ZeroPoleToTransferFun Routine

Summary

Convert transfer function from zero-pole to numerator-denominator form.

Declaration

Procedure ZeroPoleToTransferFun(num, den: TVec; z, p: TVec; k: TSample);

Description

Convert a rational polynomial defined with zeros Z and poles P and gain K in to its numerator Num and denominator Den form. The numerator will be scaled by K and both polynomials are assumed to have only real coefficents. (Poles and zeros can still be complex, if they have complex conjugated pairs.)


             num(s)      (s-sz1)*...*(s-szn)
     H(s) = -------- = K*-------------------
             den(s)      (s-sp1)*...*(s-spn)

szn - n'th zero
spn - n'th pole
K - gain of the system

See Also
ZeroPoleToStateSpace
StateSpaceToTransferFun
StateSpaceToZeroPole
TransferFunToZeroPole

Example 1

The following example computes the coefficients of the rational polynomial. The numerator has zeros at 3 and 4 and the denominator has zeros at 1 and 2. The polynomial in zero pole form can be written as:


 (x - 3)*(x - 4)
 ---------------
 (y - 2)*(y - 1)

And in transfer function form:


  x^2 - 7*x + 12
  --------------
  x^2 - 3*x + 2

Notice that powers are falling from left to right. Code example:


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

    procedure TForm1.Button1Click(Sender: TObject);
      var z,p,num,den: Vector;
          k: TSample;
      begin
          z.SetIt(false,[3,4]);
          p.SetIt(false,[1,2]);
          k := 1;
          ZeroPoleToTransferFun(num,den,z,p,k);
          ViewValues(num);
          ViewValues(den);
    //        num = [1, -7,  12]
    //        den = [1, -3,   2]
    end;


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

    void __fastcall TForm41::BitBtn1Click(TObject *Sender)
    {
      Vector z,p,num,den;
      double k;

      z->Size(2);
      z[0] = 3;
      z[1] = 4;
      p->Size(2);
      p[0] = 1;
      p[1] = 2;
      k = 1;
      ZeroPoleToTransferFun(num,den,z,p,k);
      ViewValues(num);
      ViewValues(den);
      //        num = [1, -7,  12]
      //        den = [1, -3,   2]
    }


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

  private void button1_Click(object sender, EventArgs e)
  {
     Vector z = new Vector(0);
     Vector p = new Vector(0);
     Vector num = new Vector(0);
     Vector den = new Vector(0);
     double k;

     z.SetIt(false,new double[2] {3,4});
     p.SetIt(false,new double[2] {1,2});
     k = 1;
     LinearSystems.ZeroPoleToTransferFun(num,den,z,p,k);
     MtxVecEdit.ViewValues(num,"Numerator",true);
     MtxVecEdit.ViewValues(den,"Denominator",true);
//        num = [1, -7,  12]
//        den = [1, -3,   2]
  }