This Biquad class implements a second-order recursive linear filter, containing two poles and two zeros. More...

#include <biquad.hpp>

Public Types
using	value_type = T

Public Member Functions
constexpr	biquad () noexcept=default

constexpr	biquad (const biquad &) noexcept=default

constexpr	biquad (biquad &&) noexcept=default

constexpr biquad &	operator= (const biquad &) noexcept=default

constexpr biquad &	operator= (biquad &&) noexcept=default

constexpr	biquad (const std::complex< T > &pole, const std::complex< T > &zero)
	Initialize a Biquad filter with one single pole and zero. More...

constexpr	biquad (const std::complex< T > &pole_first, const std::complex< T > &zero_first, const std::complex< T > &pole_second, const std::complex< T > &zero_second)
	Initialize a Biquad filter with a pair of zero-pole. More...

constexpr	biquad (value_type a0, value_type a1, value_type a2, value_type b0, value_type b1, value_type b2) noexcept
	Initialize a Biquad fitler with the given coefficients. More...

	~biquad ()=default
	Default destructor. More...

constexpr value_type	a0 () const noexcept
	Returns the value of the coefficient \( a_0 \). More...

constexpr value_type	a1 () const noexcept
	Returns the value of the coefficient \( a_1 \). More...

constexpr value_type	a2 () const noexcept
	Returns the value of the coefficient \( a_2 \). More...

constexpr value_type	b0 () const noexcept
	Returns the value of the coefficient \( b_0 \). More...

constexpr value_type	b1 () const noexcept
	Returns the value of the coefficient \( b_1 \). More...

constexpr value_type	b2 () const noexcept
	Returns the value of the coefficient \( b_2 \). More...

constexpr void	set_a0 (T value) noexcept
	Updates the value of the coefficient \( a_0 \). More...

constexpr void	set_a1 (T value) noexcept
	Updates the value of the coefficient \( a_1 \). More...

constexpr void	set_a2 (T value) noexcept
	Updates the value of the coefficient \( a_2 \). More...

constexpr void	set_b0 (T value) noexcept
	Updates the value of the coefficient \( b_0 \). More...

constexpr void	set_b1 (T value) noexcept
	Updates the value of the coefficient \( b_1 \). More...

constexpr void	set_b2 (T value) noexcept
	Updates the value of the coefficient \( b_2 \). More...

template<typename InputIt , typename OutputIt >
constexpr void	filter (InputIt first, InputIt last, OutputIt d_first)
	Filters the signal in the range [first, last) and stores the result in another range, beginning at d_first. More...

constexpr void	reset () noexcept
	Reset the filter to the original state. More...

constexpr bool	stability () const noexcept
	Checks if the Biquad Filter is stable. More...

constexpr	operator bool () const noexcept
	Boolean operator to checks if the filter is stable. More...

constexpr value_type	tick (T value) noexcept
	Computes the output of filtering one digital time-step. More...

Detailed Description

template<typename T>
class edsp::filter::biquad< T >

This Biquad class implements a second-order recursive linear filter, containing two poles and two zeros.

In the Z domain, its transfer function is:

\[ H(z)={\frac {b_{0}+b_{1}z^{{-1}}+b_{2}z^{{-2}}}{a_{0}+a_{1}z^{{-1}}+a_{2}z^{{-2}}}} \]

Which is often normalized by dividing all coefficients by a0. This class performs the filtering with a Direct Form I:

\[ y[n]={\frac {1}{a_{0}}}\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]-a_{1}y[n-1]-a_{2}y[n-2]\right) \]

Member Typedef Documentation

◆ value_type

template<typename T>

using edsp::filter::biquad< T >::value_type = T

Constructor & Destructor Documentation

◆ biquad() [1/6]

template<typename T>

constexpr edsp::filter::biquad< T >::biquad ( )

defaultnoexcept

◆ biquad() [2/6]

template<typename T>

constexpr edsp::filter::biquad< T >::biquad ( const biquad< T > & )

defaultnoexcept

◆ biquad() [3/6]

template<typename T>

constexpr edsp::filter::biquad< T >::biquad ( biquad< T > && )

defaultnoexcept

◆ biquad() [4/6]

template<typename T >

constexpr edsp::filter::biquad< T >::biquad	(	const std::complex< T > &	pole,
		const std::complex< T > &	zero
	)

Initialize a Biquad filter with one single pole and zero.

Parameters

pole	Complex value representing the pole.
zero	Complex value representing the zero.

◆ biquad() [5/6]

template<typename T >

constexpr edsp::filter::biquad< T >::biquad	(	const std::complex< T > &	pole_first,
		const std::complex< T > &	zero_first,
		const std::complex< T > &	pole_second,
		const std::complex< T > &	zero_second
	)

Initialize a Biquad filter with a pair of zero-pole.

Parameters

pole_first	Complex value representing the first pole.
zero_first	Complex value representing the first zero.
pole_second	Complex value representing the second pole.
zero_second	Complex value representing the second zeo.

◆ biquad() [6/6]

template<typename T >

constexpr edsp::filter::biquad< T >::biquad	(	value_type	a0,
		value_type	a1,
		value_type	a2,
		value_type	b0,
		value_type	b1,
		value_type	b2
	)

noexcept

Initialize a Biquad fitler with the given coefficients.

Parameters

a0	Value of the coefficient \( a_0 \).
a1	Value of the coefficient \( a_1 \).
a2	Value of the coefficient \( a_2 \).
b0	Value of the coefficient \( b_0 \).
b1	Value of the coefficient \( b_1 \).
b2	Value of the coefficient \( b_2 \).

◆ ~biquad()

template<typename T>

edsp::filter::biquad< T >::~biquad ( )

default

Default destructor.

Member Function Documentation

◆ a0()

template<typename T >

constexpr biquad< T >::value_type edsp::filter::biquad< T >::a0 ( ) const

noexcept

Returns the value of the coefficient \( a_0 \).

Returns: Value of the coefficient \( a_0 \).

◆ a1()

template<typename T >

constexpr biquad< T >::value_type edsp::filter::biquad< T >::a1 ( ) const

noexcept

Returns the value of the coefficient \( a_1 \).

Returns: Value of the coefficient \( a_1 \).

◆ a2()

template<typename T >

constexpr biquad< T >::value_type edsp::filter::biquad< T >::a2 ( ) const

noexcept

Returns the value of the coefficient \( a_2 \).

Returns: Value of the coefficient \( a_2 \).

◆ b0()

template<typename T >

constexpr biquad< T >::value_type edsp::filter::biquad< T >::b0 ( ) const

noexcept

Returns the value of the coefficient \( b_0 \).

Returns: Value of the coefficient \( b_0 \).

◆ b1()

template<typename T >

constexpr biquad< T >::value_type edsp::filter::biquad< T >::b1 ( ) const

noexcept

Returns the value of the coefficient \( b_1 \).

Returns: Value of the coefficient \( b_1 \).

◆ b2()

template<typename T >

constexpr biquad< T >::value_type edsp::filter::biquad< T >::b2 ( ) const

noexcept

Returns the value of the coefficient \( b_2 \).

Returns: Value of the coefficient \( b_2 \).

◆ filter()

template<typename T >

template<typename InputIt , typename OutputIt >

constexpr void edsp::filter::biquad< T >::filter	(	InputIt	first,
		InputIt	last,
		OutputIt	d_first
	)

Filters the signal in the range [first, last) and stores the result in another range, beginning at d_first.

Parameters

first	Input iterator defining the beginning of the input range.
last	Input iterator defining the ending of the input range.
d_first	Output iterator defining the beginning of the destination range.

See also: tick

◆ operator bool()

template<typename T >

constexpr edsp::filter::biquad< T >::operator bool ( ) const

explicitnoexcept

Boolean operator to checks if the filter is stable.

See also: stability

◆ operator=() [1/2]

template<typename T>

constexpr biquad& edsp::filter::biquad< T >::operator= ( const biquad< T > & )

defaultnoexcept

◆ operator=() [2/2]

template<typename T>

constexpr biquad& edsp::filter::biquad< T >::operator= ( biquad< T > && )

defaultnoexcept

◆ reset()

template<typename T >

constexpr void edsp::filter::biquad< T >::reset ( )

noexcept

Reset the filter to the original state.

◆ set_a0()

template<typename T >

constexpr void edsp::filter::biquad< T >::set_a0 ( T value )

noexcept

Updates the value of the coefficient \( a_0 \).

Returns: value Value of the coefficient \( a_0 \).

◆ set_a1()

template<typename T >

constexpr void edsp::filter::biquad< T >::set_a1 ( T value )

noexcept

Updates the value of the coefficient \( a_1 \).

Returns: value Value of the coefficient \( a_1 \).

◆ set_a2()

template<typename T >

constexpr void edsp::filter::biquad< T >::set_a2 ( T value )

noexcept

Updates the value of the coefficient \( a_2 \).

Returns: value Value of the coefficient \( a_2 \).

◆ set_b0()

template<typename T >

constexpr void edsp::filter::biquad< T >::set_b0 ( T value )

noexcept

Updates the value of the coefficient \( b_0 \).

Returns: value Value of the coefficient \( b_0 \).

◆ set_b1()

template<typename T >

constexpr void edsp::filter::biquad< T >::set_b1 ( T value )

noexcept

Updates the value of the coefficient \( b_1 \).

Returns: value Value of the coefficient \( b_1 \).

◆ set_b2()

template<typename T >

constexpr void edsp::filter::biquad< T >::set_b2 ( T value )

noexcept

Updates the value of the coefficient \( b_2 \).

Returns: value Value of the coefficient \( b_2 \).

◆ stability()

template<typename T >

constexpr bool edsp::filter::biquad< T >::stability ( ) const

noexcept

Checks if the Biquad Filter is stable.

In general, the two poles of the biquad filter must be inside the unit circle for it to be stable

Returns: true if the filter is stable, false otherwise.

◆ tick()

template<typename T >

constexpr biquad< T >::value_type edsp::filter::biquad< T >::tick ( T value )

noexcept

Computes the output of filtering one digital time-step.

Parameters

value Input value to be filtered.

Returns: Filtered value.

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

filter/biquad.hpp

Public Types

Public Member Functions

Detailed Description

template<typename T> class edsp::filter::biquad< T >

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ biquad() [1/6]

◆ biquad() [2/6]

◆ biquad() [3/6]

◆ biquad() [4/6]

◆ biquad() [5/6]

◆ biquad() [6/6]

◆ ~biquad()

Member Function Documentation

◆ a0()

◆ a1()

◆ a2()

◆ b0()

◆ b1()

◆ b2()

◆ filter()

◆ operator bool()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ reset()

◆ set_a0()

◆ set_a1()

◆ set_a2()

◆ set_b0()

◆ set_b1()

◆ set_b2()

◆ stability()

◆ tick()

template<typename T>
class edsp::filter::biquad< T >