Bug 1265395 - Implement new low pass filter equation; r=padenot

If run against the version of the test using the old equations, 18 of the
26460 values would be larger than the maximum difference threshold, so I
updated the test code to use the new equations as well.

I also had to make a small increase to the maximum allowable glitch for
the tail test.

MozReview-Commit-ID: LrB3HufFWpJ

--HG--
extra : rebase_source : 5b011653b3c0d8a00c2a96185c703b5457058936

dom/media/webaudio/blink/Biquad.cpp

@@ -110,22 +110,19 @@ void Biquad::setLowpassParams(double cutoff, double resonance)
     } else if (cutoff > 0) {
         // Compute biquad coefficients for lowpass filter
         resonance = std::max(0.0, resonance); // can't go negative
-        double g = pow(10.0, 0.05 * resonance);
-        double d = sqrt((4 - sqrt(16 - 16 / (g * g))) / 2);
+        double g = pow(10.0, -0.05 * resonance);
+        double w0 = M_PI * cutoff;
+        double cos_w0 = cos(w0);
+        double alpha = 0.5 * sin(w0) * g;
 
-        double theta = M_PI * cutoff;
-        double sn = 0.5 * d * sin(theta);
-        double beta = 0.5 * (1 - sn) / (1 + sn);
-        double gamma = (0.5 + beta) * cos(theta);
-        double alpha = 0.25 * (0.5 + beta - gamma);
+        double b0 = 0.5 * (1.0 - cos_w0);
+        double b1 = 1.0 - cos_w0;
+        double b2 = b0;
+        double a0 = 1.0 + alpha;
+        double a1 = -2.0 * cos_w0;
+        double a2 = 1.0 - alpha;
 
-        double b0 = 2 * alpha;
-        double b1 = 2 * 2 * alpha;
-        double b2 = 2 * alpha;
-        double a1 = 2 * -gamma;
-        double a2 = 2 * beta;
-
-        setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
+        setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
     } else {
         // When cutoff is zero, nothing gets through the filter, so set
         // coefficients up correctly.

dom/media/webaudio/test/blink/biquad-filters.js

@@ -12,6 +12,7 @@ function createLowpassFilter(freq, q, gain) {
     var b0;
     var b1;
     var b2;
+    var a0;
     var a1;
     var a2;
 
@@ -21,25 +22,23 @@ function createLowpassFilter(freq, q, gain) {
         b0 = 1;
         b1 = 0;
         b2 = 0;
+        a0 = 1;
         a1 = 0;
         a2 = 0;
     } else {
-        var g = Math.pow(10, q / 20);
-        var d = Math.sqrt((4 - Math.sqrt(16 - 16 / (g * g))) / 2);
-        var theta = Math.PI * freq;
-        var sn = d * Math.sin(theta) / 2;
-        var beta = 0.5 * (1 - sn) / (1 + sn);
-        var gamma = (0.5 + beta) * Math.cos(theta);
-        var alpha = 0.25 * (0.5 + beta - gamma);
+        var w0 = Math.PI * freq;
+        var alpha = 0.5 * Math.sin(w0) / Math.pow(10, q / 20);
+        var cos_w0 = Math.cos(w0);
 
-        b0 = 2 * alpha;
-        b1 = 4 * alpha;
-        b2 = 2 * alpha;
-        a1 = 2 * (-gamma);
-        a2 = 2 * beta;
+        b0 = 0.5 * (1 - cos_w0);
+        b1 = 1 - cos_w0;
+        b2 = b0;
+        a0 = 1 + alpha;
+        a1 = -2.0 * cos_w0;
+        a2 = 1 - alpha;
     }
 
-    return {b0 : b0, b1 : b1, b2 : b2, a1 : a1, a2 : a2};
+    return normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
 }
 
 function createHighpassFilter(freq, q, gain) {