Implement Biquad lowpass and highpass filters according to spec

third_party/WebKit/LayoutTests/webaudio/resources/biquad-filters.js

 // A biquad filter has a z-transform of
 // H(z) = (b0 + b1 / z + b2 / z^2) / (1 + a1 / z + a2 / z^2)
 //
 // The formulas for the various filters were taken from
 // http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt.
 
 
 // Lowpass filter.
 function createLowpassFilter(freq, q, gain) {
     var b0;
     var b1;
     var b2;
+    var a0;
     var a1;
     var a2;
 
     if (freq == 1) {
         // The formula below works, except for roundoff.  When freq = 1,
         // the filter is just a wire, so hardwire the coefficients.
         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 alpha = Math.sin(theta) / (2 * Math.pow(10, q / 20));
+        var cosw = Math.cos(theta);
+        var beta = (1 - cosw) / 2;
 
-        b0 = 2 * alpha;
-        b1 = 4 * alpha;
-        b2 = 2 * alpha;
-        a1 = 2 * (-gamma);
-        a2 = 2 * beta;
+        b0 = beta;
+        b1 = 2 * beta;
+        b2 = beta;
+        a0 = 1 + alpha;
+        a1 = -2 * cosw;
+        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) {
     var b0;
     var b1;
     var b2;
+    var a0;
     var a1;
     var a2;
 
     if (freq == 1) {
         // The filter is 0
         b0 = 0;
         b1 = 0;
         b2 = 0;
+        a0 = 1;
         a1 = 0;
         a2 = 0;
     } else if (freq == 0) {
         // The filter is 1.  Computation of coefficients below is ok, but
         // there's a pole at 1 and a zero at 1, so round-off could make
         // the filter unstable.
         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 alpha = Math.sin(theta) / (2 * Math.pow(10, q / 20));
+        var cosw = Math.cos(theta);
+        var beta = (1 + cosw) / 2;
 
-        b0 = 2 * alpha;
-        b1 = -4 * alpha;
-        b2 = 2 * alpha;
-        a1 = 2 * (-gamma);
-        a2 = 2 * beta;
+        b0 = beta;
+        b1 = -2 * beta;
+        b2 = beta;
+        a0 = 1 + alpha;
+        a1 = -2 * cosw;
+        a2 = 1 - alpha;
     }
 
-    return {b0 : b0, b1 : b1, b2 : b2, a1 : a1, a2 : a2};
+    return normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
 }
 
 function normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2) {
     var scale = 1 / a0;
 
     return {b0 : b0 * scale,
             b1 : b1 * scale,
             b2 : b2 * scale,
             a1 : a1 * scale,
             a2 : a2 * scale};
@@ skipping 266 matching lines @@
                       "bandpass": "Bandpass filter",
                       "lowshelf": "Lowshelf filter",
                       "highshelf": "Highshelf filter",
                       "peaking": "Peaking filter",
                       "notch": "Notch filter",
                       "allpass": "Allpass filter"};
 
 function createFilter(filterType, freq, q, gain) {
     return filterCreatorFunction[filterType](freq, q, gain);
 }