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/*
* 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
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