LinearSystems.LowpassToBandpass Method

Overload List

#	Signature	Description
1	procedure LowpassToBandpass(const a: TMtx; const b: TVec; const c: TVec; var D: Double; CenterFreq: Double; BW: Double);	Convert a lowpass filter prototype in state space form to a bandstop filter.
2	procedure LowpassToBandpass(const z: TVec; const p: TVec; var k: Double; CenterFreq: Double; BW: Double);	Frequency transformation from a lowpass to a bandpass filter in s-domain.

Overload 1: procedure LowpassToBandpass(const a: TMtx; const b: TVec; const c: TVec; var D: Double; CenterFreq: Double; BW: Double);

Convert a lowpass filter prototype in state space form to a bandstop filter.

#	Name	Type	Description
1	a	TMtx
2	b	TVec
3	c	TVec
4	D	Double
5	CenterFreq	Double	scalar
6	BW	Double	scalar

Result: stored in self (calling object)

Overload 2: procedure LowpassToBandpass(const z: TVec; const p: TVec; var k: Double; CenterFreq: Double; BW: Double);

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

#	Name	Type	Description
1	z	TVec
2	p	TVec
3	k	Double
4	CenterFreq	Double	scalar
5	BW	Double	scalar

Result: stored in self (calling object)

Remarks:

Transform a lowpass filter prototype in zero-pole form to bandpass filter, where the passband of width BW is centered around the frequency CenterFreq. Assumed sampling frequency is 2. The transformation is defined as ([1], p. 258): s -> (s^2 + W_u W_l)/(s (W_u - W_l))

Wl - lower cutoff frequency
Wu - upper 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 lowpass filter.

References:

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

Examples

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

procedure TForm1.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,0.2,40,z,p,k);  //design analog protype
    Wc := Sqrt(0.2*0.6);
    BW := 0.6-0.2;
    LowpassToBandpass(z,p,k,Wc,BW);  //frequency transformation in s-domain
    ZeroPoleToTransferFun(num,den,z,p,k);
    //Define the frequency grid (logarithmic)
    FreqFr.Length := 1000;
    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;