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

The function returns modified z (zeros), p (poles) and k (gain).

public LowpassToHighpassZ(TVec z, TVec p, ref double k, double Freq, double PrototypeFreq);

C# Example

Elliptic highpass filter design. The cutoff frequency of a lowpass analog filter prototype transformed in to z domain is obtained with BilinearUnwarp method. The analog prototype filter has a normalized cutoff frequency at 1 rad/sec.

  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);
    Vector Response = new Vector(0);
    double k, Wc;
    double FS = 2;
    int Order = 4; //design a fifth order filter.

    IIRFilters.EllipticAnalog(Order,0.1,30, z, p, out k);  //design analog protype
    LinearSystems.Bilinear(z, p, ref k, FS,true);
    Wc = 0.5;
    LinearSystems.LowpassToHighpassZ(z, p, ref k, Wc, LinearSystems.BilinearUnwarp(1,FS));
    LinearSystems.ZeroPoleToTransferFun(num,den, z, p, k);
    SignalUtils.FrequencyResponse(num, den, Response, 64, false, TSignalWindowType.wtRectangular, 0); //zero padding set to 64

//Alternative:
//            ...
//            LinearSystems.ZeroPoleToTransferFun(num,den, z, p, k);
//            LinearSystems.LowpassToHighpassZ(num,den, Wc, LinearSystems.BilinearUnwarp(1,FS));

    TeeChart.DrawIt(Response, "Frequency response", false);
    //TeeChart.DrawIt(20 * MtxExpr.Log10(MtxExpr.Abs(Response)), "Magnitude", false);
    //TeeChart.DrawIt(MtxExpr.PhaseSpectrum(Response) * (180 / Math.PI), "Phase", false);
  }