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diff --git a/Transceiver52M/Complex.h b/Transceiver52M/Complex.h
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+/**@file templates for Complex classes
+unlike the built-in complex<> templates, these inline most operations for speed
+*/
+
+/*
+* Copyright 2008 Free Software Foundation, Inc.
+*
+* This software is distributed under multiple licenses; see the COPYING file in the main directory for licensing information for this specific distribuion.
+*
+* This use of this software may be subject to additional restrictions.
+* See the LEGAL file in the main directory for details.
+
+    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.
+
+*/
+
+
+
+
+#ifndef COMPLEXCPP_H
+#define COMPLEXCPP_H
+
+#include <math.h>
+#include <ostream>
+
+
+template<class Real> class Complex {
+
+public:
+
+  Real r, i;
+
+  /**@name constructors */
+  //@{
+  /**@name from real */
+  //@{
+  Complex(Real real, Real imag) {r=real; i=imag;}	// x=complex(a,b)
+  Complex(Real real) {r=real; i=0;}			// x=complex(a)
+  //@}
+  /**@name from nothing */
+  //@{
+  Complex() {r=(Real)0; i=(Real)0;}			// x=complex()
+  //@}
+  /**@name from other complex */
+  //@{
+  Complex(const Complex<float>& z) {r=z.r; i=z.i;}	// x=complex(z)
+  Complex(const Complex<double>& z) {r=z.r; i=z.i;}	// x=complex(z)
+  Complex(const Complex<long double>& z) {r=z.r; i=z.i;}	// x=complex(z)
+  //@}
+  //@}
+
+  /**@name casting up from basic numeric types */
+  //@{
+  Complex& operator=(char a) { r=(Real)a; i=(Real)0; return *this; }
+  Complex& operator=(int a) { r=(Real)a; i=(Real)0; return *this; }
+  Complex& operator=(long int a) { r=(Real)a; i=(Real)0; return *this; }
+  Complex& operator=(short a) { r=(Real)a; i=(Real)0; return *this; }
+  Complex& operator=(float a) { r=(Real)a; i=(Real)0; return *this; }
+  Complex& operator=(double a) { r=(Real)a; i=(Real)0; return *this; }
+  Complex& operator=(long double a) { r=(Real)a; i=(Real)0; return *this; }
+  //@}
+
+  /**@name arithmetic */
+  //@{
+  /**@ binary operators */
+  //@{
+  Complex operator+(const Complex<Real>& a) const { return Complex<Real>(r+a.r, i+a.i); }
+  Complex operator+(Real a) const { return Complex<Real>(r+a,i); }
+  Complex operator-(const Complex<Real>& a) const { return Complex<Real>(r-a.r, i-a.i); }
+  Complex operator-(Real a) const { return Complex<Real>(r-a,i); }
+  Complex operator*(const Complex<Real>& a) const { return Complex<Real>(r*a.r-i*a.i, r*a.i+i*a.r); }
+  Complex operator*(Real a) const { return Complex<Real>(r*a, i*a); }
+  Complex operator/(const Complex<Real>& a) const { return operator*(a.inv()); }
+  Complex operator/(Real a) const { return Complex<Real>(r/a, i/a); }
+  //@}
+  /*@name component-wise product */
+  //@{
+  Complex operator&(const Complex<Real>& a) const { return Complex<Real>(r*a.r, i*a.i); }
+  //@}
+  /*@name inplace operations */
+  //@{
+  Complex& operator+=(const Complex<Real>&);
+  Complex& operator-=(const Complex<Real>&);
+  Complex& operator*=(const Complex<Real>&);
+  Complex& operator/=(const Complex<Real>&);
+  Complex& operator+=(Real);
+  Complex& operator-=(Real);
+  Complex& operator*=(Real);
+  Complex& operator/=(Real);
+  //@}
+  //@}
+
+  /**@name comparisons */
+  //@{
+  bool operator==(const Complex<Real>& a) const { return ((i==a.i)&&(r==a.r)); }
+  bool operator!=(const Complex<Real>& a) const { return ((i!=a.i)||(r!=a.r)); }
+  bool operator<(const Complex<Real>& a) const { return norm2()<a.norm2(); }
+  bool operator>(const Complex<Real>& a) const { return norm2()>a.norm2(); }
+  //@}
+
+  /// reciprocation
+  Complex inv() const;	
+
+  // unary functions -- inlined
+  /**@name unary functions */
+  //@{
+  /**@name inlined */
+  //@{
+  Complex conj() const { return Complex<Real>(r,-i); }
+  Real norm2() const { return i*i+r*r; }
+  Complex flip() const { return Complex<Real>(i,r); }
+  Real real() const { return r;}
+  Real imag() const { return i;}
+  Complex neg() const { return Complex<Real>(-r, -i); }
+  bool isZero() const { return ((r==(Real)0) && (i==(Real)0)); }
+  //@}
+  /**@name not inlined due to outside calls */
+  //@{
+  Real abs() const { return ::sqrt(norm2()); }
+  Real arg() const { return ::atan2(i,r); }
+  float dB() const { return 10.0*log10(norm2()); }
+  Complex exp() const { return expj(i)*(::exp(r)); }
+  Complex unit() const; 			///< unit phasor with same angle
+  Complex log() const { return Complex(::log(abs()),arg()); }
+  Complex pow(double n) const { return expj(arg()*n)*(::pow(abs(),n)); }
+  Complex sqrt() const { return pow(0.5); }
+  //@}
+  //@}
+
+};
+
+
+/**@name standard Complex manifestations */
+//@{
+typedef Complex<float> complex;
+typedef Complex<double> dcomplex;
+typedef Complex<short> complex16;
+typedef Complex<long> complex32;
+//@}
+
+
+template<class Real> inline Complex<Real> Complex<Real>::inv() const
+{
+  Real nVal;
+
+  nVal = norm2();
+  return Complex<Real>(r/nVal, -i/nVal);
+}
+
+template<class Real> Complex<Real>& Complex<Real>::operator+=(const Complex<Real>& a)
+{
+  r += a.r;
+  i += a.i;
+  return *this;
+}
+
+template<class Real> Complex<Real>& Complex<Real>::operator*=(const Complex<Real>& a)
+{
+  operator*(a);
+  return *this;
+}
+
+template<class Real> Complex<Real>& Complex<Real>::operator-=(const Complex<Real>& a)
+{
+  r -= a.r;
+  i -= a.i;
+  return *this;
+}
+
+template<class Real> Complex<Real>& Complex<Real>::operator/=(const Complex<Real>& a)
+{
+  operator/(a);
+  return *this;
+}
+
+
+/* op= style operations with reals */
+
+template<class Real> Complex<Real>& Complex<Real>::operator+=(Real a)
+{
+  r += a;
+  return *this;
+}
+
+template<class Real> Complex<Real>& Complex<Real>::operator*=(Real a)
+{
+  r *=a;
+  i *=a;
+  return *this;
+}
+
+template<class Real> Complex<Real>& Complex<Real>::operator-=(Real a)
+{
+  r -= a;
+  return *this;
+}
+
+template<class Real> Complex<Real>& Complex<Real>::operator/=(Real a)
+{
+  r /= a;
+  i /= a;
+  return *this;
+}
+
+
+template<class Real> Complex<Real> Complex<Real>::unit() const
+{
+  Real absVal = abs();
+  return (Complex<Real>(r/absVal, i/absVal));
+}
+
+
+
+/**@name complex functions outside of the Complex<> class. */
+//@{
+
+/** this allows type-commutative multiplication */
+template<class Real> Complex<Real> operator*(Real a, const Complex<Real>& z)
+{
+  return Complex<Real>(z.r*a, z.i*a);
+}
+
+
+/** this allows type-commutative addition */
+template<class Real> Complex<Real> operator+(Real a, const Complex<Real>& z)
+{
+  return Complex<Real>(z.r+a, z.i);
+}
+
+
+/** this allows type-commutative subtraction */
+template<class Real> Complex<Real> operator-(Real a, const Complex<Real>& z)
+{
+  return Complex<Real>(z.r-a, z.i);
+}
+
+
+
+/// e^jphi
+template<class Real> Complex<Real> expj(Real phi)
+{
+  return Complex<Real>(cos(phi),sin(phi));
+}
+
+/// phasor expression of a complex number
+template<class Real> Complex<Real> phasor(Real C, Real phi)
+{
+  return (expj(phi)*C);
+}
+
+/// formatted stream output
+template<class Real> std::ostream& operator<<(std::ostream& os, const Complex<Real>& z)
+{
+  os << z.r << ' ';
+  //os << z.r << ", ";
+  //if (z.i>=0) { os << "+"; }
+  os << z.i << "j";
+  return os;
+}
+
+//@}
+
+
+#endif