DSP Master VCL
|
Design analog Butterworth type IIR prototype filter.
Design analog butterworth lowpass prototype filter of order Order. Place the resulting transfer function in zero-pole form in Z (zeros), P (poles) and K (gain). The cutoff frequency of the prototype filter is preset to 1 rad/sec.
The filter has all zeros in infinity. The transfer function is defined as ([1], p. 277):
k0
H(s) = -------------------------
(s - s[1])*...*(s - s[n])
The poles of the filter are located at
s[k] := Expj(Pi*(0.5+(2*k-1)/(2*n)));
n = order of filter
k = 1,...,n
k0 = gain
The magnitude response is down 3dB at the cutoff frequency.
References:
[1] Theory and application of digital signal processing, Lawrence R. Rabiner and Bernard Gold. Prentice-Hall, 1975.
Design an analog lowpass filter with cutoff frequency at 3 rad/sec.
uses MtxExpr, Math387, MtxVec, SignalUtils, MtxVecTee, MtxVecEdit, IirFilters, LinearSystems; 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. ButterAnalog(Order,z,p,k); //design analog protype Wc := 3; LowpassToLowpass(z,p,k,WC); //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;
#include "MtxExpr.hpp" #include "MtxVecEdit.hpp" #include "MtxVecTee.hpp" #include "SignalUtils.hpp" #include "IirFilters.hpp" #include "LinearSystems.hpp" void __fastcall TForm1::BitBtn1Click(TObject *Sender) { sVector z,p, num,den, FreqFr, Response; int Order; double k,Wc,BW; Order = 5; //design a fifth order filter. ButterAnalog(Order,z,p,k); //design analog protype Wc = 3; LowpassToLowpass(z,p,k,Wc); //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; }
Copyright (c) 1999-2024 by Dew Research. All rights reserved.
|
What do you think about this topic? Send feedback!
|