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<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" />
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<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>
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</html>