Source: modules/filter.js

Source: modules/filter.js

  1. /*
  2.  * This file is part of Toolkit.
  3.  *
  4.  * Toolkit is free software; you can redistribute it and/or
  5.  * modify it under the terms of the GNU General Public
  6.  * License as published by the Free Software Foundation; either
  7.  * version 3 of the License, or (at your option) any later version.
  8.  *
  9.  * Toolkit is distributed in the hope that it will be useful,
  10.  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  11.  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12.  * Lesser General Public License for more details.
  13.  *
  14.  * You should have received a copy of the GNU General
  15.  * Public License along with this program; if not, write to the
  16.  * Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
  17.  * Boston, MA  02110-1301  USA
  18.  */
  19. "use strict";
  20. (function(w, TK){
  21. /* These formulae for 'standard' biquad filter coefficients are
  22.  * from
  23.  *  "Cookbook formulae for audio EQ biquad filter coefficients"
  24.  *  by Robert Bristow-Johnson.
  25.  *
  26.  */
  28. function Null(O) {
  29.     /* this biquad does not do anything */
  30.     return {
  31. 	b0: 1,
  32. 	b1: 1,
  33. 	b2: 1,
  34. 	a0: 1,
  35. 	a1: 1,
  36. 	a2: 1,
  37. 	sample_rate: O.sample_rate,
  38.     };
  39. }
  41. function LowShelf(O) {
  42.     var cos = Math.cos,
  43.         sqrt = Math.sqrt,
  44.         A = Math.pow(10, O.gain / 40),
  45.         w0 = 2*Math.PI*O.freq/O.sample_rate,
  46.         alpha = Math.sin(w0)/(2*O.q);
  47.     return {
  48. 	b0:    A*( (A+1) - (A-1)*cos(w0) + 2*sqrt(A)*alpha ),
  49. 	b1:  2*A*( (A-1) - (A+1)*cos(w0)                   ),
  50. 	b2:    A*( (A+1) - (A-1)*cos(w0) - 2*sqrt(A)*alpha ),
  51. 	a0:        (A+1) + (A-1)*cos(w0) + 2*sqrt(A)*alpha,
  52. 	a1:   -2*( (A-1) + (A+1)*cos(w0)                   ),
  53. 	a2:        (A+1) + (A-1)*cos(w0) - 2*sqrt(A)*alpha,
  54. 	sample_rate: O.sample_rate,
  55.     };
  56. }
  58. function HighShelf(O) {
  59.     var cos = Math.cos;
  60.     var sqrt = Math.sqrt;
  61.     var A = Math.pow(10, O.gain / 40);
  62.     var w0 = 2*Math.PI*O.freq/O.sample_rate;
  63.     var alpha = Math.sin(w0)/(2*O.q);
  64.     return {
  65. 	b0:    A*( (A+1) + (A-1)*cos(w0) + 2*sqrt(A)*alpha ),
  66. 	b1: -2*A*( (A-1) + (A+1)*cos(w0)                   ),
  67. 	b2:    A*( (A+1) + (A-1)*cos(w0) - 2*sqrt(A)*alpha ),
  68. 	a0:        (A+1) - (A-1)*cos(w0) + 2*sqrt(A)*alpha,
  69. 	a1:    2*( (A-1) - (A+1)*cos(w0)                   ),
  70. 	a2:        (A+1) - (A-1)*cos(w0) - 2*sqrt(A)*alpha,
  71. 	sample_rate: O.sample_rate,
  72.     };
  73. }
  75. function Peaking(O) {
  76.     var cos = Math.cos;
  77.     var A = Math.pow(10, O.gain / 40);
  78.     var w0 = 2*Math.PI*O.freq/O.sample_rate;
  79.     var alpha = Math.sin(w0)/(2*O.q);
  80.     return {
  81.         b0:   1 + alpha*A,
  82.         b1:  -2*cos(w0),
  83.         b2:   1 - alpha*A,
  84.         a0:   1 + alpha/A,
  85.         a1:  -2*cos(w0),
  86.         a2:   1 - alpha/A,
  87.         sample_rate: O.sample_rate,
  88.     };
  89. }
  91. function Notch(O) {
  92.     var cos = Math.cos;
  93.     var w0 = 2*Math.PI*O.freq/O.sample_rate;
  94.     var alpha = Math.sin(w0)/(2*O.q);
  95.     return {
  96. 	b0:   1,
  97. 	b1:  -2*cos(w0),
  98. 	b2:   1,
  99. 	a0:   1 + alpha,
  100. 	a1:  -2*cos(w0),
  101. 	a2:   1 - alpha,
  102.         sample_rate: O.sample_rate,
  103.     };
  104. }
  106. /* This is a standard lowpass filter with transfer function
  107.  * H(s) = 1/(1+s)
  108.  */
  109. function LowPass1(O) {
  110.     var w0 = 2*Math.PI*O.freq/O.sample_rate,
  111.         s0 = Math.sin(w0),
  112.         c0 = Math.cos(w0);
  113.     return {
  114. 	b0: 1-c0,
  115. 	b1: 2*(1-c0),
  116.         b2: 1-c0,
  117. 	a0: 1 - c0 + s0,
  118. 	a1: 2*(1-c0),
  119.         a2: 1 - c0 - s0,
  120.         sample_rate: O.sample_rate,
  121.     };
  122. }
  124. function LowPass2(O) {
  125.     var cos = Math.cos;
  126.     var w0 = 2*Math.PI*O.freq/O.sample_rate;
  127.     var alpha = Math.sin(w0)/(2*O.q);
  128.     return {
  129. 	b0:  (1 - cos(w0))/2,
  130. 	b1:   1 - cos(w0),
  131. 	b2:  (1 - cos(w0))/2,
  132. 	a0:   1 + alpha,
  133. 	a1:  -2*cos(w0),
  134. 	a2:   1 - alpha,
  135.         sample_rate: O.sample_rate,
  136.     };
  137. }
  139. function LowPass4(O) {
  140.     O = LowPass2(O);
  141.     O.factor = 2;
  142.     return O;
  143. }
  145. /* This is a standard highpass filter with transfer function
  146.  * H(s) = s/(1+s)
  147.  */
  148. function HighPass1(O) {
  149.     var w0 = 2*Math.PI*O.freq/O.sample_rate,
  150.         s0 = Math.sin(w0),
  151.         c0 = Math.cos(w0);
  152.     return {
  153. 	b0: s0,
  154. 	b1: 0,
  155.         b2: -s0,
  156. 	a0: 1 - c0 + s0,
  157. 	a1: 2*(1-c0),
  158.         a2: 1 - c0 - s0,
  159.         sample_rate: O.sample_rate,
  160.     };
  161. }
  163. function HighPass2(O) {
  164.     var cos = Math.cos;
  165.     var w0 = 2*Math.PI*O.freq/O.sample_rate;
  166.     var alpha = Math.sin(w0)/(2*O.q);
  167.     return {
  168. 	b0:  (1 + cos(w0))/2,
  169. 	b1: -(1 + cos(w0)),
  170. 	b2:  (1 + cos(w0))/2,
  171. 	a0:   1 + alpha,
  172. 	a1:  -2*cos(w0),
  173. 	a2:   1 - alpha,
  174.         sample_rate: O.sample_rate,
  175.     };
  176. }
  178. function HighPass4(O) {
  179.     O = HighPass2(O);
  180.     O.factor = 2;
  181.     return O;
  182. }
  184. var Filters = {
  185.     Null: Null,
  186.     LowShelf:  LowShelf,
  187.     HighShelf: HighShelf,
  188.     Peaking:   Peaking,
  189.     Notch:        Notch,
  190.     LowPass1:     LowPass1,
  191.     LowPass2:     LowPass2,
  192.     LowPass4:     LowPass4,
  193.     HighPass1:    HighPass1,
  194.     HighPass2:    HighPass2,
  195.     HighPass4:    HighPass4,
  196. };
  198. var standard_biquads = {
  199.     "null":       BiquadFilter(Null),
  200.     "low-shelf":  BiquadFilter(LowShelf),
  201.     "high-shelf": BiquadFilter(HighShelf),
  202.     parametric:   BiquadFilter(Peaking),
  203.     notch:        BiquadFilter(Notch),
  204.     lowpass1:     BiquadFilter(LowPass1),
  205.     lowpass2:     BiquadFilter(LowPass2),
  206.     lowpass3:     BiquadFilter(LowPass1, LowPass2),
  207.     lowpass4:     BiquadFilter(LowPass4),
  208.     highpass1:    BiquadFilter(HighPass1),
  209.     highpass2:    BiquadFilter(HighPass2),
  210.     highpass3:    BiquadFilter(HighPass1, HighPass2),
  211.     highpass4:    BiquadFilter(HighPass4),
  212. };
  214. var NullModule = { freq2gain: function(f) { return 0.0; } };
  216. function BilinearModule(w, O) {
  217.     var log = Math.log;
  218.     var sin = Math.sin;
  220.     var LN10_10 = (O.factor||1.0) * 10/Math.LN10;
  221.     var PI = +(Math.PI/O.sample_rate);
  222.     var Ra = +((O.a0 + O.a1) * (O.a0 + O.a1) / 4);
  223.     var Rb = +((O.b0 + O.b1) * (O.b0 + O.b1) / 4);
  224.     var Ya = +(O.a1 * O.a0);
  225.     var Yb = +(O.b1 * O.b0);
  227.     if (Ra === Rb && Ya === Yb) return NullModule;
  229.     function freq2gain(f) {
  230.         f = +f;
  231.         var S = +sin(PI * f)
  232.         S *= S;
  233.         return LN10_10 * log( (Rb - S * Yb) /
  234.                               (Ra - S * Ya) );
  235.     }
  237.     return { freq2gain: freq2gain };
  238. }
  240. function BiquadModule(w, O) {
  241.     var log = Math.log;
  242.     var sin = Math.sin;
  244.     var LN10_10 = (O.factor||1.0) * 10/Math.LN10;
  245.     var PI = +(Math.PI/O.sample_rate);
  246.     var Ra = +((O.a0 + O.a1 + O.a2) * (O.a0 + O.a1 + O.a2) / 4);
  247.     var Rb = +((O.b0 + O.b1 + O.b2) * (O.b0 + O.b1 + O.b2) / 4);
  248.     var Xa = +(4 * O.a0 * O.a2);
  249.     var Ya = +(O.a1 * (O.a0 + O.a2));
  250.     var Xb = +(4 * O.b0 * O.b2);
  251.     var Yb = +(O.b1 * (O.b0 + O.b2));
  253.     if (Ra === Rb && Ya === Yb && Xa === Xb) return NullModule;
  255.     function freq2gain(f) {
  256.         f = +f;
  257.         var S = +sin(PI * f)
  258.         S *= S;
  259.         return LN10_10 * log( (Rb - S * (Xb * (1 - S) + Yb)) /
  260.                               (Ra - S * (Xa * (1 - S) + Ya)) );
  261.     }
  263.     return { freq2gain: freq2gain };
  264. }
  266. function BiquadFilter1(trafo) {
  267.     function factory(stdlib, O) {
  268.         return BiquadModule(stdlib, trafo(O));
  269.     }
  271.     return factory;
  272. }
  274. function BiquadFilterN(trafos) {
  275.     function factory(stdlib, O) {
  276.         var A = new Array(trafos.length);
  277.         var i;
  279.         for (i = 0; i < trafos.length; i ++) {
  280.             A[i] = BiquadModule(stdlib, trafos[i](O)).freq2gain;
  281.         }
  283.         return {
  284.             freq2gain: function(f) {
  285.                 var ret = 0.0;
  286.                 var i;
  288.                 for (i = 0; i < A.length; i++) {
  289.                     ret += A[i](f);
  290.                 }
  292.                 return ret;
  293.             }
  294.         };
  295.     }
  297.     return factory;
  298. }
  300. function BiquadFilter() {
  301.     if (arguments.length === 1) return BiquadFilter1(arguments[0]);
  303.     return BiquadFilterN.call(this, Array.prototype.slice.call(arguments));
  304. }
  306. TK.BiquadFilter = BiquadFilter;
  308. function reset() {
  309.     this.freq2gain = null;
  310.     /**
  311.      * Is fired when a filters drawing function is reset.
  312.      * 
  313.      * @event TK.Filter#reset
  314.      */
  315.     this.fire_event("reset");
  316. }
  318. TK.Filter = TK.class({
  319.     /**
  320.      * TK.Filter provides the math for calculating a gain from
  321.      * a given frequency for different types of biquad filters.
  322.      *
  323.      * @param {Object} [options={ }] - An object containing initial options.
  324.      * 
  325.      * @property {Stgring|Function} [options.type="parametric"] - The type of the filter. Possible values are
  326.      *   <code>parametric</code>, <code>notch</code>, <code>low-shelf</code>,
  327.      *   <code>high-shelf</code>, <code>lowpass[n]</code> or <code>highpass[n]</code>.
  328.      * @property {Number} [options.freq=1000] - The initial frequency.
  329.      * @property {Number} [options.gain=0] - The initial gain.
  330.      * @property {Number} [options.q=1] - The initial Q of the filter.
  331.      * @property {Number} [options.sample_rate=44100] - The sample rate.
  332.      *
  333.      * @mixin TK.Filter
  334.      * 
  335.      * @extends TK.Base
  336.      * 
  337.      * @mixes TK.AudioMath
  338.      * @mixes TK.Notes
  339.      */
  340.      
  341.      /**
  342.       * Returns the gain for a given frequency
  343.       * 
  344.       * @method TK.Filter#freq2gain
  345.       * 
  346.       * @param {number} frequency - The frequency to calculate the gain for.
  347.       * 
  348.       * @returns {number} gain - The gain at the given frequency.
  349.       */ 
  350.     _class: "Filter",
  351.     Extends: TK.Base,
  352.     _options: {
  353.         type: "string|function",
  354.         freq: "number",
  355.         gain: "number",
  356.         q: "number",
  357.         sample_rate: "number",
  358.     },
  359.     options: {
  360.         type: "parametric",
  361.         freq: 1000,
  362.         gain: 0,
  363.         q:    1,
  364.         sample_rate: 44100,
  365.     },
  366.     static_events: {
  367.         set_freq: reset,
  368.         set_type: reset,
  369.         set_q: reset,
  370.         set_gain: reset,
  371.         initialized: reset,
  372.     },
  373.     create_freq2gain: function() {
  374.         var O = this.options;
  375.         var m;
  377.         if (typeof(O.type) === "string") {
  378.             m = standard_biquads[O.type];
  380.             if (!m) {
  381.                 TK.error("Unknown standard filter: "+O.type);
  382.                 return;
  383.             }
  384.         } else if (typeof(O.type) === "function") {
  385.             m = O.type;
  386.         } else {
  387.             TK.error("Unsupported option 'type'.");
  388.             return;
  389.         }
  390.         this.freq2gain = m(window, O).freq2gain;
  391.     },
  392.     get_freq2gain: function() {
  393.         if (this.freq2gain === null) this.create_freq2gain();
  394.         return this.freq2gain;
  395.     },
  396.     reset: reset,
  397. });
  399. TK.Filters = Filters;
  401. })(this, this.TK);