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// Taken from 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
// 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 w0 = Math.PI * freq;
var alpha = 0.5 * Math.sin(w0) / Math.pow(10, q / 20);
var cos_w0 = Math.cos(w0);
b0 = 0.5 * (1 - cos_w0);
b1 = 1 - cos_w0;
b2 = b0;
a0 = 1 + alpha;
a1 = -2.0 * cos_w0;
a2 = 1 - alpha;
}
return normalizeFilterCoefficients(b0, b1, b2, a0, a1, 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;
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 w0 = Math.PI * freq;
var alpha = 0.5 * Math.sin(w0) / Math.pow(10, q / 20);
var cos_w0 = Math.cos(w0);
b0 = 0.5 * (1 + cos_w0);
b1 = -1 - cos_w0;
b2 = b0;
a0 = 1 + alpha;
a1 = -2.0 * cos_w0;
a2 = 1 - alpha;
}
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};
}
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;
}
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;
}
// Map the filter type name to a function that computes the filter coefficents for the given filter
// type.
var filterCreatorFunction = {"lowpass": createLowpassFilter,
"highpass": createHighpassFilter,
"bandpass": createBandpassFilter,
"lowshelf": createLowShelfFilter,
"highshelf": createHighShelfFilter,
"peaking": createPeakingFilter,
"notch": createNotchFilter,
"allpass": createAllpassFilter};
var filterTypeName = {"lowpass": "Lowpass filter",
"highpass": "Highpass filter",
"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);
}