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<head>
<title>Test Biquad Tail-Time</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>
<script src="test-tail-time.js"></script>
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<body>
<script>
let audit = Audit.createTaskRunner();
let sampleRate = 16384;
let renderSeconds = 1;
// For a lowpass filter:
// b0 = (1-cos(w0))/2
// b1 = 1-cos(w0)
// b2 = (1-cos(w0))/2
// a0 = 1 + alpha
// a1 = -2*cos(w0)
// a2 = 1 - alpha
//
// where alpha = sin(w0)/(2*10^(Q/20)) and w0 = 2*%pi*f0/Fs.
//
// Equivalently a1 = -2*cos(w0)/(1+alpha), a2 = (1-alpha)/(1+alpha). The
// poles of this filter are at
//
// cos(w0)/(1+alpha) +/- sqrt(alpha^2-sin(w0)^2)/(1+alpha)
//
// But alpha^2-sin(w0)^2 = sin(w0)^2*(1/4/10^(Q/10) - 1). Thus the poles
// are complex if 1/4/10^(Q/10) < 1; real distinct if 1/4/10^(Q/10) > 1;
// and repeated if 1/4/10^(Q/10) = 1.
// Array of tests to run. |descripton| is the task description for
// audit.define. |parameters| is option for |testTailTime|.
let tests = [
{
descripton:
{label: 'lpf-complex-roots', description: 'complex roots'},
sampleRate: sampleRate,
renderDuration: renderSeconds,
parameters: {
prefix: 'LPF complex roots',
filterOptions: {type: 'lowpass', Q: 40, frequency: sampleRate / 4}
},
// Node computed tail frame is 2079.4 which matches the real tail, so
// tail output should be exactly 0.
threshold: 0,
},
{
descripton: {
label: 'lpf-real-distinct-roots',
description: 'real distinct roots'
},
sampleRate: sampleRate,
renderDuration: renderSeconds,
parameters: {
prefix: 'LPF real distinct roots',
filterOptions:
{type: 'lowpass', Q: -50, frequency: sampleRate / 8}
},
// Node computed tail frame is 1699 which matches the real tail, so
// tail output should be exactly 0.
threshold: 0,
},
{
descripton:
{label: 'lpf-repeated-root', description: 'repeated real root'},
sampleRate: sampleRate,
renderDuration: renderSeconds,
parameters: {
prefix: 'LPF repeated roots (approximately)',
// For a repeated root, we need 1/4/10^(Q/10) = 1, or Q =
// -10*log(4)/log(10). This isn't exactly representable as a float,
// we the roots might not actually be repeated. In fact the roots
// are actually complex at 6.402396e-5*exp(i*1.570796).
filterOptions: {
type: 'lowpass',
Q: -10 * Math.log10(4),
frequency: sampleRate / 4
}
},
// Node computed tail frame is 2.9 which matches the real tail, so
// tail output should be exactly 0.
threshold: 0,
},
{
descripton: {label: 'lpf-real-roots-2', description: 'complex roots'},
sampleRate: sampleRate,
renderDuration: renderSeconds,
parameters: {
prefix: 'LPF repeated roots 2',
// This tests an extreme case where approximate impulse response is
// h(n) = C*r^(n-1) and C < 1/32768. Thus, the impulse response is
// always less than the response threshold of 1/32768.
filterOptions:
{type: 'lowpass', Q: -100, frequency: sampleRate / 4}
},
// Node computed tail frame is 0 which matches the real tail, so
// tail output should be exactly 0.
threshold: 0,
},
{
descripton: 'huge tail',
// The BiquadFilter has an internal maximum tail of 30 sec so we want
// to render for at least 30 sec to test this. Use the smallest
// sample rate we can to limit memory and CPU usage!
sampleRate: 3000,
renderDuration: 31,
parameters: {
prefix: 'LPF repeated roots (approximately)',
hugeTaileTime: true,
// For the record, for this lowpass filter, the computed tail time
// is approximately 2830.23 sec, with poles at
// 0.999998960442086*exp(i*0.209439510236777). This is very close to
// being marginally stable.
filterOptions: {
type: 'lowpass',
Q: 100,
frequency: 100,
},
// Node computed tail frame is 8.49069e6 which is clamped to 30 sec
// so tail output should be exactly 0 after 30 sec.
threshold: 0,
},
},
{
descripton: 'ginormous tail',
// Or this lowpass filter, the complex poles are actually computed to
// be on the unit circle so the tail infinite. This just tests that
// nothing bad happens in computing the tail time. Thus, any small
// sample rate and short duration for the test; the results aren't
// really interesting. (But they must pass, of course!)
sampleRate: 3000,
renderDuration: 0.25,
parameters: {
prefix: 'LPF repeated roots (approximately)',
filterOptions: {
type: 'lowpass',
Q: 500,
frequency: 100,
},
},
// Node computed tail frame is 90000 which matches the real tail, so
// tail output should be exactly 0.
threshold: 0,
}
]
// Define an appropriate task for each test.
tests.forEach(entry => {
audit.define(entry.descripton, (task, should) => {
let context = new OfflineAudioContext(
1, entry.renderDuration * entry.sampleRate, entry.sampleRate);
testTailTime(should, context, entry.parameters)
.then(() => task.done());
});
});
audit.run();
</script>
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