LinearSystems::LowpassToLowpass Function

LinearSystems Namespace

Overload List

#SignatureDescription
1void LowpassToLowpass(TVec *z, TVec *p, double &k, double Freq);Frequency transformation from a lowpass to a lowpass filter in s-domain.
2void LowpassToLowpass(TMtx *a, TVec *b, TVec *c, double &D, double Freq);Transform a lowpass filter prototype in state space form to a lowpass filter.

Overload 1: void LowpassToLowpass(TVec *z, TVec *p, double &k, double Freq);

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

#NameTypeDescription
1zTVec *
2pTVec *
3kdouble &
4Freqdouble
Remarks:

Transform a lowpass filter prototype in zero-pole form to a lowpass filter, where the new cutoff frequency is Freq. Assumed sampling frequency is 2. The transformation is defined as ([1], p. 258): s -> s/W_u

Wu - new cutoff frequency

References:

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

Examples
#include "MtxExpr.h"
#include "Units.IIrFilters.h"
#include "Units.LinearSystems.h"
#include "Units.SignalUtils.h"

using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Signal;
using namespace Dew::Signal::Units::IIRFilters;
using namespace Dew::Signal::Units::LinearSystems;
using namespace Dew::Signal::Units::SignalUtils;

void Example()
{
    Vector z, p, num, den, FreqFr, Response;
    int Order;
    double k, Wc, BW;

    Order = 5; //design a fifth order filter.
    EllipticAnalog(Order, 0.2, 40, z, p, k);  //design analog protype
    Wc = 0.7;
    LowpassToLowpass(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
}
Declared in Dew::Signal::Units::LinearSystems · Dew.Signal/Units.LinearSystems.h · Cross-compiler

Overload 2: void LowpassToLowpass(TMtx *a, TVec *b, TVec *c, double &D, double Freq);

Transform a lowpass filter prototype in state space form to a lowpass filter.

#NameTypeDescription
1aTMtx *
2bTVec *
3cTVec *
4Ddouble &
5Freqdouble
Examples
#include "MtxExpr.h"
#include "Units.IIrFilters.h"
#include "Units.LinearSystems.h"
#include "Units.SignalUtils.h"

using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Signal;
using namespace Dew::Signal::Units::IIRFilters;
using namespace Dew::Signal::Units::LinearSystems;
using namespace Dew::Signal::Units::SignalUtils;

void Example()
{
    Vector z(0);
    Vector p(0);
    Vector num(0);
    Vector den(0);
    Vector Response(0);
    Vector FreqFr(0);
    double k, Wc, BW;
    double FS = 2;
    int Order = 5; //design a fifth order filter.

    EllipticAnalog(Order, 0.2, 40, z, p, k);  //design analog protype
    Wc = 0.7;
    LowpassToLowpass(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, 0); //Laplace
}
See Also: LinearSystems::LowpassToBandstop, LinearSystems::LowpassToBandpass, LinearSystems::LowpassToLowpassZ, LinearSystems::LowpassToBandpassZ, LinearSystems::LowpassToBandstopZ, LinearSystems::LowpassToHighpassZ
Declared in Dew::Signal::Units::LinearSystems · Dew.Signal/Units.LinearSystems.h · Cross-compiler