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/*
* DSPIfilters.h - Inline classes for biquad filters
* Copyright (c) 2000 by Tom Schouten
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
#ifndef DSPIfilters_h
#define DSPIfilters_h
#include "DSPIcomplex.h"
#include "DSPI.h"
//#include <stdio.h>
/* orthogonal biquad */
class DSPIfilterOrtho {
public:
inline DSPIfilterOrtho(){resetState();resetCoef();resetSCoef();}
inline ~DSPIfilterOrtho(){}
inline void resetState(){d1A = d1B = d2A = d2B = 0.0;}
inline void resetCoef(){ai = ar = c0 = c1 = c2 = 0.0;}
inline void resetSCoef(){s_ai = s_ar = s_c0 = s_c1 = s_c2 = 0.0;}
/*
* Biquad filters remarks
*
* Q is defined with reference to the analog prototype:
* poles/zeros = w0 * (1/Q +- sqrt(1 - 1/Q^2))
*
* the num/den polynomial then has the form:
* 1 + 2s/Qw0 + (s/w0)^2
*
* if Q < 1 => real valued poles/zeros
* if Q > 1 => complex values poles/zeros
* if Q = inf => imaginary poles/zeros
* if Q = sqrt(2) => 'maximally flat' poles/zeros
*
* the analog prototypes are converted to the digital domain
* using the bilinear transform. hence the prewarping.
*/
// make sure freq and Q are positive and within bounds
inline void checkBounds(t_float &freq, t_float &Q)
{
freq = fabs(freq);
Q = fabs(Q);
t_float epsilon = .0001; // stability guard
t_float fmin = 0.0 + epsilon;
t_float fmax = 0.5 - epsilon;
t_float Qmin = 1.1;
if (freq < fmin) freq = fmin;
if (freq > fmax) freq = fmax;
if (Q < Qmin) Q = Qmin;
}
inline void setAP(t_float freq, t_float Q) // allpass
{
// prototype: H(s) = (1 - 2s/Qw0 + (s/w0)^2) / (1 + 2s/Qw0 + (s/w0)^2)
// s_p = - s_z (analog: symmetric wrt. im axis)
// z_p = 1/z_z (digiatl: summ wrt. unit circle)
checkBounds(freq, Q);
// prewarp for bilin transfo
freq = bilin_prewarp(freq);
t_float zeta = 1.0/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0-zeta*zeta))*freq);
DSPIcomplex z = 1.0 / p;
setPoleZeroNormalized(p, z, DSPIcomplex(1,0));
}
inline void setLP(t_float freq, t_float Q) // low pass
{
// prototype: H(s) = 1 / (1 + 2s/Qw0 + (s/w0)^2)
// the bilinear transform has 2 zeros at NY
checkBounds(freq, Q);
freq = bilin_prewarp(freq);
t_float zeta = 1/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0-zeta*zeta))*freq);
setPoleZeroNormalized(p, DSPIcomplex(-1, 0), DSPIcomplex(1, 0));
}
inline void setHP(t_float freq, t_float Q) // hi pass
{
// prototype: H(s) = (s/w0)^2 / (1 + 2s/Qw0 + (s/w0)^2)
// the bilinear transform has 2 zeros at DC
checkBounds(freq, Q);
freq = bilin_prewarp(freq);
t_float zeta = 1/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0-zeta*zeta))*freq);
setPoleZeroNormalized(p, DSPIcomplex(1, 0), DSPIcomplex(-1, 0));
}
inline void setBP(t_float freq, t_float Q) // band pass (1-allpass)
{
// prototype: 1/2 * (1 - H_allpass(z))
setAP(freq, Q);
t_float h = -0.5;
c0 *= h;
c1 *= h;
c2 *= h;
c0 -= h;
}
inline void setBR(t_float freq, t_float Q) // band reject
{
// prototype: H(s) = (1 - (s/w0)^2) / (1 + 2s/Qw0 + (s/w0)^2)
checkBounds(freq, Q);
// pole phasor
DSPIcomplex z = DSPIcomplex(2.0 * M_PI * freq);
// prewarp for bilin transfo
freq = bilin_prewarp(freq);
t_float zeta = 1/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0-zeta*zeta))*freq);
setPoleZeroNormalized(p, z, DSPIcomplex(1,0));
}
inline void setHS(t_float freq, t_float gain) // low shelf
{
// hi shelf = LP - g(LP-1)
t_float Q = M_SQRT2;
setLP(freq, Q);
c0 -= gain * (c0 - 1.0);
c1 -= gain * (c1);
c2 -= gain * (c2);
}
inline void setLS(t_float freq, t_float gain) // low shelf
{
// hi shelf = HP - g(HP-1)
t_float Q = M_SQRT2;
setHP(freq, Q);
c0 -= gain * (c0 - 1.0);
c1 -= gain * (c1);
c2 -= gain * (c2);
}
inline void setEQ(t_float freq, t_float Q, t_float gain)// param EQ
{
// EQ = (1+A)/2 + (1-A)/2 AP
t_float a0 = 0.5 * (1.0 + gain);
t_float a1 = 0.5 * (1.0 - gain);
setAP(freq, Q);
c0 *= a1;
c1 *= a1;
c2 *= a1;
c0 += a0;
}
inline void setPoleZero
(
const DSPIcomplex& a, // pole
const DSPIcomplex& b // zero
)
{
ar = a.r();
ai = a.i();
c0 = 1.0;
c1 = 2.0 * (a.r() - b.r());
c2 = (a.norm2() - b.norm2() - c1 * a.r()) / a.i();
}
inline void setPoleZeroNormalized
(
const DSPIcomplex& a, // pole
const DSPIcomplex& b, // zero
const DSPIcomplex& c // gain = 1 at this freq
)
{
setPoleZero(a, b);
DSPIcomplex invComplexGain = ((c-a)*(c-a.conj()))/((c-b)*(c-b.conj()));
t_float invGain = invComplexGain.norm();
c0 *= invGain;
c1 *= invGain;
c2 *= invGain;
}
// one channel bang
inline void Bang
(
t_float &input,
t_float &output
)
{
t_float d1t = ar * d1A + ai * d2A + input;
t_float d2t = ar * d2A - ai * d1A;
output = c0 * input + c1 * d1A + c2 * d2A;
d1A = d1t;
d2A = d2t;
}
// one channel bang smooth
// a default s could be s = (1 - (.1)^(1/n))
inline void BangSmooth
(
t_float &input, // input ref
t_float &output, // output ref
t_float s // smooth pole
)
{
t_float d1t = s_ar * d1A + s_ai * d2A + input;
t_float d2t = s_ar * d2A - s_ai * d1A;
s_ar += s * (ar - s_ar);
s_ai += s * (ai - s_ai);
output = s_c0 * input + s_c1 * d1A + s_c2 * d2A;
d1A = d1t;
d2A = d2t;
s_c0 += s * (c0 - s_c0);
s_c1 += s * (c1 - s_c1);
s_c2 += s * (c2 - s_c2);
}
// two channel bang
inline void Bang2
(
t_float &input1,
t_float &input2,
t_float &output1,
t_float &output2
)
{
t_float d1tA = ar * d1A + ai * d2A + input1;
t_float d1tB = ar * d1B + ai * d2B + input2;
t_float d2tA = ar * d2A - ai * d1A;
t_float d2tB = ar * d2B - ai * d1B;
output1 = c0 * input1 + d1A * c1 + d2A * c2;
output2 = c0 * input2 + d1B * c1 + d2B * c2;
d1A = d1tA;
d2A = d2tA;
d1B = d1tB;
d2B = d2tB;
}
// two channel bang smooth
inline void Bang2Smooth
(
t_float &input1,
t_float &input2,
t_float &output1,
t_float &output2,
t_float s
)
{
t_float d1tA = s_ar * d1A + s_ai * d2A + input1;
t_float d1tB = s_ar * d1B + s_ai * d2B + input2;
t_float d2tA = s_ar * d2A - s_ai * d1A;
t_float d2tB = s_ar * d2B - s_ai * d1B;
s_ar += s * (ar - s_ar);
s_ai += s * (ai - s_ai);
output1 = s_c0 * input1 + d1A * s_c1 + d2A * s_c2;
output2 = s_c0 * input2 + d1B * s_c1 + d2B * s_c2;
d1A = d1tA;
d2A = d2tA;
d1B = d1tB;
d2B = d2tB;
s_c0 += s * (c0 - s_c0);
s_c1 += s * (c1 - s_c1);
s_c2 += s * (c2 - s_c2);
}
inline void killDenormals()
{
// state data
t_float zero = 0.0;
d1A = DSPI_IS_DENORMAL(d1A) ? zero : d1A;
d2A = DSPI_IS_DENORMAL(d2A) ? zero : d2A;
d1B = DSPI_IS_DENORMAL(d1B) ? zero : d1B;
d2B = DSPI_IS_DENORMAL(d2B) ? zero : d2B;
/* test on athlon showed nuking smooth data does not
* present a noticable difference in performance however
* nuking state data is really necessary
// smooth data
t_float dai = ai - s_ai;
t_float dar = ar - s_ar;
t_float dc0 = c0 - s_c0;
t_float dc1 = c1 - s_c1;
t_float dc2 = c2 - s_c2;
s_ai = DSPI_IS_DENORMAL(dai) ? ai : s_ai;
s_ar = DSPI_IS_DENORMAL(dar) ? ar : s_ar;
s_c0 = DSPI_IS_DENORMAL(dc0) ? c0 : s_c0;
s_c1 = DSPI_IS_DENORMAL(dc0) ? c1 : s_c1;
s_c2 = DSPI_IS_DENORMAL(dc0) ? c2 : s_c2;
*/
}
private:
// state data
t_float d1A;
t_float d2A;
t_float d1B;
t_float d2B;
// pole data
t_float ai;
t_float s_ai;
t_float ar;
t_float s_ar;
// zero data
t_float c0;
t_float s_c0;
t_float c1;
t_float s_c1;
t_float c2;
t_float s_c2;
};
class DSPIfilterSeries{
public:
inline DSPIfilterSeries() {DSPIfilterSeries(1);}
inline ~DSPIfilterSeries() {delete [] biquad;};
inline DSPIfilterSeries(int numberOfSections)
{
// create a set of biquads
sections = numberOfSections;
biquad = new DSPIfilterOrtho[numberOfSections];
}
inline void setButterHP(t_float freq)
{
/* This member function computes the poles for a highpass butterworth filter.
* The filter is transformed to the digital domain using a bilinear transform.
* Every biquad section is normalized at NY.
*/
t_float epsilon = .0001; // stability guard
t_float min = 0.0 + epsilon;
t_float max = 0.5 - epsilon;
if (freq < min) freq = min;
if (freq > max) freq = max;
// prewarp cutoff frequency
t_float omega = bilin_prewarp(freq);
DSPIcomplex NY(-1,0); //normalize at NY
DSPIcomplex DC(1,0); //all zeros will be at DC
DSPIcomplex pole( (2*sections + 1) * M_PI / (4*sections)); // first pole of lowpass filter with omega == 1
DSPIcomplex pole_inc(M_PI / (2*sections)); // phasor to get to next pole, see Porat p. 331
for (int i=0; i<sections; i++)
{
// setup the biquad with the computed pole and zero and unit gain at NY
biquad[i].setPoleZeroNormalized(
bilin_stoz(omega/pole), // LP -> HP -> digital transfo
DC, // all zeros at DC
NY); // normalized (gain == 1) at NY
pole *= pole_inc; // compe next (lowpass) pole
}
}
inline void setButterLP(t_float freq)
{
/* This member function computes the poles for a lowpass butterworth filter.
* The filter is transformed to the digital domain using a bilinear transform.
* Every biquad section is normalized at DC.
* Doing it this way, only the pole locations need to be transformed.
* The constant gain factor can be computed by setting the DC gain of every section to 1.
* An analog butterworth is all-pole, meaning the bilinear transform has all zeros at -1
*/
t_float epsilon = .0001; // stability guard
t_float min = 0.0 + epsilon;
t_float max = 0.5 - epsilon;
if (freq < min) freq = min;
if (freq > max) freq = max;
// prewarp cutoff frequency
t_float omega = bilin_prewarp(freq);
DSPIcomplex DC(1,0); //normalize at DC
DSPIcomplex NY(-1,0); //all zeros will be at NY
DSPIcomplex pole( (2*sections + 1) * M_PI / (4*sections));
pole *= omega; // first pole, see Porat p. 331
DSPIcomplex pole_inc(M_PI / (2*sections)); // phasor to get to next pole, see Porat p. 331
for (int i=0; i<sections; i++)
{
// setup the biquad with the computed pole and zero and unit gain at DC
biquad[i].setPoleZeroNormalized(bilin_stoz(pole), NY, DC);
pole *= pole_inc;
}
}
inline void resetState()
{
for (int i=0; i<sections; i++) biquad[i].resetState();
}
inline void Bang(t_float &input, t_float &output)
{
t_float x = input;
for (int i=0; i<sections; i++)
{
biquad[i].Bang(x, x);
}
output = x;
}
inline void Bang2(t_float &input1, t_float &input2, t_float &output1, t_float &output2)
{
t_float x = input1;
t_float y = input2;
for (int i=0; i<sections; i++)
{
biquad[i].Bang2(x, y, x, y);
}
output1 = x;
output2 = y;
}
inline void BangSmooth(t_float &input, t_float &output, t_float s)
{
t_float x = input;
for (int i=0; i<sections; i++)
{
biquad[i].BangSmooth(x, x, s);
}
output = x;
}
inline void Bang2(t_float &input1, t_float &input2, t_float &output1, t_float &output2, t_float s)
{
t_float x = input1;
t_float y = input2;
for (int i=0; i<sections; i++)
{
biquad[i].Bang2Smooth(x, y, x, y, s);
}
output1 = x;
output2 = y;
}
private:
int sections;
DSPIfilterOrtho *biquad;
t_float gain;
};
#endif //DSPIfilters_h
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