Example 1

- frequency of the sine falls exactly on the spectral bin (ideal case)
- frequency of the sine is not alligned with the frequency spectrum grid.

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


    procedure TForm1.Button1Click(Sender: TObject);
    var h,h1,Re,Im: Vector;
    begin
          h := Sin(Ramp(256,0,2*Pi*6/256));
          SignalUtils.Hilbert(h);
          h.CplxToReal(Re,Im);
          DrawIt([Re,Im],['Real','Imag'],'Integer frequency');
          h1.SetIt(false,[Re.DotProd(Im)]);
          ViewValues(h1,'Dot product between Re and Im',True);

          h := Sin(Ramp(256,0,2*Pi*6.5/256));
          SignalUtils.Hilbert(h);
          h.CplxToReal(Re,Im);
          DrawIt([Re,Im],['Real','Imag'],'Non-integer frequency');
          h1.SetIt(false,[Re.DotProd(Im)]);
          ViewValues(h1,'Dot product between Re and Im',True);

          h := Sin(Ramp(256,0,2*Pi*6.5/256));
          Re.Copy(h);
          Im.Copy(h);
          KaiserImpulse(h1,[0.95,1],0.01,ftHilbertIII);
    //Or use remez:    RemezImpulse(h1,[0.05,0.95],0.01,ftHilbertIII);
          FirFilter(Im,h1);  //also compensates for integer filter delay (if filter is Odd length (type III))
          DrawIt([Re,Im],['Real ','Imag'],'With FIR filter');
          h1.SetIt(false,[Re.DotProd(Im)]);  //dot product between Re and Im should be zero
          ViewValues(h1,'Dot product between Re and Im',True);
    end;

    #include "MtxVecCPP.h"  //MtxVecCPP.cpp must be included in the project
    #include "MtxVecEdit.hpp"
    #include "MtxVecTee.hpp"
    #include "SignalUtils.hpp"

    void __fastcall TForm1::BitBtn1Click(TObject *Sender)
    {
      	Vector h,h1, Re, Im;

        h = Sin(Ramp(256,0,2*PI*6/256));
        Signalutils::Hilbert(h);
        h->CplxToReal(Re,Im);
        DrawIt(OPENARRAY(TVec*,(Re, Im)), OPENARRAY(AnsiString,("Real","Imag")),"Integer frequency");
        h1->SetIt(false,OPENARRAY(double,(Re->DotProd(Im))) );
        ViewValues(h1,"Dot product between Re and Im",True);

        h = Sin(Ramp(256,0,2*PI*6.5/256));
        Signalutils::Hilbert(h);
        h->CplxToReal(Re,Im);
        DrawIt(OPENARRAY(TVec*,(Re,Im)), OPENARRAY(AnsiString,("Real","Imag")),"Non-Integer frequency");
        h1->SetIt(false,OPENARRAY(double,(Re->DotProd(Im))));
        ViewValues(h1,"Dot product between Re and Im",True);

        h = Sin(Ramp(256,0,2*PI*6.5/256));
        Re->Copy(h);
        Im->Copy(h);
        KaiserImpulse(h1,OPENARRAY(double,(0.95,1)),0.01,ftHilbertIII);
        //Or use remez:    RemezImpulse(h1,OPENARRAY(double,(0.05,0.95)),0.01,ftHilbertIII);
        FirFilter(Im,h1);  //also compensates for integer filter delay (if filter is Odd length (type III))
        DrawIt(OPENARRAY(TVec*,(Re,Im)), OPENARRAY(AnsiString,("Real","Imag")),"FIR Filter");
        h1->SetIt(false,OPENARRAY(double,(Re->DotProd(Im))));  //dot product between Re and Im should be zero
        ViewValues(h1,"Dot product between Re and Im",True);
    }

    using Dew.Math;
    using Dew.Math.Units;
    using Dew.Signal;
    using Dew.Signal.Units;
    using Dew.Math.Tee;
    using Dew.Math.Editors;
    using Dew.Signal.Tee;

    private void button1_Click(object sender, EventArgs e)
    {
        Vector h = MtxExpr.Sin(MtxExpr.Ramp(256, 0, 2 * Math387.PI * 6/256));
        Vector Re = new Vector(0);
        Vector Im = new Vector(0);
        Vector h1 = new Vector(0);

        SignalUtils.Hilbert(h);
        h.CplxToReal(Re, Im);
        TeeChart.DrawIt(new TVec[2] {Re,Im}, new string[2] {"Real","Imag"} ,"Integer frequency",false);
        h1.SetIt(false,new double[1] {Re.DotProd(Im)});
        MtxVecEdit.ViewValues(h1,"Dot product between Re and Im",true);

        h = MtxExpr.Sin(MtxExpr.Ramp(256, 0, 2 * Math387.PI * 6.5/256));
        SignalUtils.Hilbert(h);
        h.CplxToReal(Re, Im);
        TeeChart.DrawIt(new TVec[2] {Re,Im}, new string[2] {"Real","Imag"} ,"Non-integer frequency",false);
        h1.SetIt(false,new double[1] {Re.DotProd(Im)});
        MtxVecEdit.ViewValues(h1,"Dot product between Re and Im",true);

        h = MtxExpr.Sin(MtxExpr.Ramp(256, 0, 2 * Math387.PI * 6.5/256));
        Re.Copy(h);
        Im.Copy(h);
        SignalUtils.KaiserImpulse(h1,new double[2] {0.95,1}, 0.01, TFilterType.ftHilbertIII,1,2,true);
   //Or use remez:    OptimalFIR.RemezImpulse(h1,new double[2] {0.05,0.95}, 0.01, TFilterType.ftHilbertIII);
        SignalUtils.FirFilter(Im,h1,1,1);  //also compensates for integer filter delay (if filter is Odd length (type III))
        TeeChart.DrawIt(new TVec[2] {Re,Im}, new string[2] {"Real","Imag"} ,"With FIR Filter",false);
        h1.SetIt(false,new double[1] {Re.DotProd(Im)});  //dot product between Re and Im should be zero
        MtxVecEdit.ViewValues(h1, "Dot product between Re and Im", true);
    }