LinearSystems.LowpassToHighpass Method

Overload List

#	Signature	Description
1	void LowpassToHighpass(TMtx A, TVec B, TVec C, ref Double D, Double Freq)	Transform a lowpass filter prototype in state space form to highpass filter.
2	void LowpassToHighpass(TVec z, TVec p, ref Double k, Double Freq)	Frequency transformation from a lowpass to a highpass filter in s-domain.

Overload 1: void LowpassToHighpass(TMtx A, TVec B, TVec C, ref Double D, Double Freq)

Transform a lowpass filter prototype in state space form to highpass filter.

#	Name	Type	Description
1	A	TMtx	source TMtx
2	B	TVec	source TVec
3	C	TVec	source TVec
4	D	Double (ref)	output
5	Freq	Double	scalar

Result: stored in self (calling object)

Examples

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);
    Vector FreqFr = new Vector(0);
    double k,Wc;
    double FS = 2;
    int Order = 5; //design a fifth order filter.

    IIRFilters.EllipticAnalog(Order,0.2,40,z,p,out k);  //design analog protype
    Wc = 0.2;
    LinearSystems.LowpassToHighpass(z,p,ref k,Wc);  //frequency transformation in s-domain
    LinearSystems.ZeroPoleToTransferFun(num,den,z,p,k);
    //Define the frequency grid (logarithmic)
        FreqFr.Length = 1000;
        SignalUtils.LogRamp(FreqFr,-1,1); //between 0.1 (=10^(-1)) and 10 (=10^1) rad/sec
        SignalUtils.FrequencyResponseS(num,den,FreqFr,Response,0); //Laplace
        MtxVecTee.DrawIt(Response,"Frequency response",false); //Y axis linear, X axis logarithmic
}

Overload 2: void LowpassToHighpass(TVec z, TVec p, ref Double k, Double Freq)

Frequency transformation from a lowpass to a highpass filter in s-domain.

#	Name	Type	Description
1	z	TVec	source TVec
2	p	TVec	source TVec
3	k	Double (ref)	output
4	Freq	Double	scalar

Result: stored in self (calling object)

Remarks:

Transform a lowpass filter prototype in zero-pole form to a highpass filter, where the new cutoff frequency is Freq. Assumed sampling frequency is 2. The transformation is defined as ([1], p. 258): s -> W_u/s

Wu - new cutoff frequency

The routine also adds zeros at 0. It adds one zero, if the lowpass filter order is odd and already has zeros. If the filter does not have zeros, it adds sufficient zeros at 0 to match the order of the filter.

References:

[1] Theory and application of digital signal processing, Lawrence R. Rabiner and Bernard Gold. Prentice-Hall, 1975