Example

A sample lowpass filter design with sampling frequency 8000Hz, transition band between at 1500Hz and 2000Hz with 60 dB attenuation (20 * Log10(0.001)) and 0.001 ripple in the passband. To try out other setups comment out the lowpass and comment in the desired filter.

  uses MtxExpr, Math387, MtxVec, SignalUtils, MtxVecTee, MtxVecEdit, OptimalFIR;

  procedure TForm1.Button1Click(Sender: TObject);
  var z,Response,Weights: Vector;
      n: integer;
      err: Double;
  begin
        n := RemezLength([0, 1500, 2000, 4000], [1, 0], [0.001, 0.001],Weights, 8000);
        z.Size(n);
        Remez(z,[0, 1500, 2000, 4000], [1, 0], TDoubleArray(Weights), rmtBandpass,err,8000);

  //Design a highpass
  //      n := RemezLength([0, 1500, 2000, 4000], [0, 1], [0.001, 0.001],Weights, 8000);
  //      z.Size(n);
  //      Remez(z,[0, 1500, 2000, 4000], [0, 1], TDoubleArray(Weights), rmtBandpass,err,8000);

  //Design a bandpass (Sampling frequency = 2)
  //      n := RemezLength([0, 0.15, 0.25, 0.45, 0.55, 1], [0, 1, 0], [0.001, 0.001, 0.001],Weights);
  //      z.Size(n);
  //      Remez(z,[0, 0.15, 0.25, 0.45, 0.55, 1], [0, 1, 0], TDoubleArray(Weights), rmtBandpass, err);

  //Design a bandstop (Sampling frequency = 2)
  //      n := RemezLength([0, 0.15, 0.25, 0.45, 0.55, 1], [1, 0, 1], [0.001, 0.001, 0.001],Weights);
  //      z.Size(n);
  //      Remez(z,[0, 0.15, 0.25, 0.45, 0.55, 1], [1, 0, 1], TDoubleArray(Weights), rmtBandpass, err);

  //Design a multiband (Sampling frequency = 2)
  //      n := RemezLength([0.00, 0.10, 0.20, 0.30, 0.40,
  //                        0.45, 0.55, 0.60, 0.70, 1.00], [1, 0, 1, 0, 1], [0.001, 0.001, 0.001, 0.001, 0.001],Weights);
  //      z.Size(n);
  //      Remez(z,[0.00, 0.10, 0.20, 0.30, 0.40,
  //                      0.45, 0.55, 0.60, 0.70, 1.00], [1, 0, 1, 0, 1], TDoubleArray(Weights), rmtBandpass, err);

  //Design a hilbert (type III) transformer  (Sampling frequency = 2)
  //        n := RemezLength([0, 0, 0.1, 0.9, 1, 1], [0,1,0], [0.01,0.01,0.01],Weights);
  //        if not Odd(n) then Inc(n); //odd length type III filter
  //        z.Size(n);
  //        Remez(z,[0.1, 0.9], [1], [1], rmtHilbert,err);

  //Design a hilbert (type IV) transformer  (Sampling frequency = 2)
  //        n := RemezLength([0, 0, 0.1, 0.9, 1, 1], [0,1,0], [0.01,0.01,0.01],Weights);
  //        if Odd(n) then Inc(n); //even length type IV filter
  //        z.Size(n);
  //        Remez(z,[0.1, 1], [1], [1], rmtHilbert,err);

  //Design a differentiator (type III) (Sampling frequency = 2)
  //        n := RemezLength([0, 0, 0.1, 0.9, 1, 1], [0,1,0], [0.01,0.01,0.01],Weights);
  //        if not Odd(n) then Inc(n); //odd length type III filter
  //        z.Size(n);
  //        Remez(z,[0.1, 0.9], [1], [1], rmtDifferentiator,err);

  h//Design a differentiator (type IV) (Sampling frequency = 2)
  //        n := RemezLength([0, 0, 0.1, 0.9, 1, 1], [0,1,0], [0.01,0.01,0.01],Weights);
  //        if Odd(n) then Inc(n); //even length type IV filter
  //        z.Size(n);
  //        Remez(z,[0.1, 1], [1], [1], rmtDifferentiator,err);

  //Design a double differentiator (Sampling frequency = 2)
  //        n := RemezLength([0, 0, 0.05, 0.95, 1, 1], [0,1,0], [0.01,0.01,0.01],Weights);
  //        if Odd(n) then Inc(n); //even length type IV filter
  //        z.Size(n);
  //        Remez(z,[0.05, 1], [1], [1], rmtDoubleDifferentiator,err);

  //Design an integrator (Sampling frequency = 2)
  //        n := RemezLength([0, 0, 0.05, 0.95, 1, 1], [0,1,0], [0.01,0.01,0.01],Weights);
  //        if Odd(n) then Inc(n); //even length type IV filter
  //        z.Size(n);
  //        Remez(z,[0.05, 1], [1], [1], rmtIntegrator,err);

  //Design a double integrator  (Sampling frequency = 2)
  //        n := RemezLength([0, 0, 0.05, 0.95, 1, 1], [0,1,0], [0.01,0.01,0.01],Weights);
  //        if Odd(n) then Inc(n); //even length type IV filter
  //        z.Size(n);
  //        Remez(z,[0.05, 1], [1], [1], rmtDoubleIntegrator,err);

        FrequencyResponse(z,nil,Response,8);
        DrawIt(Response);
  end;

  #include "MtxExpr.hpp"
  #include "MtxVecEdit.hpp"
  #include "MtxVecTee.hpp"
  #include "SignalUtils.hpp"
  #include "OptimalFIR.hpp"

  void __fastcall TForm1::BitBtn1Click(TObject *Sender)
  {
      sVector z, Response, Weights;
      int n;
      double err;

      n = RemezLength(OPENARRAY(double,(0, 1500, 2000, 4000)), OPENARRAY(double,(1, 0)), OPENARRAY(double,(0.001, 0.001)),Weights, 8000);
      z.Size(n);
      remez(z,OPENARRAY(double,(0, 1500, 2000, 4000)), OPENARRAY(double,(1, 0)), Weights.PValues1D(0), Weights.Length-1, rmtBandPass,err,8000);

    //Design a highpass
  //        n = RemezLength(OPENARRAY(double,(0, 1500, 2000, 4000)), OPENARRAY(double,(0, 1)), OPENARRAY(double,(0.001, 0.001)),Weights, 8000);
  //        z.Size(n);
  //        remez(z,OPENARRAY(double,(0, 1500, 2000, 4000)), OPENARRAY(double,(0, 1)), Weights.PValues1D(0), Weights.Length-1, rmtBandPass,err,8000);

    //Design a bandpass (Sampling frequency = 2)
  //        n = RemezLength(OPENARRAY(double,(0, 0.15, 0.25, 0.45, 0.55, 1)), OPENARRAY(double,(0, 1, 0)), OPENARRAY(double,(0.001, 0.001, 0.001)),Weights);
  //        z.Size(n);
  //        remez(z,OPENARRAY(double,(0, 0.15, 0.25, 0.45, 0.55, 1)), OPENARRAY(double,(0, 1, 0)), Weights.PValues1D(0), Weights.Length-1, rmtBandPass, err);

    //Design a bandstop (Sampling frequency = 2)
  //        n = RemezLength(OPENARRAY(double,(0, 0.15, 0.25, 0.45, 0.55, 1)), OPENARRAY(double,(1, 0, 1)), OPENARRAY(double,(0.001, 0.001, 0.001)),Weights);
  //        z.Size(n);
  //        remez(z,OPENARRAY(double,(0, 0.15, 0.25, 0.45, 0.55, 1)), OPENARRAY(double,(1, 0, 1)), Weights.PValues1D(0), Weights.Length-1, rmtBandPass, err);

    //Design a multiband (Sampling frequency = 2)
  //        n = RemezLength(OPENARRAY(double,(0.00, 0.10, 0.20, 0.30, 0.40, 0.45, 0.55, 0.60, 0.70, 1.00)),
  //                              OPENARRAY(double,(1, 0, 1, 0, 1)), OPENARRAY(double,(0.001, 0.001, 0.001, 0.001, 0.001)),Weights);
  //        z.Size(n);
  //        remez(z,OPENARRAY(double,(0.00, 0.10, 0.20, 0.30, 0.40, 0.45, 0.55, 0.60, 0.70, 1.00)),
  //                    OPENARRAY(double,(1, 0, 1, 0, 1)), Weights.PValues1D(0), Weights.Length-1, rmtBandPass, err);

    //Design a hilbert (type III) transformer  (Sampling frequency = 2)
  //          n = RemezLength(OPENARRAY(double,(0, 0, 0.1, 0.9, 1, 1)), OPENARRAY(double,(0,1,0)), OPENARRAY(double,(0.01,0.01,0.01)),Weights);
  //          if ((n%2) == 0) n++; //odd length type III filter
  //          z.Size(n);
  //          remez(z,OPENARRAY(double,(0.1, 0.9)), OPENARRAY(double,(1)), OPENARRAY(double,(1)), rmtHilbert,err);

    //Design a hilbert (type IV) transformer  (Sampling frequency = 2)
  //          n = RemezLength(OPENARRAY(double,(0, 0, 0.1, 0.9, 1, 1)), OPENARRAY(double,(0,1,0)), OPENARRAY(double,(0.01,0.01,0.01)),Weights);
  //          if (!((n%2) == 0)) n++; //odd length type IV filter
  //          z.Size(n);
  //          remez(z,OPENARRAY(double,(0.1, 1)), OPENARRAY(double,(1)), OPENARRAY(double,(1)), rmtHilbert,err);

    //Design a differentiator (type III) (Sampling frequency = 2)
  //          n = RemezLength(OPENARRAY(double,(0, 0, 0.1, 0.9, 1, 1)), OPENARRAY(double,(0,1,0)), OPENARRAY(double,(0.01,0.01,0.01)),Weights);
  //          if ((n%2) == 0) n++; //odd length type III filter
  //          z.Size(n);
  //          remez(z,OPENARRAY(double,(0.1, 0.9)), OPENARRAY(double,(1)), OPENARRAY(double,(1)), rmtDifferentiator,err);

    //Design a differentiator (type IV) (Sampling frequency = 2)
  //          n = RemezLength(OPENARRAY(double,(0, 0, 0.1, 0.9, 1, 1)), OPENARRAY(double,(0,1,0)), OPENARRAY(double,(0.01,0.01,0.01)),Weights);
  //          if (!((n%2) == 0)) n++; //even length type IV filter
  //          z.Size(n);
  //          remez(z,OPENARRAY(double,(0.1, 1)), OPENARRAY(double,(1)), OPENARRAY(double,(1)), rmtDifferentiator,err);

    //Design a double differentiator (Sampling frequency = 2)
  //          n = RemezLength(OPENARRAY(double,(0, 0, 0.05, 0.95, 1, 1)), OPENARRAY(double,(0,1,0)), OPENARRAY(double,(0.01,0.01,0.01)),Weights);
  //          if (!((n%2) == 0)) n++; //even length type IV filter
  //          z.Size(n);
  //          remez(z,OPENARRAY(double,(0.05, 1)), OPENARRAY(double,(1)), OPENARRAY(double,(1)), rmtDoubleDifferentiator,err);

  //  Design an integrator (Sampling frequency = 2)
  //          n = RemezLength(OPENARRAY(double,(0, 0, 0.05, 0.95, 1, 1)), OPENARRAY(double,(0,1,0)), OPENARRAY(double,(0.01,0.01,0.01)),Weights);
  //          if (!((n%2) == 0)) n++; //even length type IV filter
  //          z.Size(n);
  //          remez(z,OPENARRAY(double,(0.05, 1)), OPENARRAY(double,(1)), OPENARRAY(double,(1)), rmtIntegrator,err);

    //Design a double integrator  (Sampling frequency = 2)
  //          n = RemezLength(OPENARRAY(double,(0, 0, 0.05, 0.95, 1, 1)), OPENARRAY(double,(0,1,0)), OPENARRAY(double,(0.01,0.01,0.01)),Weights);
  //          if (!((n%2) == 0)) n++; //even length type IV filter
  //          z.Size(n);
  //          remez(z,OPENARRAY(double,(0.05, 1)), OPENARRAY(double,(1)), OPENARRAY(double,(1)), rmtDoubleIntegrator,err);

      FrequencyResponse(z,NULL,Response,8);
      DrawIt(Response);

  }