[PD-cvs] externals/creb/modules++ DSPI.h, NONE, 1.1 DSPIcomplex.h, NONE, 1.1 DSPIfilters.h, NONE, 1.1 filters.h, NONE, 1.1
Hans-Christoph Steiner
eighthave at users.sourceforge.net
Tue Aug 22 03:20:22 CEST 2006
Update of /cvsroot/pure-data/externals/creb/modules++
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv23744/creb/modules++
Added Files:
DSPI.h DSPIcomplex.h DSPIfilters.h filters.h
Log Message:
fixed things so that all but one of the objects compile into a libdir
--- NEW FILE: DSPIcomplex.h ---
/*
* DSPIcomplex.h - Quick and dirty inline class for complex numbers
* (mainly to compute filter poles/zeros, not to be used inside loops)
* 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 DSPIcomplex_h
#define DSPIcomplex_h
#include <math.h>
#include <iostream>
class DSPIcomplex
{
public:
inline DSPIcomplex() {_r = _i = 0;}
inline DSPIcomplex(const float &a, const float &b) {setCart(a, b);}
inline DSPIcomplex(const float &phasor) {setAngle(phasor);}
inline void setAngle(const float &angle) {_r = cos(angle); _i = sin(angle);}
inline void setPolar(const float &phasor, const float &norm)
{_r = norm * cos(phasor); _i = norm * sin(phasor);}
inline void setCart(const float &a, const float &b) {_r = a; _i = b;}
inline const float& r() const {return _r;}
inline const float& i() const {return _i;}
inline float norm2() const {return _r*_r+_i*_i;}
inline float norm() const {return sqrt(norm2());}
inline void normalize() {float n = 1.0f / norm(); _r *= n; _i *= n;}
inline DSPIcomplex conj() const {return DSPIcomplex(_r, -_i);}
inline float angle() const {return atan2(_i, _r);}
inline DSPIcomplex operator+ (const DSPIcomplex &a) const
{
return DSPIcomplex(_r + a.r(), _i + a.i());
}
inline DSPIcomplex operator+ (float f) const
{
return DSPIcomplex(_r + f, _i);
}
inline DSPIcomplex operator- (const DSPIcomplex &a) const
{
return DSPIcomplex(_r - a.r(), _i - a.i());
}
inline DSPIcomplex operator- (float f) const
{
return DSPIcomplex(_r - f, _i);
}
inline DSPIcomplex operator* (const DSPIcomplex &a) const
{
return DSPIcomplex(_r * a.r() - _i * a.i(), _i * a.r() + _r * a.i());
}
inline DSPIcomplex operator* (float f) const
{
return DSPIcomplex(_r * f, _i * f);
}
inline DSPIcomplex operator/ (const DSPIcomplex &a) const
{
float n_t = 1.0f / a.norm2();
return DSPIcomplex(n_t * (_r * a.r() + _i * a.i()), n_t * (_i * a.r() - _r * a.i()));
}
inline DSPIcomplex operator/ (float f) const
{
float n_t = 1.0f / f;
return DSPIcomplex(n_t * _r, n_t * _i);
}
inline friend std::ostream& operator<< (std::ostream& o, DSPIcomplex& a)
{
return o << "(" << a.r() << "," << a.i() << ")";
}
inline friend DSPIcomplex operator+ (float f, DSPIcomplex& a)
{
return(DSPIcomplex(a.r() + f, a.i()));
}
inline friend DSPIcomplex operator- (float f, DSPIcomplex& a)
{
return(DSPIcomplex(f - a.r(), - a.i()));
}
inline friend DSPIcomplex operator/ (float f, DSPIcomplex& a)
{
return(DSPIcomplex(f,0) / a);
}
// ????
inline friend DSPIcomplex operator* (float f, DSPIcomplex& a)
{
return(DSPIcomplex(f*a.r(), f*a.i()));
}
inline DSPIcomplex& operator *= (float f)
{
_r *= f;
_i *= f;
return *this;
}
inline DSPIcomplex& operator /= (float f)
{
_r /= f;
_i /= f;
return *this;
}
inline DSPIcomplex& operator *= (DSPIcomplex& a)
{
float r_t = _r * a.r() - _i * a.i();
_i = _r * a.i() + _i * a.r();
_r = r_t;
return *this;
}
inline DSPIcomplex& operator /= (DSPIcomplex& a)
{
float n_t = a.norm2();
float r_t = n_t * (_r * a.r() + _i * a.i());
_i = n_t * (_i * a.r() - _r * a.i());
_r = r_t;
return *this;
}
float _r;
float _i;
};
// COMPLEX LOG
inline DSPIcomplex dspilog(DSPIcomplex a) /* complex log */
{
float r_t = log(a.norm());
float i_t = a.angle();
return DSPIcomplex(r_t, i_t);
}
// COMPLEX EXP
inline DSPIcomplex dspiexp(DSPIcomplex a) /* complex exp */
{
return (DSPIcomplex(a.i()) * exp(a.r()));
}
// BILINEAR TRANSFORM analog -> digital
inline DSPIcomplex bilin_stoz(DSPIcomplex a)
{
DSPIcomplex a2 = a * 0.5f;
return((1.0f + a2)/(1.0f - a2));
}
// BILINEAR TRANSFORM digital -> analog
inline DSPIcomplex bilin_ztos(DSPIcomplex a)
{
return ((a - 1.0f) / (a + 1.0f))*2.0f;
}
// not really a complex function but a nice complement to the bilinear routines
inline float bilin_prewarp(float freq)
{
return 2.0f * tan(M_PI * freq);
}
#endif //DSPIcomplex_h
--- NEW FILE: DSPI.h ---
#ifndef DSPI_h
#define DSPI_h
#define DSPImin(x,y) (((x)<(y)) ? (x) : (y))
#define DSPImax(x,y) (((x)>(y)) ? (x) : (y))
#define DSPIclip(min, x, max) (DSPImin(DSPImax((min), (x)), max))
// test if floating point number is denormal
#define DSPI_IS_DENORMAL(f) (((*(unsigned int *)&(f))&0x7f800000) == 0)
// test if almost denormal, choose whichever is fastest
#define DSPI_IS_ALMOST_DENORMAL(f) (((*(unsigned int *)&(f))&0x7f800000) < 0x08000000)
//#define DSPI_IS_ALMOST_DENORMAL(f) (fabs(f) < 3.e-34)
#endif
--- NEW FILE: DSPIfilters.h ---
/*
* 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 = 0.0f;}
inline void resetCoef(){ai = ar = c0 = c1 = c2 = 0.0f;}
inline void resetSCoef(){s_ai = s_ar = s_c0 = s_c1 = s_c2 = 0.0f;}
/*
* 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(float &freq, float &Q)
{
freq = fabs(freq);
Q = fabs(Q);
float epsilon = .0001f; // stability guard
float fmin = 0.0f + epsilon;
float fmax = 0.5f - epsilon;
float Qmin = 1.1f;
if (freq < fmin) freq = fmin;
if (freq > fmax) freq = fmax;
if (Q < Qmin) Q = Qmin;
}
inline void setAP(float freq, 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);
float zeta = 1.0f/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0f-zeta*zeta))*freq);
DSPIcomplex z = 1.0f / p;
setPoleZeroNormalized(p, z, DSPIcomplex(1,0));
}
inline void setLP(float freq, 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);
float zeta = 1/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0f-zeta*zeta))*freq);
setPoleZeroNormalized(p, DSPIcomplex(-1, 0), DSPIcomplex(1, 0));
}
inline void setHP(float freq, 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);
float zeta = 1/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0f-zeta*zeta))*freq);
setPoleZeroNormalized(p, DSPIcomplex(1, 0), DSPIcomplex(-1, 0));
}
inline void setBP(float freq, float Q) // band pass (1-allpass)
{
// prototype: 1/2 * (1 - H_allpass(z))
setAP(freq, Q);
float h = -0.5f;
c0 *= h;
c1 *= h;
c2 *= h;
c0 -= h;
}
inline void setBR(float freq, 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(2.0f * M_PI * freq);
// prewarp for bilin transfo
freq = bilin_prewarp(freq);
float zeta = 1/Q;
DSPIcomplex p = bilin_stoz(DSPIcomplex(-zeta, (1.0f-zeta*zeta))*freq);
setPoleZeroNormalized(p, z, DSPIcomplex(1,0));
}
inline void setHS(float freq, float gain) // low shelf
{
// hi shelf = LP - g(LP-1)
float Q = M_SQRT2;
setLP(freq, Q);
c0 -= gain * (c0 - 1.0f);
c1 -= gain * (c1);
c2 -= gain * (c2);
}
inline void setLS(float freq, float gain) // low shelf
{
// hi shelf = HP - g(HP-1)
float Q = M_SQRT2;
setHP(freq, Q);
c0 -= gain * (c0 - 1.0f);
c1 -= gain * (c1);
c2 -= gain * (c2);
}
inline void setEQ(float freq, float Q, float gain)// param EQ
{
// EQ = (1+A)/2 + (1-A)/2 AP
float a0 = 0.5f * (1.0f + gain);
float a1 = 0.5f * (1.0f - 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 = 1.0f;
c1 = 2.0f * (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()));
float invGain = invComplexGain.norm();
c0 *= invGain;
c1 *= invGain;
c2 *= invGain;
}
// one channel bang
inline void Bang
(
float &input,
float &output
)
{
float d1t = ar * d1A + ai * d2A + input;
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
(
float &input, // input ref
float &output, // output ref
float s // smooth pole
)
{
float d1t = s_ar * d1A + s_ai * d2A + input;
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
(
float &input1,
float &input2,
float &output1,
float &output2
)
{
float d1tA = ar * d1A + ai * d2A + input1;
float d1tB = ar * d1B + ai * d2B + input2;
float d2tA = ar * d2A - ai * d1A;
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
(
float &input1,
float &input2,
float &output1,
float &output2,
float s
)
{
float d1tA = s_ar * d1A + s_ai * d2A + input1;
float d1tB = s_ar * d1B + s_ai * d2B + input2;
float d2tA = s_ar * d2A - s_ai * d1A;
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
float zero = 0.0f;
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
float dai = ai - s_ai;
float dar = ar - s_ar;
float dc0 = c0 - s_c0;
float dc1 = c1 - s_c1;
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
float d1A;
float d2A;
float d1B;
float d2B;
// pole data
float ai;
float s_ai;
float ar;
float s_ar;
// zero data
float c0;
float s_c0;
float c1;
float s_c1;
float c2;
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(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.
*/
float epsilon = .0001f; // stability guard
float min = 0.0f + epsilon;
float max = 0.5f - epsilon;
if (freq < min) freq = min;
if (freq > max) freq = max;
// prewarp cutoff frequency
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(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
*/
float epsilon = .0001f; // stability guard
float min = 0.0f + epsilon;
float max = 0.5f - epsilon;
if (freq < min) freq = min;
if (freq > max) freq = max;
// prewarp cutoff frequency
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(float &input, float &output)
{
float x = input;
for (int i=0; i<sections; i++)
{
biquad[i].Bang(x, x);
}
output = x;
}
inline void Bang2(float &input1, float &input2, float &output1, float &output2)
{
float x = input1;
float y = input2;
for (int i=0; i<sections; i++)
{
biquad[i].Bang2(x, y, x, y);
}
output1 = x;
output2 = y;
}
inline void BangSmooth(float &input, float &output, float s)
{
float x = input;
for (int i=0; i<sections; i++)
{
biquad[i].BangSmooth(x, x, s);
}
output = x;
}
inline void Bang2(float &input1, float &input2, float &output1, float &output2, float s)
{
float x = input1;
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;
float gain;
};
#endif //DSPIfilters_h
--- NEW FILE: filters.h ---
/* this file contains a 37th attempt to write a general purpose iir filter toolset */
/* defined as inline functions with call by reference to enable compiler ref/deref optim */
/* the typedef */
#ifndef T
#define T float
#endif
/* the prototype for a word */
#define P static inline void
#define PP static void
/* the 'reference' arguments */
#define A *a
#define B *b
#define C *c
#define D *d
#define X *x
#define Y *y
#define S *s
/* the opcodes */
/* add */
P cadd (T X, T Y, T A, T B, T C, T D) { X = A + C; Y = B + D;}
P cadd2 (T A, T B, T C, T D) { A += C; B += D;}
P vcadd (T X, T A, T C) { cadd(x,x+1,a,a+1,c,c+1); }
P vcadd2 (T A, T C) { cadd2(a,a+1,c,c+1); }
/* mul */
P cmul_r (T X, T A, T B, T C, T D) { X = A * C - B * D;}
P cmul_i (T Y, T A, T B, T C, T D) { Y = A * D + B * C;}
P cmul (T X, T Y, T A, T B, T C, T D)
{
cmul_r (x, a, b, c, d);
cmul_i (y, a, b, c, d);
}
P cmul2 (T A, T B, T C, T D)
{
T x = A;
T y = B;
cmul (&x, &y, a, b, c, d);
A = x;
B = y;
}
P vcmul (T X, T A, T C) { cmul(x,x+1,a,a+1,c,c+1); }
P vcmul2 (T A, T C) { cmul2(a,a+1,c,c+1); }
/* norm */
static inline float vcnorm(T X) { return hypot(x[0], x[1]); }
/* swap */
P vcswap(T Y, T X)
{
float t[2] = {x[0], x[1]};
x[0] = y[0];
x[1] = y[1];
y[0] = t[0];
y[1] = t[1];
}
/* inverse */
P vcinv(T Y, T X)
{
float scale = 1.0f / vcnorm(x);
y[0] = scale * x[0];
y[1] = scale * x[1];
}
P vcinv1(T X)
{
float scale = 1.0f / vcnorm(x);
x[0] *= scale;
x[1] *= scale;
}
/* exp */
/* X = exp(Y) */
P vcexp2 (T Y, T X)
{
T r = exp(x[0]);
y[0] = cos (x[1]);
y[1] = sin (x[1]);
y[0] *= r;
y[1] *= r;
}
P vcexp1 (T X)
{
T y[2];
vcexp2(y,x);
x[0] = y[0];
x[1] = y[1];
}
/*
FILTERS
the transfer function is defined in terms of the "engineering"
bilateral z-transform of the discrete impulse response h[n].
H(z) = Sum{n = -inf -> inf} h[n] z^(-n)
a unit delay operating on a singnal S(z) is therefore
represented as z^(-1) S(z)
*/
/* biquads */
/* biquad, orthogonal (poles & zeros), real in, out, state, pole, output */
P biq_orth_r (T X, T Y, T S, T A, T C)
{
Y = X + c[0] * s[0] - c[1] * s[1]; /* mind sign of c[1] */
vcmul2(s, a);
S += X;
}
/* biquad, orthogonal, complex one-pole, with scaling */
/* complex one pole: (output = s[0] + is[1]): C / (1-A z^(-1)) */
P one_pole_complex (T X, T Y, T S, T A, T C)
{
vcmul(y, s, a);
vcadd2(y, x);
s[0] = y[0];
s[1] = y[1];
vcmul(y, s, c);
}
/* complex conj two pole: (output = s[0] : (Re(C) - Re(C*Conj(A))) / (1 - A z^(-1)) (1 - Conj(A) z^(-1)) */
P two_pole_complex_conj (T X, T Y, T S, T A, T C)
{
vcmul2(s, a);
s[0] += x[0];
y[0] = s[0] * c[0] - s[1] * c[1];
}
/* support functions for IIR filter design */
/* evaluate pole and allzero TF in z^-1 given the complex zeros/poles:
p(z) (or p(z)^-1) = \product (1-z_i z^-1) */
PP eval_zero_poly(float *val, float *arg, float *zeros, int nb_zeros)
{
int i;
float a[2] = {arg[0], arg[1]};
vcinv1(a);
val[0] = 1.0f;
val[1] = 0.0f;
a[0] *= -1;
a[1] *= -1;
for (i=0; i<nb_zeros; i++){
float t[2];
vcmul(t, a, zeros + 2*i);
t[0] += 1.0f;
vcmul2(val, t);
}
}
PP eval_pole_poly(float *val, float *arg, float *poles, int nb_poles)
{
eval_zero_poly(val, arg, poles, nb_poles);
vcinv1(val);
}
/* since it's more efficient to store half of the poles for a real impulse
response, these functions compute p(z) conj(p(conj(z))) */
PP eval_conj_zero_poly(float *val, float *arg, float *zeros, int nb_zeros)
{
float t[2];
float a[2] = {arg[0], arg[1]};
eval_zero_poly(t, a, zeros, nb_zeros);
a[1] *= -1;
eval_zero_poly(val, a, zeros, nb_zeros);
val[1] *= -1;
vcmul2(val, t);
}
PP eval_conj_pole_poly(float *val, float *arg, float *poles, int nb_poles)
{
eval_conj_zero_poly(val, arg, poles, nb_poles);
vcinv1(val);
}
PP eval_conj_pole_zero_ratfunc(float *val, float *arg, float *poles, float *zeros, int nb_poles, int nb_zeros)
{
float t[2];
eval_conj_zero_poly(t, arg, zeros, nb_zeros);
eval_conj_pole_poly(val, arg, poles, nb_zeros);
vcmul2(val, t);
}
/* bandlimited IIR impulse:
* design analog butterworth filter
* obtain the partial fraction expansion of the transfer function
* determine the state increment as a function of fractional delay of impulse location
(sample the impulse response)
*/
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