control::filter::Biquad< T, S > Class Template Reference

#include <biquad.h>

Inheritance diagram for control::filter::Biquad< T, S >:

Public Member Functions
	Biquad (T b0, T b1, T b2, T a1, T a2)
	Biquad (T b0, T b1, T b2, T a0, T a1, T a2)
	Biquad (TCS< T > z, TCS< T > p, T k)
T	step (T x)
TCS< T >	poles ()
TCS< T >	zeros ()
bool	stable ()
void	reset ()

Protected Member Functions
std::tuple< T, T, T, T, T >	zpk2coef (TCS< T > z, TCS< T > p, T k)
std::tuple< T, T >	zero2coef (TCS< T > z)
TCS< T >	solve (T a, T b, T c)

Protected Attributes
T	wz [2] = {0, 0}
S	B [3]
S	A [2]

Detailed Description

template<typename T = float, typename S = const T>
class control::filter::Biquad< T, S >

Biquad

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

Normalized by dividing all coefficients by a0.

Template Parameters

T	arithmetic type
S	parameter type (const T)

Constructor & Destructor Documentation

Biquad() [1/3]

template<typename T = float, typename S = const T>

control::filter::Biquad< T, S >::Biquad ( T  b0, T  b1, T  b2, T  a1, T  a2  )

inline

Initialize a biquad filter with normalized (5) coefficients

Parameters

T	b0
T	b1
T	b2
T	a1
T	a2

Biquad() [2/3]

template<typename T = float, typename S = const T>

control::filter::Biquad< T, S >::Biquad ( T  b0, T  b1, T  b2, T  a0, T  a1, T  a2  )

inline

Initialize a biquad with unnormalized (6) coefficients

Parameters

b0
b1
b2
a0
a1
a2

Biquad() [3/3]

template<typename T = float, typename S = const T>

control::filter::Biquad< T, S >::Biquad ( TCS< T >  z, TCS< T >  p, T  k  )

inline

Initialize a biquad with ZPK

Parameters

TCS<T>	z zeros
TCS<T>	p poles
T	k gain

Member Function Documentation

poles()

template<typename T = float, typename S = const T>

TCS<T> control::filter::Biquad< T, S >::poles ( )

inline

Poles of the biquad

Get a tuple of two complex values that represent the biquads poles. Poles of a biquad are the solution to the denominator, a quadratic equation.

Returns

TCS<T>

reset()

template<typename T = float, typename S = const T>

void control::filter::Biquad< T, S >::reset ( )

inline

Reset the biquad

solve()

template<typename T = float, typename S = const T>

TCS<T> control::filter::Biquad< T, S >::solve ( T  a, T  b, T  c  )

inlineprotected

Solve a quadratic polynomial

ax^2+bx+c -> k(x-z1)(x-z2)

Parameters

a	T
b	T
c	T

Returns

TCS<T> zeros

stable()

template<typename T = float, typename S = const T>

bool control::filter::Biquad< T, S >::stable ( )

inline

Stability of the biquad

Checks stability through evaluating the magnitude of the poles

Returns

bool whether stable

step()

template<typename T = float, typename S = const T>

T control::filter::Biquad< T, S >::step ( T  x )

inlinevirtual

Step the biquad

Parameters

T	x input value

Returns

T output value

Implements control::system::SISO< T >.

zero2coef()

template<typename T = float, typename S = const T>

std::tuple<T, T> control::filter::Biquad< T, S >::zero2coef ( TCS< T >  z )

inlineprotected

Coefficients of quadratic poly. corresponding to zeros

Gets the coefficients of the quadratic polynomial s.t. its solutions are p

(x-z1)(x-z2) -> x^2-(z1+z2)+z1*z2

Parameters

TCS<T>

z tuple of two complex Ts

Returns

std::tuple<T,T> tuple of two Ts

zeros()

template<typename T = float, typename S = const T>

TCS<T> control::filter::Biquad< T, S >::zeros ( )

inline

Zeros of the biquad

See also

poles()

Returns

TCS<T>

zpk2coef()

template<typename T = float, typename S = const T>

std::tuple<T, T, T, T, T> control::filter::Biquad< T, S >::zpk2coef ( TCS< T >  z, TCS< T >  p, T  k  )

inlineprotected

Convert ZPK to coefs

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The documentation for this class was generated from the following file:

• include/control/filter/biquad.h