; k < nChannels; ++k)
      source[k].start();

    return context.startRendering().then(function (result) {
      var errorThresholds = [3.7671e-5, 3.0071e-5, 2.6241e-5];

      // Check the difference signal on each channel
      for (channel = 0; channel < result.numberOfChannels; ++channel) {
        // Find the max amplitude of the result, which should be near zero.
        var data = result.getChannelData(channel);
        var maxError = data.reduce(function(reducedValue, currentValue) {
          return Math.max(reducedValue, Math.abs(currentValue));
        });

        ok(maxError <= errorThresholds[channel], "Max difference between IIR and Biquad on channel " + channel);
      }
    });
  }());

  testPromises.push(function () {
    // Apply an IIRFilter to the given input signal.
    //
    // IIR filter in the time domain is
    //
    //   y[n] = sum(ff[k]*x[n-k], k, 0, M) - sum(fb[k]*y[n-k], k, 1, N)
    //
    function iirFilter(input, feedforward, feedback) {
      // For simplicity, create an x buffer that contains the input, and a y buffer that contains
      // the output.  Both of these buffers have an initial work space to implement the initial
      // memory of the filter.
      var workSize = Math.max(feedforward.length, feedback.length);
      var x = new Float32Array(input.length + workSize);

      // Float64 because we want to match the implementation that uses doubles to minimize
      // roundoff.
      var y = new Float64Array(input.length + workSize);

      // Copy the input over.
      for (var k = 0; k < input.length; ++k)
        x[k + feedforward.length] = input[k];

      // Run the filter
      for (var n = 0; n < input.length; ++n) {
        var index = n + workSize;
        var yn = 0;
        for (var k = 0; k < feedforward.length; ++k)
          yn += feedforward[k] * x[index - k];
        for (var k = 0; k < feedback.length; ++k)
          yn -= feedback[k] * y[index - k];

        y[index] = yn;
      }

      return y.slice(workSize).map(Math.fround);
    }

    // Cascade the two given biquad filters to create one IIR filter.
    function cascadeBiquads(f1Coef, f2Coef) {
      // The biquad filters are:
      //
      // f1 = (b10 + b11/z + b12/z^2)/(1 + a11/z + a12/z^2);
      // f2 = (b20 + b21/z + b22/z^2)/(1 + a21/z + a22/z^2);
      //
      // To cascade them, multiply the two transforms together to get a fourth order IIR filter.

      var numProduct = [f1Coef.b0 * f2Coef.b0,
        f1Coef.b0 * f2Coef.b1 + f1Coef.b1 * f2Coef.b0,
        f1Coef.b0 * f2Coef.b2 + f1Coef.b1 * f2Coef.b1 + f1Coef.b2 * f2Coef.b0,
        f1Coef.b1 * f2Coef.b2 + f1Coef.b2 * f2Coef.b1,
        f1Coef.b2 * f2Coef.b2
      ];

      var denProduct = [1,
        f2Coef.a1 + f1Coef.a1,
        f2Coef.a2 + f1Coef.a1 * f2Coef.a1 + f1Coef.a2,
        f1Coef.a1 * f2Coef.a2 + f1Coef.a2 * f2Coef.a1,
        f1Coef.a2 * f2Coef.a2
      ];

      return {
        ff: numProduct,
        fb: denProduct
      }
    }

    // Find the magnitude of the root of the quadratic that has the maximum magnitude.
    //
    // The quadratic is z^2 + a1 * z + a2 and we want the root z that has the largest magnitude.
    function largestRootMagnitude(a1, a2) {
      var discriminant = a1 * a1 - 4 * a2;
      if (discriminant < 0) {
        // Complex roots:  -a1/2 +/- i*sqrt(-d)/2.  Thus the magnitude of each root is the same
        // and is sqrt(a1^2/4 + |d|/4)
        var d = Math.sqrt(-discriminant);
        return Math.hypot(a1 / 2, d / 2);
      } else {
        // Real roots
        var d = Math.sqrt(discriminant);
        return Math.max(Math.abs((-a1 + d) / 2), Math.abs((-a1 - d) / 2));
      }
    }

    // Cascade 2 lowpass biquad filters and compare that with the equivalent 4th order IIR
    // filter.

    var nyquist = sampleRate / 2;
    // Compute the coefficients of a lowpass filter.

    // First some preliminary stuff.  Compute the coefficients of the biquad.  This is used to
    // figure out how frames to use in the test.
    var biquadType = "lowpass";
    var biquadCutoff = 350;
    var biquadQ = 5;
    var biquadGain = 1;

    var coef = createFilter(biquadType,
      biquadCutoff / nyquist,
      biquadQ,
      biquadGain);

    // Cascade the biquads together to create an equivalent IIR filter.
    var cascade = cascadeBiquads(coef, coef);

    // Since we're cascading two identical biquads, the root of denominator of the IIR filter is
    // repeated, so the root of the denominator with the largest magnitude occurs twice.  The
    // impulse response of the IIR filter will be roughly c*(r*r)^n at time n, where r is the
    // root of largest magnitude.  This approximation gets better as n increases.  We can use
    // this to get a rough idea of when the response has died down to a small value.

    // This is the value we will use to determine how many frames to render.  Rendering too many
    // is a waste of time and also makes it hard to compare the actual result to the expected
    // because the magnitudes are so small that they could be mostly round-off noise.
    //
    // Find magnitude of the root with largest magnitude
    var rootMagnitude = largestRootMagnitude(coef.a1, coef.a2);

    // Find n such that |r|^(2*n) <= eps.  That is, n = log(eps)/(2*log(r)).  Somewhat
    // arbitrarily choose eps = 1e-20;
    var eps = 1e-20;
    var framesForTest = Math.floor(Math.log(eps) / (2 * Math.log(rootMagnitude)));

    // We're ready to create the graph for the test.  The offline context has two channels:
    // channel 0 is the expected (cascaded biquad) result and channel 1 is the actual IIR filter
    // result.
    var context = new OfflineAudioContext(2, framesForTest, sampleRate);

    // Use a simple impulse with a large (arbitrary) amplitude as the source
    var amplitude = 1;
    var buffer = context.createBuffer(1, testFrames, sampleRate);
    buffer.getChannelData(0)[0] = amplitude;
    var source = context.createBufferSource();
    source.buffer = buffer;

    // Create the two biquad filters.  Doesn't really matter what, but for simplicity we choose
    // identical lowpass filters with the same parameters.
    var biquad1 = context.createBiquadFilter();
    biquad1.type = biquadType;
    biquad1.frequency.value = biquadCutoff;
    biquad1.Q.value = biquadQ;

    var biquad2 = context.createBiquadFilter();
    biquad2.type = biquadType;
    biquad2.frequency.value = biquadCutoff;
    biquad2.Q.value = biquadQ;

    var iir = context.createIIRFilter(cascade.ff, cascade.fb);

    // Create the merger to get the signals into multiple channels
    var merger = context.createChannelMerger(2);

    // Create the graph, filtering the source through two biquads.
    source.connect(biquad1);
    biquad1.connect(biquad2);
    biquad2.connect(merger, 0, 0);

    source.connect(iir);
    iir.connect(merger, 0, 1);

    merger.connect(context.destination);

    // Now filter the source through the IIR filter.
    var y = iirFilter(buffer.getChannelData(0), cascade.ff, cascade.fb);

    // Rock and roll!
    source.start();

    return context.startRendering().then(function(result) {
      var expected = result.getChannelData(0);
      var actual = result.getChannelData(1);

      compareChannels(actual, expected);

    });
  }());

  // Wait for all tests
  Promise.all(testPromises).then(function () {
    SimpleTest.finish();
  }, function () {
    SimpleTest.finish();
  });
});
</script>
</pre>
</body>
</html>