LayoutTests/webaudio/resources/biquad-testing.js - WebKit - Git at Google

 // Globals, to make testing and debugging easier.
 var context;
 var filter;
 var signal;
 var renderedBuffer;
 var renderedData;

 var sampleRate = 44100.0;
 var pulseLengthFrames = .1 * sampleRate;

 // Maximum allowed error for the test to succeed.  Experimentally determined.
 var maxAllowedError = 5.9e-8;

 // This must be large enough so that the filtered result is
 // essentially zero.  See comments for createTestAndRun.
 var timeStep = .1;

 // Maximum number of filters we can process (mostly for setting the
 // render length correctly.)
 var maxFilters = 5;

 // How long to render.  Must be long enough for all of the filters we
 // want to test.
 var renderLengthSeconds = timeStep * (maxFilters + 1) ;

 var renderLengthSamples = Math.round(renderLengthSeconds * sampleRate);

 // Number of filters that will be processed.
 var nFilters;

 // 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 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;
         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);

         b0 = 2 * alpha;
         b1 = 4 * alpha;
         b2 = 2 * alpha;
         a1 = 2 * (-gamma);
         a2 = 2 * beta;
     }

     return {b0 : b0, b1 : b1, b2 : b2, a1 : a1, a2 : a2};
 }

 function createHighpassFilter(freq, q, gain) {
     var b0;
     var b1;
     var b2;
     var a1;
     var a2;

     if (freq == 1) {
         // The filter is 0
         b0 = 0;
         b1 = 0;
         b2 = 0;
         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;
         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);

         b0 = 2 * alpha;
         b1 = -4 * alpha;
         b2 = 2 * alpha;
         a1 = 2 * (-gamma);
         a2 = 2 * beta;
     }

     return {b0 : b0, b1 : b1, b2 : b2, a1 : a1, a2 : 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};
 }

 function createBandpassFilter(freq, q, gain) {
     var b0;
     var b1;
     var b2;
     var a0;
     var a1;
     var a2;
     var coef;

     if (freq > 0 && freq < 1) {
         var w0 = Math.PI * freq;
         if (q > 0) {
             var alpha = Math.sin(w0) / (2 * q);
             var k = Math.cos(w0);

             b0 = alpha;
             b1 = 0;
             b2 = -alpha;
             a0 = 1 + alpha;
             a1 = -2 * k;
             a2 = 1 - alpha;

             coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
         } else {
             // q = 0, and frequency is not 0 or 1.  The above formula has a
             // divide by zero problem.  The limit of the z-transform as q
             // approaches 0 is 1, so set the filter that way.
             coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
         }
     } else {
         // When freq = 0 or 1, the z-transform is identically 0,
         // independent of q.
         coef = {b0 : 0, b1 : 0, b2 : 0, a1 : 0, a2 : 0}
     }

     return coef;
 }

 function createLowShelfFilter(freq, q, gain) {
     // q not used
     var b0;
     var b1;
     var b2;
     var a0;
     var a1;
     var a2;
     var coef;

     var S = 1;
     var A = Math.pow(10, gain / 40);

     if (freq == 1) {
         // The filter is just a constant gain
         coef = {b0 : A * A, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
     } else if (freq == 0) {
         // The filter is 1
         coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
     } else {
         var w0 = Math.PI * freq;
         var alpha = 1 / 2 * Math.sin(w0) * Math.sqrt((A + 1 / A) * (1 / S - 1) + 2);
         var k = Math.cos(w0);
         var k2 = 2 * Math.sqrt(A) * alpha;
         var Ap1 = A + 1;
         var Am1 = A - 1;

         b0 = A * (Ap1 - Am1 * k + k2);
         b1 = 2 * A * (Am1 - Ap1 * k);
         b2 = A * (Ap1 - Am1 * k - k2);
         a0 = Ap1 + Am1 * k + k2;
         a1 = -2 * (Am1 + Ap1 * k);
         a2 = Ap1 + Am1 * k - k2;
         coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
     }

     return coef;
 }

 function createHighShelfFilter(freq, q, gain) {
     // q not used
     var b0;
     var b1;
     var b2;
     var a0;
     var a1;
     var a2;
     var coef;

     var A = Math.pow(10, gain / 40);

     if (freq == 1) {
         // When freq = 1, the z-transform is 1
         coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
     } else if (freq > 0) {
         var w0 = Math.PI * freq;
         var S = 1;
         var alpha = 0.5 * Math.sin(w0) * Math.sqrt((A + 1 / A) * (1 / S - 1) + 2);
         var k = Math.cos(w0);
         var k2 = 2 * Math.sqrt(A) * alpha;
         var Ap1 = A + 1;
         var Am1 = A - 1;

         b0 = A * (Ap1 + Am1 * k + k2);
         b1 = -2 * A * (Am1 + Ap1 * k);
         b2 = A * (Ap1 + Am1 * k - k2);
         a0 = Ap1 - Am1 * k + k2;
         a1 = 2 * (Am1 - Ap1*k);
         a2 = Ap1 - Am1 * k-k2;

         coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
     } else {
         // When freq = 0, the filter is just a gain
         coef = {b0 : A * A, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
     }

     return coef;
 }

 function createPeakingFilter(freq, q, gain) {
     var b0;
     var b1;
     var b2;
     var a0;
     var a1;
     var a2;
     var coef;

     var A = Math.pow(10, gain / 40);

     if (freq > 0 && freq < 1) {
         if (q > 0) {
             var w0 = Math.PI * freq;
             var alpha = Math.sin(w0) / (2 * q);
             var k = Math.cos(w0);

             b0 = 1 + alpha * A;
             b1 = -2 * k;
             b2 = 1 - alpha * A;
             a0 = 1 + alpha / A;
             a1 = -2 * k;
             a2 = 1 - alpha / A;

             coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
         } else {
             // q = 0, we have a divide by zero problem in the formulas
             // above.  But if we look at the z-transform, we see that the
             // limit as q approaches 0 is A^2.
             coef = {b0 : A * A, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
         }
     } else {
         // freq = 0 or 1, the z-transform is 1
         coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
     }

     return coef;
 }

 function createNotchFilter(freq, q, gain) {
     var b0;
     var b1;
     var b2;
     var a0;
     var a1;
     var a2;
     var coef;

     if (freq > 0 && freq < 1) {
         if (q > 0) {
             var w0 = Math.PI * freq;
             var alpha = Math.sin(w0) / (2 * q);
             var k = Math.cos(w0);

             b0 = 1;
             b1 = -2 * k;
             b2 = 1;
             a0 = 1 + alpha;
             a1 = -2 * k;
             a2 = 1 - alpha;
             coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
         } else {
             // When q = 0, we get a divide by zero above.  The limit of the
             // z-transform as q approaches 0 is 0, so set the coefficients
             // appropriately.
             coef = {b0 : 0, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
         }
     } else {
         // When freq = 0 or 1, the z-transform is 1
         coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
     }

     return coef;
 }

 function createAllpassFilter(freq, q, gain) {
     var b0;
     var b1;
     var b2;
     var a0;
     var a1;
     var a2;
     var coef;

     if (freq > 0 && freq < 1) {
         if (q > 0) {
             var w0 = Math.PI * freq;
             var alpha = Math.sin(w0) / (2 * q);
             var k = Math.cos(w0);

             b0 = 1 - alpha;
             b1 = -2 * k;
             b2 = 1 + alpha;
             a0 = 1 + alpha;
             a1 = -2 * k;
             a2 = 1 - alpha;
             coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
         } else {
             // q = 0
             coef = {b0 : -1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
         }
     } else {
         coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
     }

     return coef;
 }

 // Array of functions to compute the filter coefficients.  This must
 // be arraned in the same order as the filter types in the idl file.
 var filterCreatorFunction = [createLowpassFilter,
                              createHighpassFilter,
                              createBandpassFilter,
                              createLowShelfFilter,
                              createHighShelfFilter,
                              createPeakingFilter,
                              createNotchFilter,
                              createAllpassFilter];

 var filterTypeName = ["Lowpass filter",
                       "Highpass filter",
                       "Bandpass filter",
                       "Lowshelf filter",
                       "Highshelf filter",
                       "Peaking filter",
                       "Notch filter",
                       "Allpass filter"];

 var filterTypeIndex = {"lowpass": 0,
                        "highpass": 1,
                        "bandpass": 2,
                        "lowshelf": 3,
                        "highshelf": 4,
                        "peaking": 5,
                        "notch": 6,
                        "allpass": 7};

 function createFilter(filterType, freq, q, gain) {
     return filterCreatorFunction[filterType](freq, q, gain);
 }

 function filterData(filterCoef, signal, len) {
     var y = new Array(len);
     var b0 = filterCoef.b0;
     var b1 = filterCoef.b1;
     var b2 = filterCoef.b2;
     var a1 = filterCoef.a1;
     var a2 = filterCoef.a2;

     // Prime the pump. (Assumes the signal has length >= 2!)
     y[0] = b0 * signal[0];
     y[1] = b0 * signal[1] + b1 * signal[0] - a1 * y[0];

     // Filter all of the signal that we have.
     for (var k = 2; k < Math.min(signal.length, len); ++k) {
         y[k] = b0 * signal[k] + b1 * signal[k-1] + b2 * signal[k-2] - a1 * y[k-1] - a2 * y[k-2];
     }

     // If we need to filter more, but don't have any signal left,
     // assume the signal is zero.
     for (var k = signal.length; k < len; ++k) {
         y[k] = - a1 * y[k-1] - a2 * y[k-2];
     }

     return y;
 }

 function createImpulseBuffer(context, length) {
     var impulse = context.createBuffer(1, length, context.sampleRate);
     var data = impulse.getChannelData(0);
     for (var k = 1; k < data.length; ++k) {
         data[k] = 0;
     }
     data[0] = 1;

     return impulse;
 }


 function createTestAndRun(context, filterType, filterParameters) {
     // To test the filters, we apply a signal (an impulse) to each of
     // the specified filters, with each signal starting at a different
     // time.  The output of the filters is summed together at the
     // output.  Thus for filter k, the signal input to the filter
     // starts at time k * timeStep.  For this to work well, timeStep
     // must be large enough for the output of each filter to have
     // decayed to zero with timeStep seconds.  That way the filter
     // outputs don't interfere with each other.

     nFilters = Math.min(filterParameters.length, maxFilters);

     signal = new Array(nFilters);
     filter = new Array(nFilters);

     impulse = createImpulseBuffer(context, pulseLengthFrames);

     // Create all of the signal sources and filters that we need.
     for (var k = 0; k < nFilters; ++k) {
         signal[k] = context.createBufferSource();
         signal[k].buffer = impulse;

         filter[k] = context.createBiquadFilter();
         filter[k].type = filterType;
         filter[k].frequency.value = context.sampleRate / 2 * filterParameters[k].cutoff;
         filter[k].detune.value = (filterParameters[k].detune === undefined) ? 0 : filterParameters[k].detune;
         filter[k].Q.value = filterParameters[k].q;
         filter[k].gain.value = filterParameters[k].gain;

         signal[k].connect(filter[k]);
         filter[k].connect(context.destination);

         signal[k].noteOn(timeStep * k);
     }

     context.oncomplete = checkFilterResponse(filterType, filterParameters);
     context.startRendering();
 }

 function addSignal(dest, src, destOffset) {
     // Add src to dest at the given dest offset.
     for (var k = destOffset, j = 0; k < dest.length, j < src.length; ++k, ++j) {
         dest[k] += src[j];
     }
 }

 function generateReference(filterType, filterParameters) {
     var result = new Array(renderLengthSamples);
     var data = new Array(renderLengthSamples);
     // Initialize the result array and data.
     for (var k = 0; k < result.length; ++k) {
         result[k] = 0;
         data[k] = 0;
     }
     // Make data an impulse.
     data[0] = 1;

     for (var k = 0; k < nFilters; ++k) {
         // Filter an impulse
         var detune = (filterParameters[k].detune === undefined) ? 0 : filterParameters[k].detune;
         var frequency = filterParameters[k].cutoff * Math.pow(2, detune / 1200); // Apply detune, converting from Cents.

         var filterCoef = createFilter(filterType,
                                       frequency,
                                       filterParameters[k].q,
                                       filterParameters[k].gain);
         var y = filterData(filterCoef, data, renderLengthSamples);

         // Accumulate this filtered data into the final output at the desired offset.
         addSignal(result, y, timeToSampleFrame(timeStep * k, sampleRate));
     }

     return result;
 }

 function checkFilterResponse(filterType, filterParameters) {
     return function(event) {
         renderedBuffer = event.renderedBuffer;
         renderedData = renderedBuffer.getChannelData(0);

         reference = generateReference(filterType, filterParameters);

         var len = Math.min(renderedData.length, reference.length);

         var success = true;

         // Maximum error between rendered data and expected data
         var maxError = 0;

         // Sample offset where the maximum error occurred.
         var maxPosition = 0;

         // Number of infinities or NaNs that occurred in the rendered data.
         var invalidNumberCount = 0;

         if (nFilters != filterParameters.length) {
             testFailed("Test wanted " + filterParameters.length + " filters but only " + maxFilters + " allowed.");
             success = false;
         }

         // Compare the rendered signal with our reference, keeping
         // track of the maximum difference (and the offset of the max
         // difference.)  Check for bad numbers in the rendered output
         // too.  There shouldn't be any.
         for (var k = 0; k < len; ++k) {
             var err = Math.abs(renderedData[k] - reference[k]);
             if (err > maxError) {
                 maxError = err;
                 maxPosition = k;
             }
             if (!isValidNumber(renderedData[k])) {
                 ++invalidNumberCount;
             }
         }

         if (invalidNumberCount > 0) {
             testFailed("Rendered output has " + invalidNumberCount + " infinities or NaNs.");
             success = false;
         } else {
             testPassed("Rendered output did not have infinities or NaNs.");
         }

         if (maxError <= maxAllowedError) {
             testPassed(filterTypeName[filterType] + " response is correct.");
         } else {
             testFailed(filterTypeName[filterType] + " response is incorrect.  Max err = " + maxError + " at " + maxPosition + ".  Threshold = " + maxAllowedError);
             success = false;
         }

         if (success) {
             testPassed("Test signal was correctly filtered.");
         } else {
             testFailed("Test signal was not correctly filtered.");
         }
         finishJSTest();
     }
 }
	// Globals, to make testing and debugging easier.
	var context;
	var filter;
	var signal;
	var renderedBuffer;
	var renderedData;

	var sampleRate = 44100.0;
	var pulseLengthFrames = .1 * sampleRate;

	// Maximum allowed error for the test to succeed. Experimentally determined.
	var maxAllowedError = 5.9e-8;

	// This must be large enough so that the filtered result is
	// essentially zero. See comments for createTestAndRun.
	var timeStep = .1;

	// Maximum number of filters we can process (mostly for setting the
	// render length correctly.)
	var maxFilters = 5;

	// How long to render. Must be long enough for all of the filters we
	// want to test.
	var renderLengthSeconds = timeStep * (maxFilters + 1) ;

	var renderLengthSamples = Math.round(renderLengthSeconds * sampleRate);

	// Number of filters that will be processed.
	var nFilters;

	// 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 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;
	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);

	b0 = 2 * alpha;
	b1 = 4 * alpha;
	b2 = 2 * alpha;
	a1 = 2 * (-gamma);
	a2 = 2 * beta;
	}

	return {b0 : b0, b1 : b1, b2 : b2, a1 : a1, a2 : a2};
	}

	function createHighpassFilter(freq, q, gain) {
	var b0;
	var b1;
	var b2;
	var a1;
	var a2;

	if (freq == 1) {
	// The filter is 0
	b0 = 0;
	b1 = 0;
	b2 = 0;
	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;
	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);

	b0 = 2 * alpha;
	b1 = -4 * alpha;
	b2 = 2 * alpha;
	a1 = 2 * (-gamma);
	a2 = 2 * beta;
	}

	return {b0 : b0, b1 : b1, b2 : b2, a1 : a1, a2 : 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};
	}

	function createBandpassFilter(freq, q, gain) {
	var b0;
	var b1;
	var b2;
	var a0;
	var a1;
	var a2;
	var coef;

	if (freq > 0 && freq < 1) {
	var w0 = Math.PI * freq;
	if (q > 0) {
	var alpha = Math.sin(w0) / (2 * q);
	var k = Math.cos(w0);

	b0 = alpha;
	b1 = 0;
	b2 = -alpha;
	a0 = 1 + alpha;
	a1 = -2 * k;
	a2 = 1 - alpha;

	coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
	} else {
	// q = 0, and frequency is not 0 or 1. The above formula has a
	// divide by zero problem. The limit of the z-transform as q
	// approaches 0 is 1, so set the filter that way.
	coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}
	} else {
	// When freq = 0 or 1, the z-transform is identically 0,
	// independent of q.
	coef = {b0 : 0, b1 : 0, b2 : 0, a1 : 0, a2 : 0}
	}

	return coef;
	}

	function createLowShelfFilter(freq, q, gain) {
	// q not used
	var b0;
	var b1;
	var b2;
	var a0;
	var a1;
	var a2;
	var coef;

	var S = 1;
	var A = Math.pow(10, gain / 40);

	if (freq == 1) {
	// The filter is just a constant gain
	coef = {b0 : A * A, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	} else if (freq == 0) {
	// The filter is 1
	coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	} else {
	var w0 = Math.PI * freq;
	var alpha = 1 / 2 * Math.sin(w0) * Math.sqrt((A + 1 / A) * (1 / S - 1) + 2);
	var k = Math.cos(w0);
	var k2 = 2 * Math.sqrt(A) * alpha;
	var Ap1 = A + 1;
	var Am1 = A - 1;

	b0 = A * (Ap1 - Am1 * k + k2);
	b1 = 2 * A * (Am1 - Ap1 * k);
	b2 = A * (Ap1 - Am1 * k - k2);
	a0 = Ap1 + Am1 * k + k2;
	a1 = -2 * (Am1 + Ap1 * k);
	a2 = Ap1 + Am1 * k - k2;
	coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
	}

	return coef;
	}

	function createHighShelfFilter(freq, q, gain) {
	// q not used
	var b0;
	var b1;
	var b2;
	var a0;
	var a1;
	var a2;
	var coef;

	var A = Math.pow(10, gain / 40);

	if (freq == 1) {
	// When freq = 1, the z-transform is 1
	coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	} else if (freq > 0) {
	var w0 = Math.PI * freq;
	var S = 1;
	var alpha = 0.5 * Math.sin(w0) * Math.sqrt((A + 1 / A) * (1 / S - 1) + 2);
	var k = Math.cos(w0);
	var k2 = 2 * Math.sqrt(A) * alpha;
	var Ap1 = A + 1;
	var Am1 = A - 1;

	b0 = A * (Ap1 + Am1 * k + k2);
	b1 = -2 * A * (Am1 + Ap1 * k);
	b2 = A * (Ap1 + Am1 * k - k2);
	a0 = Ap1 - Am1 * k + k2;
	a1 = 2 * (Am1 - Ap1*k);
	a2 = Ap1 - Am1 * k-k2;

	coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
	} else {
	// When freq = 0, the filter is just a gain
	coef = {b0 : A * A, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}

	return coef;
	}

	function createPeakingFilter(freq, q, gain) {
	var b0;
	var b1;
	var b2;
	var a0;
	var a1;
	var a2;
	var coef;

	var A = Math.pow(10, gain / 40);

	if (freq > 0 && freq < 1) {
	if (q > 0) {
	var w0 = Math.PI * freq;
	var alpha = Math.sin(w0) / (2 * q);
	var k = Math.cos(w0);

	b0 = 1 + alpha * A;
	b1 = -2 * k;
	b2 = 1 - alpha * A;
	a0 = 1 + alpha / A;
	a1 = -2 * k;
	a2 = 1 - alpha / A;

	coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
	} else {
	// q = 0, we have a divide by zero problem in the formulas
	// above. But if we look at the z-transform, we see that the
	// limit as q approaches 0 is A^2.
	coef = {b0 : A * A, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}
	} else {
	// freq = 0 or 1, the z-transform is 1
	coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}

	return coef;
	}

	function createNotchFilter(freq, q, gain) {
	var b0;
	var b1;
	var b2;
	var a0;
	var a1;
	var a2;
	var coef;

	if (freq > 0 && freq < 1) {
	if (q > 0) {
	var w0 = Math.PI * freq;
	var alpha = Math.sin(w0) / (2 * q);
	var k = Math.cos(w0);

	b0 = 1;
	b1 = -2 * k;
	b2 = 1;
	a0 = 1 + alpha;
	a1 = -2 * k;
	a2 = 1 - alpha;
	coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
	} else {
	// When q = 0, we get a divide by zero above. The limit of the
	// z-transform as q approaches 0 is 0, so set the coefficients
	// appropriately.
	coef = {b0 : 0, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}
	} else {
	// When freq = 0 or 1, the z-transform is 1
	coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}

	return coef;
	}

	function createAllpassFilter(freq, q, gain) {
	var b0;
	var b1;
	var b2;
	var a0;
	var a1;
	var a2;
	var coef;

	if (freq > 0 && freq < 1) {
	if (q > 0) {
	var w0 = Math.PI * freq;
	var alpha = Math.sin(w0) / (2 * q);
	var k = Math.cos(w0);

	b0 = 1 - alpha;
	b1 = -2 * k;
	b2 = 1 + alpha;
	a0 = 1 + alpha;
	a1 = -2 * k;
	a2 = 1 - alpha;
	coef = normalizeFilterCoefficients(b0, b1, b2, a0, a1, a2);
	} else {
	// q = 0
	coef = {b0 : -1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}
	} else {
	coef = {b0 : 1, b1 : 0, b2 : 0, a1 : 0, a2 : 0};
	}

	return coef;
	}

	// Array of functions to compute the filter coefficients. This must
	// be arraned in the same order as the filter types in the idl file.
	var filterCreatorFunction = [createLowpassFilter,
	createHighpassFilter,
	createBandpassFilter,
	createLowShelfFilter,
	createHighShelfFilter,
	createPeakingFilter,
	createNotchFilter,
	createAllpassFilter];

	var filterTypeName = ["Lowpass filter",
	"Highpass filter",
	"Bandpass filter",
	"Lowshelf filter",
	"Highshelf filter",
	"Peaking filter",
	"Notch filter",
	"Allpass filter"];

	var filterTypeIndex = {"lowpass": 0,
	"highpass": 1,
	"bandpass": 2,
	"lowshelf": 3,
	"highshelf": 4,
	"peaking": 5,
	"notch": 6,
	"allpass": 7};

	function createFilter(filterType, freq, q, gain) {
	return filterCreatorFunction[filterType](freq, q, gain);
	}

	function filterData(filterCoef, signal, len) {
	var y = new Array(len);
	var b0 = filterCoef.b0;
	var b1 = filterCoef.b1;
	var b2 = filterCoef.b2;
	var a1 = filterCoef.a1;
	var a2 = filterCoef.a2;

	// Prime the pump. (Assumes the signal has length >= 2!)
	y[0] = b0 * signal[0];
	y[1] = b0 * signal[1] + b1 * signal[0] - a1 * y[0];

	// Filter all of the signal that we have.
	for (var k = 2; k < Math.min(signal.length, len); ++k) {
	y[k] = b0 * signal[k] + b1 * signal[k-1] + b2 * signal[k-2] - a1 * y[k-1] - a2 * y[k-2];
	}

	// If we need to filter more, but don't have any signal left,
	// assume the signal is zero.
	for (var k = signal.length; k < len; ++k) {
	y[k] = - a1 * y[k-1] - a2 * y[k-2];
	}

	return y;
	}

	function createImpulseBuffer(context, length) {
	var impulse = context.createBuffer(1, length, context.sampleRate);
	var data = impulse.getChannelData(0);
	for (var k = 1; k < data.length; ++k) {
	data[k] = 0;
	}
	data[0] = 1;

	return impulse;
	}


	function createTestAndRun(context, filterType, filterParameters) {
	// To test the filters, we apply a signal (an impulse) to each of
	// the specified filters, with each signal starting at a different
	// time. The output of the filters is summed together at the
	// output. Thus for filter k, the signal input to the filter
	// starts at time k * timeStep. For this to work well, timeStep
	// must be large enough for the output of each filter to have
	// decayed to zero with timeStep seconds. That way the filter
	// outputs don't interfere with each other.

	nFilters = Math.min(filterParameters.length, maxFilters);

	signal = new Array(nFilters);
	filter = new Array(nFilters);

	impulse = createImpulseBuffer(context, pulseLengthFrames);

	// Create all of the signal sources and filters that we need.
	for (var k = 0; k < nFilters; ++k) {
	signal[k] = context.createBufferSource();
	signal[k].buffer = impulse;

	filter[k] = context.createBiquadFilter();
	filter[k].type = filterType;
	filter[k].frequency.value = context.sampleRate / 2 * filterParameters[k].cutoff;
	filter[k].detune.value = (filterParameters[k].detune === undefined) ? 0 : filterParameters[k].detune;
	filter[k].Q.value = filterParameters[k].q;
	filter[k].gain.value = filterParameters[k].gain;

	signal[k].connect(filter[k]);
	filter[k].connect(context.destination);

	signal[k].noteOn(timeStep * k);
	}

	context.oncomplete = checkFilterResponse(filterType, filterParameters);
	context.startRendering();
	}

	function addSignal(dest, src, destOffset) {
	// Add src to dest at the given dest offset.
	for (var k = destOffset, j = 0; k < dest.length, j < src.length; ++k, ++j) {
	dest[k] += src[j];
	}
	}

	function generateReference(filterType, filterParameters) {
	var result = new Array(renderLengthSamples);
	var data = new Array(renderLengthSamples);
	// Initialize the result array and data.
	for (var k = 0; k < result.length; ++k) {
	result[k] = 0;
	data[k] = 0;
	}
	// Make data an impulse.
	data[0] = 1;

	for (var k = 0; k < nFilters; ++k) {
	// Filter an impulse
	var detune = (filterParameters[k].detune === undefined) ? 0 : filterParameters[k].detune;
	var frequency = filterParameters[k].cutoff * Math.pow(2, detune / 1200); // Apply detune, converting from Cents.

	var filterCoef = createFilter(filterType,
	frequency,
	filterParameters[k].q,
	filterParameters[k].gain);
	var y = filterData(filterCoef, data, renderLengthSamples);

	// Accumulate this filtered data into the final output at the desired offset.
	addSignal(result, y, timeToSampleFrame(timeStep * k, sampleRate));
	}

	return result;
	}

	function checkFilterResponse(filterType, filterParameters) {
	return function(event) {
	renderedBuffer = event.renderedBuffer;
	renderedData = renderedBuffer.getChannelData(0);

	reference = generateReference(filterType, filterParameters);

	var len = Math.min(renderedData.length, reference.length);

	var success = true;

	// Maximum error between rendered data and expected data
	var maxError = 0;

	// Sample offset where the maximum error occurred.
	var maxPosition = 0;

	// Number of infinities or NaNs that occurred in the rendered data.
	var invalidNumberCount = 0;

	if (nFilters != filterParameters.length) {
	testFailed("Test wanted " + filterParameters.length + " filters but only " + maxFilters + " allowed.");
	success = false;
	}

	// Compare the rendered signal with our reference, keeping
	// track of the maximum difference (and the offset of the max
	// difference.) Check for bad numbers in the rendered output
	// too. There shouldn't be any.
	for (var k = 0; k < len; ++k) {
	var err = Math.abs(renderedData[k] - reference[k]);
	if (err > maxError) {
	maxError = err;
	maxPosition = k;
	}
	if (!isValidNumber(renderedData[k])) {
	++invalidNumberCount;
	}
	}

	if (invalidNumberCount > 0) {
	testFailed("Rendered output has " + invalidNumberCount + " infinities or NaNs.");
	success = false;
	} else {
	testPassed("Rendered output did not have infinities or NaNs.");
	}

	if (maxError <= maxAllowedError) {
	testPassed(filterTypeName[filterType] + " response is correct.");
	} else {
	testFailed(filterTypeName[filterType] + " response is incorrect. Max err = " + maxError + " at " + maxPosition + ". Threshold = " + maxAllowedError);
	success = false;
	}

	if (success) {
	testPassed("Test signal was correctly filtered.");
	} else {
	testFailed("Test signal was not correctly filtered.");
	}
	finishJSTest();
	}
	}