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BiQuad Class Reference
Public Member Functions

BiQuad Class Reference

BiQuad class implements a single filter. More...

#include <BiQuad.h>

Public Member Functions

 BiQuad ()
 Initialize a unity TF biquad.
 BiQuad (double b0, double b1, double b2, double a1, double a2)
 Initialize a normalized biquad filter.
 BiQuad (double b0, double b1, double b2, double a0, double a1, double a2)
 Initialize a biquad filter with all six coefficients.
void PIDF (double Kp, double Ki, double Kd, double N, double Ts)
 Initialize a PIDF biquad.
double step (double x)
 Execute one digital timestep and return the result...
std::vector< std::complex
< double > > 		poles ()
 Return poles of the BiQuad filter.
std::vector< std::complex
< double > > 		zeros ()
 Return zeros of the BiQuad filter.
bool stable ()
 Is this biquad stable? Checks if all poles lie within the unit-circle.
void setResetStateOnGainChange (bool v)
 Determines if the state variables are reset to zero on gain change.

Detailed Description

BiQuad class implements a single filter.

author: T.J.W. Lankhorst <t.j.w.lankhorst@student.utwente.nl>

Filters that - in the z domain - are the ratio of two quadratic functions. The general form is:

b0 + b1 z^-1 + b2 z^-2 H(z) = ---------------------- a0 + a1 z^-1 + a2 z^-2

Which is often normalized by dividing all coefficients by a0.

Example: 

 #include "mbed.h"
 #include <complex>

 // Example: 4th order Butterworth LP (w_c = 0.1*f_nyquist)
 BiQuad bq1( 4.16599e-04, 8.33198e-04, 4.16599e-04, -1.47967e+00, 5.55822e-01 );
 BiQuad bq2( 1.00000e+00, 2.00000e+00, 1.00000e+00, -1.70096e+00, 7.88500e-01 );

 BiQuadChain bqc;

 int main() {

    // Add the biquads to the chain
    bqc.add( &bq1 ).add( &bq2 );

    // Find the poles of the filter
    std::cout << "Filter poles" << std::endl;
    std::vector< std::complex<double> > poles = bqc.poles();
    for( size_t i = 0; i < poles.size(); i++ )
        std::cout << "\t"  << poles[i] << std::endl;

    // Find the zeros of the filter
    std::cout << "Filter zeros" << std::endl;
    std::vector< std::complex<double> > zeros = bqc.zeros();
    for( size_t i = 0; i < poles.size(); i++ )
        std::cout << "\t" << zeros[i] << std::endl;

    // Is the filter stable?
    std::cout << "This filter is " << (bqc.stable() ? "stable" : "instable") << std::endl;

    // Output the step-response of 20 samples
  std::cout << "Step response 20 samples" << std::endl;
  for( int i = 0; i < 20; i++ )
      std::cout << "\t" << bqc.step( 1.0 ) << std::endl;
 }

https://github.com/tomlankhorst/biquad

Definition at line 62 of file BiQuad.h.

Constructor & Destructor Documentation

BiQuad (  )

Initialize a unity TF biquad.

Returns:
BiQuad instance

Definition at line 3 of file BiQuad.cpp.

BiQuad ( double  b0,
double  b1,
double  b2,
double  a1,
double  a2 
)

Initialize a normalized biquad filter.

Parameters:
b0
b1
b2
a1
a2
Returns:
BiQuad instance

Definition at line 8 of file BiQuad.cpp.

BiQuad ( double  b0,
double  b1,
double  b2,
double  a0,
double  a1,
double  a2 
)

Initialize a biquad filter with all six coefficients.

Parameters:
b0
b1
b2
a0
a1
a2
Returns:
BiQuad instance

Definition at line 13 of file BiQuad.cpp.

Member Function Documentation

void PIDF ( double  Kp,
double  Ki,
double  Kd,
double  N,
double  Ts 
)

Initialize a PIDF biquad.

Based on Tustin-approx (trapezoidal) of the continous time version. Behaviour equivalent to the PID controller created with the following MATLAB expression:

C = pid( Kp, Ki, Kd, 1/N, Ts, 'IFormula', 'Trapezoidal', 'DFormula', 'Trapezoidal' );

Parameters:
KpProportional gain
KiIntegral gain
KdDerivative gain
NFilter coefficient ( N = 1/Tf )
TsTimestep

Definition at line 18 of file BiQuad.cpp.

std::vector< std::complex< double > > poles (  )

Return poles of the BiQuad filter.

Returns:
vector of std::complex poles

Definition at line 61 of file BiQuad.cpp.

void setResetStateOnGainChange ( bool  v )

Determines if the state variables are reset to zero on gain change.

Can be used for changing gain parameters on the fly.

Parameters:
vValue of the reset boolean

Definition at line 97 of file BiQuad.cpp.

bool stable (  )

Is this biquad stable? Checks if all poles lie within the unit-circle.

Returns:
boolean whether the filter is stable or not

Definition at line 89 of file BiQuad.cpp.

double step ( double  x )

Execute one digital timestep and return the result...

Parameters:
xinput of the filer
Returns:
output of the filter

Definition at line 45 of file BiQuad.cpp.

std::vector< std::complex< double > > zeros (  )

Return zeros of the BiQuad filter.

Returns:
vector of std::complex zeros

Definition at line 75 of file BiQuad.cpp.

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