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LinearSystems.ZeroPoleToTransferFun Function
LinearSystems | Functions | Example | See Also
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Convert transfer function from zero-pole to numerator-denominator form.

Pascal
procedure ZeroPoleToTransferFun(const num: TVec; const den: TVec; const z: TVec; const p: TVec; k: Double);
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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 - system gain
See Also
Example

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. 

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

    procedure TForm1.Button1Click(Sender: TObject);
      var z,p,num,den: Vector;
          k: Double;
      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 "MtxExpr.hpp"
    #include "MtxVecEdit.hpp"
    #include "MtxVecTee.hpp"
    #include "SignalUtils.hpp"
    #include "LinearSystems.hpp"

    void __fastcall TForm41::BitBtn1Click(TObject *Sender)
    {
      sVector 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]
    }
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