LinearSystems.TransferFunToZeroPole Method

procedure TransferFunToZeroPole(const z: TVec; const p: TVec; out k: Double; const Num: TVec; const Den: TVec);

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

#	Name	Type
1	z	TVec
2	p	TVec
3	k	Double
4	Num	TVec
5	Den	TVec

Result: stored in self (calling object)

Remarks:

Convert a transfer function defined with numerator Num and denominator Den in to its zero-pole form with zeros Z, poles P and gain K. The routine calls PolyRoots routine from the Polynoms unit. Numerator and denominator can be real or complex.

A rational polynomial can be converted to zero pole form by finding the roots of the numerator and denominator: (x^2 - 7x + 12)/(x^2 - 3x + 2) Zero pole form:
((x-3)(x-4))/((y-2)(y-1))

Examples

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

procedure TForm1.Button1Click(Sender: TObject);
var z,p,num,den: Vector;
k: Double;
begin
    num.SetIt(false,[1,-7,12]);
    den.SetIt(false,[1,-3, 2]);
    TransferFunToZeroPole(z,p,k,num,den);
    ViewValues(z);
    ViewValues(p);
    //        z = [4 , 3]
    //        p = [2 , 1]
    //        k = num[0]/den[0] =  1;
end;