LinearSystems.ZeroPoleToTransferFun Method

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

Syntax

Visual Basic

public static void ZeroPoleToTransferFun([In] TVec Num, [In] TVec Den, [In] TVec z, [In] TVec p, double k);

Remarks

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

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.

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] }

Group

LinearSystems Methods

Links

LinearSystems Class, LinearSystems Members, Dew.Signal.Units Namespace, LinearSystems Methods, Example, See Also

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