biquad.h

Go to the documentation of this file.

/******************************************************************************
 Copyright (c) 2012-2016 Institut für Nachrichtentechnik, Universität Rostock
 Copyright (c) 2006-2012 Quality & Usability Lab
                         Deutsche Telekom Laboratories, TU Berlin
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
 in the Software without restriction, including without limitation the rights
 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:
 
 The above copyright notice and this permission notice shall be included in
 all copies or substantial portions of the Software.
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
*******************************************************************************/
 
// https://AudioProcessingFramework.github.io/
 
 
#ifndef APF_BIQUAD_H
#define APF_BIQUAD_H
 
#include <iosfwd>  // for std::ostream
#include <cmath>  // for std::pow(), std::tan(), std::sqrt(), ...
#include <complex>
#include <vector>
#include <cassert>  // for assert()
 
#include "apf/denormalprevention.h"
#include "apf/math.h"
 
namespace apf
{
 
// TODO: make macros for trivial operators (see iterator.h)
// TODO: combine SosCoefficients and LaplaceCoefficients in common class
// template and use typedef with dummy template arguments.
 
template<typename T>
struct SosCoefficients
{
  SosCoefficients(T b0_ = T(), T b1_ = T(), T b2_ = T()
                             , T a1_ = T(), T a2_ = T())
    : b0(b0_), b1(b1_), b2(b2_)
             , a1(a1_), a2(a2_)
  {}
 
  T b0, b1, b2;
  T     a1, a2;
 
  SosCoefficients& operator+=(const SosCoefficients& rhs)
  {
    b0 += rhs.b0; b1 += rhs.b1; b2 += rhs.b2;
                  a1 += rhs.a1; a2 += rhs.a2;
    return *this;
  }
 
  SosCoefficients operator+(const SosCoefficients& rhs) const
  {
    auto tmp = SosCoefficients(*this);
    return tmp += rhs;
  }
 
  SosCoefficients& operator*=(T rhs)
  {
    b0 *= rhs; b1 *= rhs; b2 *= rhs;
               a1 *= rhs; a2 *= rhs;
    return *this;
  }
 
  SosCoefficients operator*(T rhs) const
  {
    auto tmp = SosCoefficients(*this);
    return tmp *= rhs;
  }
 
  SosCoefficients& operator/=(T rhs)
  {
    b0 /= rhs; b1 /= rhs; b2 /= rhs;
               a1 /= rhs; a2 /= rhs;
    return *this;
  }
 
  SosCoefficients operator/(T rhs) const
  {
    auto tmp = SosCoefficients(*this);
    return tmp /= rhs;
  }
 
  friend SosCoefficients operator*(T lhs, const SosCoefficients& rhs)
  {
    auto temp = SosCoefficients(rhs);
    return temp *= lhs;
  }
 
  friend SosCoefficients
  operator-(const SosCoefficients& lhs, const SosCoefficients& rhs)
  {
    return {lhs.b0 - rhs.b0, lhs.b1 - rhs.b1, lhs.b2 - rhs.b2
                           , lhs.a1 - rhs.a1, lhs.a2 - rhs.a2};
  }
 
  friend std::ostream&
  operator<<(std::ostream& stream, const SosCoefficients& c)
  {
    stream << "b0: " << c.b0 << ", b1: " << c.b1 << ", b2: " << c.b2
                             << ", a1: " << c.a1 << ", a2: " << c.a2;
    return stream;
  }
};
 
template<typename T>
struct LaplaceCoefficients
{
  LaplaceCoefficients(T b0_ = T(), T b1_ = T(), T b2_ = T()
                                 , T a1_ = T(), T a2_ = T())
    : b0(b0_), b1(b1_), b2(b2_)
             , a1(a1_), a2(a2_)
  {}
 
  T b0, b1, b2;
  T     a1, a2;
};
 
template<typename T, template<typename> class DenormalPrevention = apf::dp::ac>
class BiQuad : public SosCoefficients<T> , private DenormalPrevention<T>
{
  public:
    using argument_type = T;
    using result_type = T;
 
    BiQuad() : w0(), w1(), w2() {}
 
    BiQuad& operator=(const SosCoefficients<T>& c)
    {
      this->SosCoefficients<T>::operator=(c);
      return *this;
    }
 
    result_type operator()(argument_type in)
    {
      w0 = w1;
      w1 = w2;
      w2 = in - this->a1*w1 - this->a2*w0;
 
      this->prevent_denormals(w2);
 
      in = this->b0*w2 + this->b1*w1 + this->b2*w0;
 
      return in;
    }
 
    T w0, w1, w2;
};
 
template<typename S, typename Container = std::vector<S>>
class Cascade
{
  public:
    using argument_type = typename S::argument_type;
    using result_type = typename S::result_type;
    using size_type = typename Container::size_type;
 
    explicit Cascade(size_type n) : _sections(n) {}
 
    template<typename I>
    void set(I first, I last)
    {
      assert(_sections.size() == size_type(std::distance(first, last)));
 
      std::copy(first, last, _sections.begin());
    }
 
    result_type operator()(argument_type in)
    {
      for (auto& section: _sections)
      {
        in = section(in);
      }
      return in;
    }
 
    template<typename In, typename Out>
    void execute(In first, In last, Out result)
    {
      using out_t = typename std::iterator_traits<Out>::value_type;
 
      while (first != last)
      {
        *result++ = static_cast<out_t>(this->operator()(*first));
        ++first;
      }
    }
 
    size_type number_of_sections() const { return _sections.size(); }
 
  private:
    Container _sections;
};
 
namespace internal
{
 
template<typename T>
void roots2poly(T Roots[2][2], T& poly1, T& poly2)
{
  T two = 2.0;
 
  std::complex<T> eig[2];
 
  T tmp_arg = std::pow((Roots[0][0]+Roots[1][1])/two, two)
                    + Roots[0][1]*Roots[1][0] - Roots[0][0]*Roots[1][1];
 
  if (tmp_arg > 0)
  {
    eig[0] = (Roots[0][0]+Roots[1][1])/two + std::sqrt(tmp_arg);
    eig[1] = (Roots[0][0]+Roots[1][1])/two - std::sqrt(tmp_arg);
  }
  else
  {
    eig[0] = std::complex<T>((Roots[0][0]+Roots[1][1])/two, std::sqrt(-tmp_arg));
    eig[1] = std::complex<T>((Roots[0][0]+Roots[1][1])/two, -std::sqrt(-tmp_arg));
  }
 
  poly1 = real(-eig[0] - eig[1]);
  poly2 = real(-eig[1] * -eig[0]);
}
 
}  // namespace internal
 
template<typename T>
SosCoefficients<T> bilinear(LaplaceCoefficients<T> coeffs_in, int fs, int fp)
{
  SosCoefficients<T> coeffs_out;
 
  T one = 1.0;
  T two = 2.0;
 
  // prewarp
  T fp_temp = static_cast<T>(fp) * (two * apf::math::pi<T>());
  T lambda = fp_temp / std::tan(fp_temp / static_cast<T>(fs) / two) / two;
 
  // calculate state space representation
  T A[2][2] = { { -coeffs_in.a1, -coeffs_in.a2 }, { 1.0, 0.0 } };
  T B[2] = { 1.0, 0.0 };
  T C[2] = { coeffs_in.b1-coeffs_in.a1, coeffs_in.b2-coeffs_in.a2 };
  T D = 1.0;
 
  T t = one / lambda;
  T r = std::sqrt(t);
 
  T T1[2][2] = { { (t/two)*A[0][0] + one, (t/two)*A[0][1] },
                 { (t/two)*A[1][0], (t/two)*A[1][1] + one } };
  T T2[2][2] = { { -(t/two)*A[0][0] + one, -(t/two)*A[0][1] },
                 { -(t/two)*A[1][0], -(t/two)*A[1][1] + one} };
 
  // solve linear equation systems
  T det = T2[0][0]*T2[1][1] - T2[0][1]*T2[1][0];
  T Ad[2][2] = { { (T1[0][0]*T2[1][1] - T1[1][0]*T2[0][1]) / det,
                   (T1[0][1]*T2[1][1] - T1[1][1]*T2[0][1]) / det },
                 { (T1[1][0]*T2[0][0] - T1[0][0]*T2[1][0]) / det,
                   (T1[1][1]*T2[0][0] - T1[0][1]*T2[1][0]) / det } };
  T Bd[2] = { (t/r) * (B[0]*T2[1][1] - B[1]*T2[0][1]) / det,
              (t/r) * (B[1]*T2[0][0] - B[0]*T2[1][0]) / det };
  T Cd[2] = { (C[0]*T2[1][1] - C[1]*T2[1][0]) / det,
              (C[1]*T2[0][0] - C[0]*T2[0][1]) / det };
  T Dd = (B[0]*Cd[0] + B[1]*Cd[1]) * (t/two) + D;
 
  Cd[0] *= r;
  Cd[1] *= r;
 
  // convert roots to polynomial
  internal::roots2poly(Ad, coeffs_out.a1, coeffs_out.a2);
 
  T Tmp[2][2] = { { Ad[0][0]-Bd[0]*Cd[0], Ad[0][1]-Bd[0]*Cd[1] },
                  { Ad[1][0]-Bd[1]*Cd[0], Ad[1][1]-Bd[1]*Cd[1] } };
 
  internal::roots2poly(Tmp, coeffs_out.b1, coeffs_out.b2);
 
  coeffs_out.b0 = Dd;
  coeffs_out.b1 += (Dd-one)*coeffs_out.a1;
  coeffs_out.b2 += (Dd-one)*coeffs_out.a2;
 
  return coeffs_out;
}
 
}  // namespace apf
 
#endif