LinearSystems.RationalSubstitution Method (TVec, TVec, TSample, TVec, TVec)

Zeroes of the original polynomial are stored in z and poles in p vector.

public RationalSubstitution(TVec z, TVec p, ref double k, TVec Nz, TVec Dz);

Remarks

Nz is the nominator and Dz is the denominator of the polynom to substitude the variable with in the original polynomial. The function returns modified z and p. Nz and Dz must have the same length. k is the gain factor (not modified).

C# Example

Substitute the variable:

    z^2 - 2*z + 1                z - 1
  ------------------   , z -- >  -----
    z^2- 4*z  + 1                z - 2

   The resulting polynomial:

         -0.5
  ------------------
   z^2 - 3*z  + 1.5

  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 num = new Vector(0);
     Vector den = new Vector(0);
     Vector den1 = new Vector(0);
     Vector num1 = new Vector(0);

     num.SetIt(false,new double[3] {1,-2, 1});
     den.SetIt(false,new double[3] {1,-4, 1});

     num1.SetIt(false,new double[2] {1,-1});
     den1.SetIt(false,new double[2] {1,-2});

     LinearSystems.RationalSubstitution(num,den,num1,den1);
     MtxVecEdit.ViewValues(num,"Num",true);
     MtxVecEdit.ViewValues(den,"Den",true);

  //          num = [ 0, 0, -0.5]
  //          den = [ 1,-3,  1.5]
  }