text: /*******************************************************************************
  
  "A Collection of Useful C++ Classes for Digital Signal Processing"
   By Vincent Falco
  
  Official project location:
  http://code.google.com/p/dspfilterscpp/
  
  See Documentation.cpp for contact information, notes, and bibliography.
  
  --------------------------------------------------------------------------------
  
  License: MIT License (http://www.opensource.org/licenses/mit-license.php)
  Copyright (c) 2009 by Vincent Falco
  
  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.
  
  *******************************************************************************/
  
  #ifndef DSPFILTERS_LEGENDRE_H
  #define DSPFILTERS_LEGENDRE_H
  
  #include "DspFilters/Common.h"
  #include "DspFilters/Cascade.h"
  #include "DspFilters/Design.h"
  #include "DspFilters/Filter.h"
  #include "DspFilters/PoleFilter.h"
  #include "DspFilters/RootFinder.h"
  
  namespace Dsp {
  
  /*
   * Filters with Legendre / "Optimum-L" response characteristics
   *
   */
  
  namespace Legendre {
  
  // Numerical computation of Legendre "Optimum-L" polynomials
  
  class PolynomialFinderBase
  {
  public:
    void solve (int n);
  
    double* coef()
    {
      return m_w;
    }
  
  private:
    void legendre (double* p, int n);
  
  protected:
    int m_maxN;
    double* m_w;
    double* m_a;
    double* m_p;
    double* m_s;
    double* m_v;
    double* m_aa;
    double* m_bb;
  };
  
  template <int maxN>
  class PolynomialFinder : public PolynomialFinderBase
  {
  public:
    PolynomialFinder ()
    {
      m_maxN = maxN;
      m_w = m_ws;
      m_a = m_as;
      m_p = m_ps;
      m_s = m_ss;
      m_v = m_vs;
      m_aa = m_aas;
      m_bb = m_bbs;
    }
  
    void solve (int n)
    {
      assert (n <= maxN);
      PolynomialFinderBase::solve (n);
    }
  
  private:
    double m_ws  [2 * maxN + 1];
    double m_as  [    maxN + 1];
    double m_ps  [2 * maxN + 1];
    double m_ss  [2 * maxN + 1];
    double m_vs  [2 * maxN + 4];
    double m_aas [    maxN + 1];
    double m_bbs [    maxN + 1];
  };
  
  //------------------------------------------------------------------------------
  
  // A Workspace is necessary to construct the polynomial and find its roots
  
  struct WorkspaceBase
  {
    WorkspaceBase (PolynomialFinderBase* polyBase,
                   RootFinderBase* rootsBase)
                   : poly (*polyBase)
                   , roots (*rootsBase)
    {
    }
  
    PolynomialFinderBase& poly;
    RootFinderBase& roots;
  
  private:
    WorkspaceBase (WorkspaceBase&);
    WorkspaceBase& operator= (WorkspaceBase&);
  };
  
  template <int MaxOrder>
  struct Workspace : WorkspaceBase
  {
    Workspace ()
      : WorkspaceBase (&m_poly, &m_roots)
    {
    }
  
  private:
    PolynomialFinder <MaxOrder> m_poly;
    RootFinder <MaxOrder * 2> m_roots;
  };
  
  //------------------------------------------------------------------------------
  
  // Half-band analog prototypes (s-plane)
  
  class AnalogLowPass : public LayoutBase
  {
  public:
    AnalogLowPass ();
  
    void design (const int numPoles, WorkspaceBase* w);
  
  private:
    int m_numPoles;
  };
  
  //------------------------------------------------------------------------------
  
  // Factored implementations to reduce template instantiations
  
  struct LowPassBase : PoleFilterBase <AnalogLowPass>
  {
    void setup (int order,
                double sampleRate,
                double cutoffFrequency,
                WorkspaceBase* w);
  };
  
  struct HighPassBase : PoleFilterBase <AnalogLowPass>
  {
    void setup (int order,
                double sampleRate,
                double cutoffFrequency,
                WorkspaceBase* w);
  };
  
  struct BandPassBase : PoleFilterBase <AnalogLowPass>
  {
    void setup (int order,
                double sampleRate,
                double centerFrequency,
                double widthFrequency,
                WorkspaceBase* w);
  };
  
  struct BandStopBase : PoleFilterBase <AnalogLowPass>
  {
    void setup (int order,
                double sampleRate,
                double centerFrequency,
                double widthFrequency,
                WorkspaceBase* w);
  };
  
  //------------------------------------------------------------------------------
  
  //
  // Raw filters
  //
  
  template <int MaxOrder>
  struct LowPass : PoleFilter <LowPassBase, MaxOrder>
  {
    void setup (int order,
                double sampleRate,
                double cutoffFrequency)
    {
      Workspace <MaxOrder> w;
      LowPassBase::setup (order,
                          sampleRate,
                          cutoffFrequency,
                          &w);
    }
  };
  
  template <int MaxOrder>
  struct HighPass : PoleFilter <HighPassBase, MaxOrder>
  {
    void setup (int order,
                double sampleRate,
                double cutoffFrequency)
    {
      Workspace <MaxOrder> w;
      HighPassBase::setup (order,
                           sampleRate,
                           cutoffFrequency,
                           &w);
    }
  };
  
  template <int MaxOrder>
  struct BandPass : PoleFilter <BandPassBase, MaxOrder, MaxOrder*2>
  {
    void setup (int order,
                double sampleRate,
                double centerFrequency,
                double widthFrequency)
    {
      Workspace <MaxOrder> w;
      BandPassBase::setup (order,
                           sampleRate,
                           centerFrequency,
                           widthFrequency,
                           &w);
    }
  };
  
  template <int MaxOrder>
  struct BandStop : PoleFilter <BandStopBase, MaxOrder, MaxOrder*2>
  {
    void setup (int order,
                double sampleRate,
                double centerFrequency,
                double widthFrequency)
    {
      Workspace <MaxOrder> w;
      BandStopBase::setup (order,
                           sampleRate,
                           centerFrequency,
                           widthFrequency,
                           &w);
    }
  };
  
  //------------------------------------------------------------------------------
  
  //
  // Gui-friendly Design layer
  //
  
  namespace Design {
  
  struct TypeIBase : DesignBase
  {
    enum
    {
      NumParams = 3
    };
  
    static int getNumParams ()
    {
      return 3;
    }
  
    static const ParamInfo getParamInfo_2 ()
    {
      return ParamInfo::defaultCutoffFrequencyParam ();
    }
  };
  
  template <class FilterClass>
  struct TypeI : TypeIBase, FilterClass
  {
    void setParams (const Params& params)
    {
      FilterClass::setup (int(params[1]), params[0], params[2]);
    }
  };
  
  struct TypeIIBase : DesignBase
  {
    enum
    {
      NumParams = 4
    };
  
    static int getNumParams ()
    {
      return 4;
    }
  
    static const ParamInfo getParamInfo_2 ()
    {
      return ParamInfo::defaultCenterFrequencyParam ();
    }
  
    static const ParamInfo getParamInfo_3 ()
    {
      return ParamInfo::defaultBandwidthHzParam ();
    }
  };
  
  template <class FilterClass>
  struct TypeII : TypeIIBase, FilterClass
  {
    void setParams (const Params& params)
    {
      FilterClass::setup (int(params[1]), params[0], params[2], params[3]);
    }
  };
  
  // Factored kind and name
  
  struct LowPassDescription
  {
    static Kind getKind () { return kindLowPass; }
    static const char* getName() { return "Legendre Low Pass"; }
  };
  
  struct HighPassDescription
  {
    static Kind getKind () { return kindHighPass; }
    static const char* getName() { return "Legendre High Pass"; }
  };
  
  struct BandPassDescription
  {
    static Kind getKind () { return kindHighPass; }
    static const char* getName() { return "Legendre Band Pass"; }
  };
  
  struct BandStopDescription
  {
    static Kind getKind () { return kindHighPass; }
    static const char* getName() { return "Legendre Band Stop"; }
  };
  
  // This glues on the Order parameter
  template <int MaxOrder,
            template <class> class TypeClass,
            template <int> class FilterClass>
  struct OrderBase : TypeClass <FilterClass <MaxOrder> >
  {
    const ParamInfo getParamInfo_1 () const
    {
      return ParamInfo (idOrder, "Order", "Order",
                         1, MaxOrder, 2,
                         &ParamInfo::Int_toControlValue,
                         &ParamInfo::Int_toNativeValue,
                         &ParamInfo::Int_toString);
  
    }
  };
  
  //------------------------------------------------------------------------------
  
  //
  // Design filters
  //
  
  template <int MaxOrder>
  struct LowPass : OrderBase <MaxOrder, TypeI, Legendre::LowPass>,
                   LowPassDescription
  {
  };
  
  template <int MaxOrder>
  struct HighPass : OrderBase <MaxOrder, TypeI, Legendre::HighPass>,
                    HighPassDescription
  {
  };
  
  template <int MaxOrder>
  struct BandPass : OrderBase <MaxOrder, TypeII, Legendre::BandPass>,
                    BandPassDescription
  {
  };
  
  template <int MaxOrder>
  struct BandStop : OrderBase <MaxOrder, TypeII, Legendre::BandStop>,
                    BandStopDescription
  {
  };
  
  }
  
  }
  
  }
  
  #endif
  
  