Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure LowpassToHighpass(const A: TMtx; const B: TVec; const C: TVec; var D: Double; Freq: Double); | Transform a lowpass filter prototype in state space form to highpass filter. |
| 2 | procedure LowpassToHighpass(const z: TVec; const p: TVec; var k: Double; Freq: Double); | Frequency transformation from a lowpass to a highpass filter in s-domain. |
Overload 1: procedure LowpassToHighpass(const A: TMtx; const B: TVec; const C: TVec; var D: Double; Freq: Double);
Transform a lowpass filter prototype in state space form to highpass filter.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | A | TMtx | |
| 2 | B | TVec | |
| 3 | C | TVec | |
| 4 | D | Double | |
| 5 | Freq | Double | scalar |
Result: stored in self (calling object)
Overload 2: procedure LowpassToHighpass(const z: TVec; const p: TVec; var k: Double; Freq: Double);
Frequency transformation from a lowpass to a highpass filter in s-domain.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | z | TVec | |
| 2 | p | TVec | |
| 3 | k | Double | |
| 4 | Freq | Double | scalar |
Result: stored in self (calling object)
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
uses MtxExpr, Math387, MtxVec, MtxVecTee, MtxVecEdit,
LinearSystems, IirFilters, SignalUtils;
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,0.2,40,z,p,k); //design analog protype
Wc := 0.2;
LowpassToHighpass(z,p,k,WC); //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;