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diff --git a/testing/web-platform/tests/webaudio/the-audio-api/the-iirfilternode-interface/iirfilter.html b/testing/web-platform/tests/webaudio/the-audio-api/the-iirfilternode-interface/iirfilter.html new file mode 100644 index 0000000000..aa38a6bfca --- /dev/null +++ b/testing/web-platform/tests/webaudio/the-audio-api/the-iirfilternode-interface/iirfilter.html @@ -0,0 +1,572 @@ +<!DOCTYPE html> +<html> + <head> + <title> + Test Basic IIRFilterNode Operation + </title> + <script src="/resources/testharness.js"></script> + <script src="/resources/testharnessreport.js"></script> + <script src="../../resources/audit-util.js"></script> + <script src="../../resources/audit.js"></script> + <script src="../../resources/biquad-filters.js"></script> + </head> + <body> + <script id="layout-test-code"> + let sampleRate = 24000; + let testDurationSec = 0.25; + let testFrames = testDurationSec * sampleRate; + + let audit = Audit.createTaskRunner(); + + audit.define('coefficient-normalization', (task, should) => { + // 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. + let context = new OfflineAudioContext(2, testFrames, sampleRate); + + // Use a simple impulse as the source. + let buffer = context.createBuffer(1, 1, sampleRate); + buffer.getChannelData(0)[0] = 1; + let source = context.createBufferSource(); + source.buffer = buffer; + + // Gain node for computing the difference between the filters. + let gain = context.createGain(); + gain.gain.value = -1; + + // The IIR filters. Use a common feedforward array. + let ff = [1]; + + let fb1 = [1, .9]; + + let fb2 = new Float64Array(2); + // Scale the feedback coefficients by an arbitrary factor. + let coefScaleFactor = 2; + for (let k = 0; k < fb2.length; ++k) { + fb2[k] = coefScaleFactor * fb1[k]; + } + + let iir1; + let iir2; + + should(function() { + iir1 = context.createIIRFilter(ff, fb1); + }, 'createIIRFilter with normalized coefficients').notThrow(); + + should(function() { + iir2 = context.createIIRFilter(ff, fb2); + }, 'createIIRFilter with unnormalized coefficients').notThrow(); + + // 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. + let 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! + + context.startRendering() + .then(function(result) { + // Find the max amplitude of the result, which should be near + // zero. + let iir1Data = result.getChannelData(0); + let iir2Data = result.getChannelData(1); + + // Threshold isn't exactly zero because the arithmetic is done + // differently between the IIRFilterNode and the BiquadFilterNode. + should( + iir2Data, + 'Output of IIR filter with unnormalized coefficients') + .beCloseToArray(iir1Data, {absoluteThreshold: 2.1958e-38}); + }) + .then(() => task.done()); + }); + + audit.define('one-zero', (task, should) => { + // Create a simple 1-zero filter and compare with the expected output. + let context = new OfflineAudioContext(1, testFrames, sampleRate); + + // Use a simple impulse as the source + let buffer = context.createBuffer(1, 1, sampleRate); + buffer.getChannelData(0)[0] = 1; + let 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. + + let iir = context.createIIRFilter([0.5, 0.5], [1]); + + // Create the graph + source.connect(iir); + iir.connect(context.destination); + + // Rock and roll! + source.start(); + + context.startRendering() + .then(function(result) { + let actual = result.getChannelData(0); + let 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; + should(actual, 'IIR 1-zero output').beCloseToArray(expected, { + absoluteThreshold: 0 + }); + }) + .then(() => task.done()); + }); + + audit.define('one-pole', (task, should) => { + // 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. + let c = 0.9; + let eps = 1e-20; + let duration = Math.floor(Math.log(eps) / Math.log(Math.abs(c))); + let context = new OfflineAudioContext(1, duration, sampleRate); + + // Use a simple impulse as the source + let buffer = context.createBuffer(1, 1, sampleRate); + buffer.getChannelData(0)[0] = 1; + let source = context.createBufferSource(); + source.buffer = buffer; + + let iir = context.createIIRFilter([1], [1, c]); + + // Create the graph + source.connect(iir); + iir.connect(context.destination); + + // Rock and roll! + source.start(); + + context.startRendering() + .then(function(result) { + let actual = result.getChannelData(0); + let 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]; + } + + // Threshold isn't exactly zero due to round-off in the + // single-precision IIRFilterNode computations versus the + // double-precision Javascript computations. + should(actual, 'IIR 1-pole output').beCloseToArray(expected, { + absoluteThreshold: 2.7657e-8 + }); + }) + .then(() => task.done()); + }); + + // Return a function suitable for use as a defineTask function. 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, errorThreshold, snrThreshold) { + return (task, should) => { + let context = new OfflineAudioContext(2, testFrames, sampleRate); + + // Use a constant (step function) as the source + let buffer = createConstantBuffer(context, testFrames, 1); + let 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. + let 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. + let nyquist = sampleRate / 2; + let coef = createFilter( + filterType, biquad.frequency.value / nyquist, biquad.Q.value, + biquad.gain.value); + + let iir = context.createIIRFilter( + [coef.b0, coef.b1, coef.b2], [1, coef.a1, coef.a2]); + + let 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(); + + context.startRendering() + .then(function(result) { + // Find the max amplitude of the result, which should be near + // zero. + let expected = result.getChannelData(0); + let actual = result.getChannelData(1); + + // On MacOSX, WebAudio uses an optimized Biquad implementation + // that is different from the implementation used for Linux and + // Windows. This will cause the output to differ, even if the + // threshold passes. Thus, only print out a very small number + // of elements of the array where we have tested that they are + // consistent. + should(actual, 'IIRFilter for Biquad ' + filterType) + .beCloseToArray(expected, errorThreshold); + + let snr = 10 * Math.log10(computeSNR(actual, expected)); + should(snr, 'SNR for IIRFIlter for Biquad ' + filterType) + .beGreaterThanOrEqualTo(snrThreshold); + }) + .then(() => task.done()); + }; + } + + // Thresholds here are experimentally determined. + let biquadTestConfigs = [ + { + filterType: 'lowpass', + snrThreshold: 91.221, + errorThreshold: {relativeThreshold: 4.9834e-5} + }, + { + filterType: 'highpass', + snrThreshold: 105.4590, + errorThreshold: {absoluteThreshold: 2.9e-6, relativeThreshold: 3e-5} + }, + { + filterType: 'bandpass', + snrThreshold: 104.060, + errorThreshold: {absoluteThreshold: 2e-7, relativeThreshold: 8.7e-4} + }, + { + filterType: 'notch', + snrThreshold: 91.312, + errorThreshold: {absoluteThreshold: 0, relativeThreshold: 4.22e-5} + }, + { + filterType: 'allpass', + snrThreshold: 91.319, + errorThreshold: {absoluteThreshold: 0, relativeThreshold: 4.31e-5} + }, + { + filterType: 'lowshelf', + snrThreshold: 90.609, + errorThreshold: {absoluteThreshold: 0, relativeThreshold: 2.98e-5} + }, + { + filterType: 'highshelf', + snrThreshold: 103.159, + errorThreshold: {absoluteThreshold: 0, relativeThreshold: 1.24e-5} + }, + { + filterType: 'peaking', + snrThreshold: 91.504, + errorThreshold: {absoluteThreshold: 0, relativeThreshold: 5.05e-5} + } + ]; + + // Create a set of tasks based on biquadTestConfigs. + for (k = 0; k < biquadTestConfigs.length; ++k) { + let config = biquadTestConfigs[k]; + let name = k + ': ' + config.filterType; + audit.define( + name, + testWithBiquadFilter( + config.filterType, config.errorThreshold, config.snrThreshold)); + } + + audit.define('multi-channel', (task, should) => { + // Multi-channel test. Create a biquad filter and the equivalent IIR + // filter. Filter the same multichannel signal and compare the results. + let nChannels = 3; + let context = + new OfflineAudioContext(nChannels, testFrames, sampleRate); + + // Create a set of oscillators as the multi-channel source. + let 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; + } + + let merger = context.createChannelMerger(3); + + let biquad = context.createBiquadFilter(); + + // Create the equivalent IIR Filter node. + let nyquist = sampleRate / 2; + let coef = createFilter( + biquad.type, biquad.frequency.value / nyquist, biquad.Q.value, + biquad.gain.value); + let fb = [1, coef.a1, coef.a2]; + let ff = [coef.b0, coef.b1, coef.b2]; + + let iir = context.createIIRFilter(ff, fb); + // Gain node to compute the difference between the IIR and biquad + // filter. + let 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(); + + context.startRendering() + .then(function(result) { + let 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. + let data = result.getChannelData(channel); + let maxError = + data.reduce(function(reducedValue, currentValue) { + return Math.max(reducedValue, Math.abs(currentValue)); + }); + + should( + maxError, + 'Max difference between IIR and Biquad on channel ' + + channel) + .beLessThanOrEqualTo(errorThresholds[channel]); + } + + }) + .then(() => task.done()); + }); + + // 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. + let workSize = Math.max(feedforward.length, feedback.length); + let x = new Float32Array(input.length + workSize); + + // Float64 because we want to match the implementation that uses doubles + // to minimize roundoff. + let y = new Float64Array(input.length + workSize); + + // Copy the input over. + for (let k = 0; k < input.length; ++k) + x[k + feedforward.length] = input[k]; + + // Run the filter + for (let n = 0; n < input.length; ++n) { + let index = n + workSize; + let yn = 0; + for (let k = 0; k < feedforward.length; ++k) + yn += feedforward[k] * x[index - k]; + for (let 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. + + let 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 + ]; + + let 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) { + let 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) + let d = Math.sqrt(-discriminant); + return Math.hypot(a1 / 2, d / 2); + } else { + // Real roots + let d = Math.sqrt(discriminant); + return Math.max(Math.abs((-a1 + d) / 2), Math.abs((-a1 - d) / 2)); + } + } + + audit.define('4th-order-iir', (task, should) => { + // Cascade 2 lowpass biquad filters and compare that with the equivalent + // 4th order IIR filter. + + let 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. + let biquadType = 'lowpass'; + let biquadCutoff = 350; + let biquadQ = 5; + let biquadGain = 1; + + let coef = createFilter( + biquadType, biquadCutoff / nyquist, biquadQ, biquadGain); + + // Cascade the biquads together to create an equivalent IIR filter. + let 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 + let 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; + let eps = 1e-20; + let 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. + let context = new OfflineAudioContext(2, framesForTest, sampleRate); + + // Use a simple impulse with a large (arbitrary) amplitude as the source + let amplitude = 1; + let buffer = context.createBuffer(1, testFrames, sampleRate); + buffer.getChannelData(0)[0] = amplitude; + let 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. + let biquad1 = context.createBiquadFilter(); + biquad1.type = biquadType; + biquad1.frequency.value = biquadCutoff; + biquad1.Q.value = biquadQ; + + let biquad2 = context.createBiquadFilter(); + biquad2.type = biquadType; + biquad2.frequency.value = biquadCutoff; + biquad2.Q.value = biquadQ; + + let iir = context.createIIRFilter(cascade.ff, cascade.fb); + + // Create the merger to get the signals into multiple channels + let 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. + let y = iirFilter(buffer.getChannelData(0), cascade.ff, cascade.fb); + + // Rock and roll! + source.start(); + + context.startRendering() + .then(function(result) { + let expected = result.getChannelData(0); + let actual = result.getChannelData(1); + + should(actual, '4-th order IIRFilter (biquad ref)') + .beCloseToArray(expected, { + // Thresholds experimentally determined. + absoluteThreshold: 1.59e-7, + relativeThreshold: 2.11e-5, + }); + + let snr = 10 * Math.log10(computeSNR(actual, expected)); + should(snr, 'SNR of 4-th order IIRFilter (biquad ref)') + .beGreaterThanOrEqualTo(108.947); + }) + .then(() => task.done()); + }); + + audit.run(); + </script> + </body> +</html> |