IIRFilters.EllipticAnalog Method

procedure EllipticAnalog(Order: Integer; PassRipple: Double; StopRipple: Double; z: TVec; p: TVec; out k: Double);

Design an analog elliptic (Cauer) lowpass prototype filter of order Order, equiripple in BOTH bands (PassRipple dB passband, StopRipple dB stopband), cutoff fixed at 1 rad/s. Returns zero-pole-gain with finite imaginary-axis zeros: |H(jomega)|^2=1/(1+varepsilon^2 R_n^2(omega,xi)), varepsilon=sqrt(10^(R_p/10)-1), where R_n is the Chebyshev rational (elliptic) function. For a given order the elliptic design gives the narrowest transition band of the five families. At the passband edge omega=1 the magnitude equals 10^(-R_p/20). Domain: 1 <= Order <= MaxIirOrder, PassRipple>0, StopRipple>PassRipple (dB). Poles satisfy Re(p_k)<0 (stable). z and p must share precision or an exception is raised.

#	Name	Type	Description
1	Order	Integer
2	PassRipple	Double	scalar
3	StopRipple	Double	scalar
4	z	TVec	source TVec
5	p	TVec	source TVec
6	k	Double

Result: stored in self (calling object)

Remarks:

Design analog elliptic prototype filter of order Order. Place the resulting transfer function in zero-pole form in Z (zeros), P (poles) and K (gain). PassRipple defines the ripple (dB) of the passband and StopRipple defines the ripple of the stopband (dB). The cutoff frequency of the prototype filter is preset to 1 rad/sec. For pole and zero specifications see [1] p. 187.

References:

[1] Digital Filter Design, T.W.Parks and C.S.Burrs, John Wiley and Sons, 1987.

Examples

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

procedure TForm42.Button1Click(Sender: TObject);
var z,p, num,den, FreqFr,Response: Vector;
Order: integer;
k,Wc,BW: double;
begin
    Order := 5; //design a fifth order filter.
    EllipticAnalog(Order,0.1,20,z,p,k);  //design analog protype
    Wc := Sqrt(1*3);
    BW := 3-1;
    LowpassToBandstop(z,p,k,Wc,BW);  //frequency transformation in s-domain
    ZeroPoleToTransferFun(num,den,z,p,k);
    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;
end;