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filter-utils.txt
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filter-utils.txt
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@init
function sinh(x) local(e_x) (
x > 20 ? (
exp(x)*0.5;
) : x < -20 ? (
-0.5*exp(-x);
) : (
e_x = exp(x);
(e_x - 1/e_x)*0.5;
);
);
function filter_buffer_size() (
FILTER#;
);
function filter_init(steady_value) (
this.x1 = this.x2 = this.y1 = this.y2 = steady_value;
this.b0 = 1;
this.b1 = this.b2 = this.a1 = this.a2 = 0;
);
function filter_sample(x0) local(y0) (
y0 = this.b0*x0 + this.b1*this.x1 + this.b2*this.x2 - this.a1*this.y1 - this.a2*this.y2;
this.x2 = this.x1;
this.x1 = x0;
this.y2 = this.y1;
this.y1 = y0;
);
function filter_bandpass(normfreq, BW) local(inv_a0, b1, w0, sin_w0, Q, alpha) (
w0 = 2*$pi*max(0.000001, min(0.49, normfreq));
sin_w0 = sin(w0);
cos_w0 = cos(w0);
BW > 0 ? (
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
) : (
Q = -BW;
);
alpha = sin_w0*0.5/Q;
// TODO: this is actually a lowpass! Do the right thing.
inv_a0 = 1/(1 + alpha);
this.a1 = -2*cos_w0*inv_a0;
this.a2 = (1 - alpha)*inv_a0;
this.b0 = alpha*inv_a0;
this.b1 = 0;
this.b2 = -this.b0;
);
function filter_bandpass(normfreq, BW, gain) local(inv_a0, b1, w0, sin_w0, Q, alpha) (
this.filter_bandpass(normfreq, BW);
this.b0 += (1 - this.b0)*gain;
this.b1 += (this.a1 - this.b1)*gain;
this.b2 += (this.a2 - this.b2)*gain;
);
function filter_highshelf_gainslope(normfreq, gainFactor, slope) local(A, inv_a0, b0, w0, sin_w0, Q, alpha) (
A = sqrt(gainFactor);
w0 = 2*$pi*normfreq;
sin_w0 = sin(w0);
cos_w0 = cos(w0);
Q = 1/sqrt((A + 1/A)*(1/slope - 1) + 2);
alpha = sin_w0*0.5/Q;
sqrtA2alpha = 2*sqrt(A)*alpha;
inv_a0 = 1/((A + 1) - (A - 1)*cos_w0 + sqrtA2alpha);
this.a1 = 2*((A - 1) - (A + 1)*cos_w0)*inv_a0;
this.a2 = ((A + 1) - (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
this.b0 = A*((A + 1) + (A - 1)*cos_w0 + sqrtA2alpha)*inv_a0;
this.b1 = -2*A*((A - 1) + (A + 1)*cos_w0)*inv_a0;
this.b2= A*((A + 1) + (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
);
function filter_highshelf_gainband(freq, gainFactor, BW) local(A, inv_a0, b0, w0, sin_w0, Q, alpha) (
A = sqrt(gainFactor);
w0 = 2*$pi*freq/srate;
sin_w0 = sin(w0);
cos_w0 = cos(w0);
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
alpha = sin(w0)/(2*Q);
sqrtA2alpha = 2*sqrt(A)*alpha;
a0 = (A + 1) - (A - 1)*cos(w0) + sqrtA2alpha;
this.a1 = 2*((A - 1) - (A + 1)*cos(w0))/a0;
this.a2 = (a0 - 2*sqrtA2alpha)/a0;
this.b0 = A*((A + 1) + (A - 1)*cos(w0) + sqrtA2alpha)/a0;
this.b1 = -2*A*((A - 1) + (A + 1)*cos(w0))/a0;
this.b2 = A*((A + 1) + (A - 1)*cos(w0) - sqrtA2alpha)/a0;
/*
inv_a0 = 1/((A + 1) - (A - 1)*cos_w0 + sqrtA2alpha);
this.a1 = 2*((A - 1) - (A + 1)*cos_w0)*inv_a0;
this.a2 = ((A + 1) - (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
this.b0 = A*((A + 1) + (A - 1)*cos_w0 + sqrtA2alpha)*inv_a0;
this.b1 = -2*A*((A - 1) + (A + 1)*cos_w0)*inv_a0;
this.b2 = A*((A + 1) + (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
*/
);
function filter_highpass(normfreq, BW) local(inv_a0, b1, w0, sin_w0, Q, alpha) (
w0 = 2*$pi*min(0.49, normfreq);
sin_w0 = sin(w0);
cos_w0 = cos(w0);
BW > 0 ? (
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
) : (
Q = -BW;
);
alpha = sin_w0*0.5/Q;
inv_a0 = 1/(1 + alpha);
this.a1 = -2*cos_w0*inv_a0;
this.a2 = (1 - alpha)*inv_a0;
this.b0 = (1 + cos_w0)*0.5*inv_a0;
this.b1 = -2*this.b0;
this.b2 = this.b0;
);
function filter_lowpass(freq, BW) local(inv_a0, b0, w0, sin_w0, Q, alpha) (
w0 = 2*$pi*min(0.49, freq/srate);
sin_w0 = sin(w0);
cos_w0 = cos(w0);
BW > 0 ? (
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
) : (
Q = -BW;
);
alpha = sin_w0*0.5/Q;
inv_a0 = 1/(1 + alpha);
this.a1 = -2*cos_w0*inv_a0;
this.a2 = (1 - alpha)*inv_a0;
this.b0 = (1 - cos_w0)*0.5*inv_a0;
this.b1 = 2*this.b0;
this.b2 = this.b0;
);
function filter_band(freq, gainFactor, BW) local(A, inv_a0, b0, w0, sin_w0, cos_w0, Q, alpha) (
A = sqrt(gainFactor);
w0 = 2*$pi*freq/srate;
sin_w0 = sin(w0);
cos_w0 = cos(w0);
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
alpha = sin_w0*0.5/Q;
sqrtA2alpha = 2*sqrt(A)*alpha;
inv_a0 = 1/(1 + alpha/A);
this.a1 = (-2*cos_w0)*inv_a0;
this.a2 = (1 - alpha/A)*inv_a0;
this.b0 = (1 + alpha*A)*inv_a0;
this.b1 = this.a1;
this.b2 = (1 - alpha*A)*inv_a0;
);
function filter_notch(freq, BW) local(A, inv_a0, b0, w0, sin_w0, cos_w0, Q, alpha) (
w0 = 2*$pi*freq/srate;
sin_w0 = sin(w0);
cos_w0 = cos(w0);
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
alpha = sin_w0*0.5/Q;
sqrtA2alpha = 2*sqrt(A)*alpha;
inv_a0 = 1/(1 + alpha);
this.a1 = (-2*cos_w0)*inv_a0;
this.a2 = (1 - alpha)*inv_a0;
this.b0 = inv_a0;
this.b1 = this.a1;
this.b2 = inv_a0;
);
function filter_notch(freq, BW, gain) local(A, inv_a0, b0, w0, sin_w0, cos_w0, Q, alpha) (
this.filter_notch(freq, BW);
this.b0 += (1 - this.b0)*gain;
this.b1 += (this.a1 - this.b1)*gain;
this.b2 += (this.a2 - this.b2)*gain;
);
/**************** Buffer versions *****************/
function filter_buffer_init(freemem) local(obj) (
obj = freemem;
obj[FILTER#A1] = 0;
obj[FILTER#A2] = 0;
obj[FILTER#B0] = 1;
obj[FILTER#B1] = 0;
obj[FILTER#B2] = 0;
obj[FILTER#X1] = 0;
obj[FILTER#X2] = 0;
obj[FILTER#Y1] = 0;
obj[FILTER#Y2] = 0;
freemem + FILTER#;
);
function filter_buffer_lowpass(obj, freq, BW) local(inv_a0, b0, w0, sin_w0, Q, alpha) (
w0 = 2*$pi*min(0.49, freq/srate);
sin_w0 = sin(w0);
cos_w0 = cos(w0);
BW > 0 ? (
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
) : (
Q = -BW;
);
alpha = sin_w0*0.5/Q;
inv_a0 = 1/(1 + alpha);
obj[FILTER#A1] = -2*cos_w0*inv_a0;
obj[FILTER#A2] = (1 - alpha)*inv_a0;
b0 = obj[FILTER#B0] = (1 - cos_w0)*0.5*inv_a0;
obj[FILTER#B1] = 2*b0;
obj[FILTER#B2] = b0;
);
function filter_buffer_highpass(obj, freq, BW) local(inv_a0, b1, w0, sin_w0, Q, alpha) (
w0 = 2*$pi*min(0.49, freq/srate);
sin_w0 = sin(w0);
cos_w0 = cos(w0);
BW > 0 ? (
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
) : (
Q = -BW;
);
alpha = sin_w0*0.5/Q;
inv_a0 = 1/(1 + alpha);
obj[FILTER#A1] = -2*cos_w0*inv_a0;
obj[FILTER#A2] = (1 - alpha)*inv_a0;
b0 = obj[FILTER#B0] = (1 + cos_w0)*0.5*inv_a0;
obj[FILTER#B1] = -2*b0;
obj[FILTER#B2] = b0;
);
function filter_buffer_highshelf_gainslope(obj, freq, gainFactor, slope) local(A, inv_a0, b0, w0, sin_w0, Q, alpha) (
A = sqrt(gainFactor);
w0 = 2*$pi*freq/srate;
sin_w0 = sin(w0);
cos_w0 = cos(w0);
Q = 1/sqrt((A + 1/A)*(1/slope - 1) + 2);
alpha = sin_w0*0.5/Q;
sqrtA2alpha = 2*sqrt(A)*alpha;
inv_a0 = 1/((A + 1) - (A - 1)*cos_w0 + sqrtA2alpha);
obj[FILTER#A1] = 2*((A - 1) - (A + 1)*cos_w0)*inv_a0;
obj[FILTER#A2] = ((A + 1) - (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
obj[FILTER#B0] = A*((A + 1) + (A - 1)*cos_w0 + sqrtA2alpha)*inv_a0;
obj[FILTER#B1] = -2*A*((A - 1) + (A + 1)*cos_w0)*inv_a0;
obj[FILTER#B2] = A*((A + 1) + (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
);
function filter_buffer_highshelf_gainband(obj, freq, gainFactor, BW) local(A, inv_a0, b0, w0, sin_w0, Q, alpha) (
A = sqrt(gainFactor);
w0 = 2*$pi*freq/srate;
sin_w0 = sin(w0);
cos_w0 = cos(w0);
Q = 0.5/sinh(log(2)*0.5*BW*w0/sin_w0);
alpha = sin_w0*0.5/Q;
sqrtA2alpha = 2*sqrt(A)*alpha;
inv_a0 = 1/((A + 1) - (A - 1)*cos_w0 + sqrtA2alpha);
obj[FILTER#A1] = 2*((A - 1) - (A + 1)*cos_w0)*inv_a0;
obj[FILTER#A2] = ((A + 1) - (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
obj[FILTER#B0] = A*((A + 1) + (A - 1)*cos_w0 + sqrtA2alpha)*inv_a0;
obj[FILTER#B1] = -2*A*((A - 1) + (A + 1)*cos_w0)*inv_a0;
obj[FILTER#B2] = A*((A + 1) + (A - 1)*cos_w0 - sqrtA2alpha)*inv_a0;
);
function filter_buffer_sample(obj, x0) local(y0) (
y0 = obj[FILTER#B0]*x0 + obj[FILTER#B1]*obj[FILTER#X1] + obj[FILTER#B2]*obj[FILTER#X2] - obj[FILTER#A1]*obj[FILTER#Y1] - obj[FILTER#A2]*obj[FILTER#Y2];
obj[FILTER#Y2] = obj[FILTER#Y1];
obj[FILTER#Y1] = y0;
obj[FILTER#X2] = obj[FILTER#X1];
obj[FILTER#X1] = x0;
y0;
);