Design Chebyshev type I IIR filter.
The resulting transfer function is returned in the numerator/denumerator form with num and den.
The resulting transfer function is returned in the state-space form with A,B,C,D variables.
Example 1
Design an analog bandpass filter with transition band between 1..2 and 5..7 rad/sec and with at least 50dB attenuation in the stopband and. The passband should not have more then 0.2dB ripple. uses MtxExpr, Math387, MtxVec, SignalUtils, MtxVecTee, MtxVecEdit, IirFilters,
LinearSystems;
{$R *.dfm}
procedure TForm42.Button1Click(Sender: TObject);
var z,p, num,den, FreqFr,Response: Vector;
Order: integer;
k,Bw,Wc: TSample;
WcArray: TSampleArray; //modified 3dB frequency
begin
SetLength(WcArray,2);
Order := ChebyshevIIOrder([1,2,5,7],0.2,50,ftBandpass,WcArray,True);
ChebyshevIFilter(Order,0.2,WcArray,ftBandPass,true,num,den);
FreqFr.Length := 1000; //Define the frequency grid (logarithmic)
LogRamp(FreqFr,-1,1); //between 0.1 (=10^(-1)) and 10 (=10^1) rad/sec
FrequencyResponseS(num,den,FreqFr,Response); //Laplace
DrawIt(Response); //Y axis linear, X axis logarithmic;
//Alternative: Design a digital filter with the passband between 0.2 and 0.5 Hz (FS =2)
// SetLength(WcArray,2);
// Order := ChebyshevIOrder([0.1,0.2,0.5,0.6],0.2,50,ftBandPass,WcArray,false);
// ChebyshevIFilter(Order,0.2,WcArray,ftBandPass,false,num,den);
// FrequencyResponse(num,den,Response,64);
// FreqFr.Size(Response.Length);
// FreqFr.Ramp(0,1/FreqFr.Length);
// DrawIt(FreqFr,Response);
end;
#include "MtxVecCPP.h" //MtxVecCPP.cpp must be included in the project
#include "MtxVecEdit.hpp"
#include "MtxVecTee.hpp"
#include "SignalUtils.hpp"
#include "IirFilters.hpp"
#include "LinearSystems.hpp"
void __fastcall TForm1::BitBtn1Click(TObject *Sender)
{
Vector z,p, num, den, FreqFr, Response, WcArray;
int Order;
double k,Wc,Bw;
WcArray->Size(2);
Order = ChebyshevIIOrder(OPENARRAY(double,(1,2,5,7)),0.2,50,ftBandPass,WcArray->PValues1D(0),WcArray->Length-1,true);
ChebyshevIFilter(Order,0.2,WcArray->PValues1D(0),WcArray->Length-1,ftBandPass,true,num,den);
FreqFr->Length = 1000; //Define the frequency grid (logarithmic)
LogRamp(FreqFr,-1,1); //between 0.1 (=10^(-1)) and 10 (=10^1) rad/sec
FrequencyResponseS(num,den,FreqFr,Response); //Laplace
DrawIt(Response); //Y axis linear, X axis logarithmic;
//Alternative: Design a digital filter with the passband between 0.2 and 0.5 Hz (FS =2)
// WcArray->Size(2);
// Order = ChebyshevIOrder(OPENARRAY(double,(0.1,0.2,0.5,0.6)),0.2,50,ftBandPass,WcArray->PValues1D(0),WcArray->Length-1,false);
// ChebyshevIFilter(Order,0.2,WcArray->PValues1D(0),WcArray->Length-1,ftBandPass,false,num,den);
// FrequencyResponse(num,den,Response,64);
// FreqFr = Ramp(Response->Length,0,1.0/Response->Length);
// DrawIt(FreqFr,Response,"Frequency response",false);
}
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 Response = new Vector(0);
Vector FreqFr = new Vector(0);
double[] WcArray= new double[2];
//design analog filter
int Order = IIRFilters.ChebyshevIIOrder(new double[4] { 1, 2, 5, 7 }, 0.2, 50, TFilterType.ftBandPass, ref WcArray, true);
IIRFilters.ChebyshevIIFilter(Order, 50, WcArray, TFilterType.ftBandPass, true, num,den, TIirFrequencyTransform.ftStateSpaceAnalog); //design analog protype
FreqFr.Length = 1000;
SignalUtils.LogRamp(FreqFr, -1, 1);
SignalUtils.FrequencyResponseS(num, den, FreqFr, Response, 0);
TeeChart.DrawIt(Response, "Frequency response", false);
//Alternative: Design a digital filter with the passband between 0.2 and 0.5 Hz (FS =2)
Order = IIRFilters.ChebyshevIOrder(new double[4] { 0.1, 0.2, 0.5, 0.6 }, 0.2, 50, TFilterType.ftBandPass, ref WcArray, false);
IIRFilters.ChebyshevIFilter(Order, 0.2, WcArray, TFilterType.ftBandPass, false, num, den, TIirFrequencyTransform.ftStateSpaceAnalog); //design analog protype
FreqFr = MtxExpr.Ramp(Response.Length, 0, 1.0 / FreqFr.Length);
TeeChart.DrawIt(Response, "Frequency response", false);
}
Declaration
Function ChebyshevIFilter(Order: integer; PassRipple: TSample; const CutoffFreq: array of TSample; FilterType: TFilterType; Analog: boolean; z, p: TVec; out k: TSample; IirFrequencyTransform: TIirFrequencyTransform = ftStateSpaceAnalog): TSample;
Description
Design Chebyshev type I filter of Order with CutoffFreq frequencies and of FilterType type. Set Analog to True, to request and analog filter design in s-plane or set it to false to obtain a digital filter design in z-plane. PassRipple defines the passband ripple in dB. The CutoffFreq must be in range between 0 and 1 (Sampling frequency = 2) in case of a digital filter design. IIrFrequencyTransform specifies when and how will the frequency band transformation be applied. The resulting transfer function is returned in the zero-pole form, with z,p,k variables.