General Wavelet class. More...

#include <Wavelet.h>

Classes
class	LiftingStep
	Instances define a lifting step in a wavelet lifting scheme. More...
class	WaveletComponent
	Superclass for LiftingStep and other possible components / operations defining a wavelet. More...
Public Member Functions
const std::string &	name () const
	Get the name of the wavelet.
bool	integerCompatible () const
	Query if wavelet is integer compatible.
bool	normalized () const
	Query if wavelet and scaling coefficients are normalized after lifting.
int	steps () const
	Get number of steps in the lifting scheme.
const LiftingStep &	liftingStep (int i) const
	Get a step of the lifting scheme.
double	normS () const
	Get the normalization factor for the scaling coefficients.
double	normD () const
	Get the normalization factor for the wavelet coefficients.
bool	operator== (const Wavelet &w) const
	Compare with another wavelet.
template<class tp_Type >
void	lift (blitz::Array< tp_Type, 1 > &s, blitz::Array< tp_Type, 1 > &d, ExtensionMode be=CONSTANT_EXT) const
	Apply the lifting scheme on the data channels s and d.
template<class tp_Type >
void	invLift (blitz::Array< tp_Type, 1 > &s, blitz::Array< tp_Type, 1 > &d, ExtensionMode be=CONSTANT_EXT) const
	Apply the inverse lifting scheme on the data channels s and d.
blitz::Array< double, 1 >	forwardFkt (unsigned int size=1<< 9, int scale=6, unsigned int trans=3) const
	Get sampled values (i.e. the form) of the forward transformation scaling or wavelet function.
blitz::Array< double, 1 >	inverseFkt (unsigned int size=1<< 9, int scale=6, unsigned int trans=3) const
	Get sampled values (i.e. the form) of the inverse transformation scaling or wavelet function.
	Wavelet ()
	Construct an empty wavelet.
	Wavelet (const std::string &name, double ns, double nd, const LiftingStep &s0, const LiftingStep &s1)
	Construct a wavelet and it's lifting scheme.
	Wavelet (const std::string &name, double ns, double nd, const LiftingStep &s0, const LiftingStep &s1, const LiftingStep &s2)
	Wavelet (const std::string &name, double ns, double nd, const LiftingStep &s0, const LiftingStep &s1, const LiftingStep &s2, const LiftingStep &s3)
Static Public Member Functions
static bool	equals (double x, double y)
	Compare two numbers within numeric limits.
Protected Attributes
std::string	m_spec
double	m_nS
double	m_nD
std::vector< LiftingStep >	m_steps

Detailed Description

General Wavelet class.

Instances define specific lifting schemes and therefore specific wavelets. Keep your lifting steps integer compatible if you want do operate on both integer an floating point data-types. Some constant instances of this class are available for instant usage, for example WL_HAAR and WL_D_4.

Constructor & Destructor Documentation

bwave::Wavelet::Wavelet	(	const std::string &	name,
		double	ns,
		double	nd,
		const LiftingStep &	s0,
		const LiftingStep &	s1
	)

Construct a wavelet and it's lifting scheme.

Parameters:

name	the name of the wavelet.
ns	normalization factor for scaling coefficients.
nd	normalization factor for wavelet coefficients.
s0	first lifting step.
s1	second lifting step, more steps can be specified.

The normalisation factors can later be queried using normS() and normD().

bwave::Wavelet::Wavelet	(	const std::string &	name,
		double	ns,
		double	nd,
		const LiftingStep &	s0,
		const LiftingStep &	s1,
		const LiftingStep &	s2
	)

See also:: Wavelet(const std::string &name, double ns, double nd, const LiftingStep &s0, const LiftingStep &s1)

bwave::Wavelet::Wavelet	(	const std::string &	name,
		double	ns,
		double	nd,
		const LiftingStep &	s0,
		const LiftingStep &	s1,
		const LiftingStep &	s2,
		const LiftingStep &	s3
	)

See also:: Wavelet(const std::string &name, double ns, double nd, const LiftingStep &s0, const LiftingStep &s1)

Member Function Documentation

bool bwave::Wavelet::equals	(	double	x,
		double	y
	)		`[static]`

Compare two numbers within numeric limits.

Returns:: true if x and y and (almost) equal, false if not.

Referenced by bwave::Wavelet::LiftingStep::operator==(), and operator==().

blitz::Array< double, 1 > bwave::Wavelet::forwardFkt ( ) const

Get sampled values (i.e. the form) of the forward transformation scaling or wavelet function.

Parameters:

size	number of samples.
scale	the scale of the function, use positive values to generate scaling, negative values to generate wavelet functions.
trans	the translation of the function.

Returns:: Array of function values.

Useful for getting the data to plot wavelet and scaling functions. Use a higher number of samples for better resolution.

References bwave::WaveletDecomp< tp_rank >::apply(), bwave::WaveletDecomp< tp_rank >::coeffs(), and bwave::WaveletDecomp< tp_rank >::normFactor().

bool bwave::Wavelet::integerCompatible ( ) const

Query if wavelet is integer compatible.

Returns:: true if wavelet is integer compatible, false if not.

Integer compatibility means that wavelet decomposition and reconstruction do not use floating point operations on the data. Wavelet decomposition and reconstruction may still lead to information loss on integer data if the lifting scheme contains scaling steps.

Not implemented yet!

blitz::Array< double, 1 > bwave::Wavelet::inverseFkt ( ) const

Get sampled values (i.e. the form) of the inverse transformation scaling or wavelet function.

See also:: forwardFkt(unsigned int size = 1<<9, int scale = 6, unsigned int trans = 3)

References bwave::WaveletDecomp< tp_rank >::applyInv(), bwave::WaveletDecomp< tp_rank >::coeffs(), and bwave::WaveletDecomp< tp_rank >::normFactor().

template<class tp_Type >

void bwave::Wavelet::invLift	(	blitz::Array< tp_Type, 1 > &	s,
		blitz::Array< tp_Type, 1 > &	d,
		ExtensionMode	be = `CONSTANT_EXT`
	)		const

Apply the inverse lifting scheme on the data channels s and d.

Parameters:

s	usually initialised with the scaling coefficients.
d	usually initialised with the wavelet coefficients.
be	extension method to use for boundary handling.

References bwave::Wavelet::LiftingStep::apply(), liftingStep(), and steps().

template<class tp_Type >

void bwave::Wavelet::lift	(	blitz::Array< tp_Type, 1 > &	s,
		blitz::Array< tp_Type, 1 > &	d,
		ExtensionMode	be = `CONSTANT_EXT`
	)		const

Apply the lifting scheme on the data channels s and d.

Parameters:

s	usually initialised with the even original data values, contains the scaling coefficients after lifting.
d	usually initialised with the odd original data values, contains the wavelet coefficients after lifting.
be	extension method to use for boundary handling.

References bwave::Wavelet::LiftingStep::apply(), liftingStep(), and steps().

const LiftingStep& bwave::Wavelet::liftingStep ( int i ) const [inline]

Get a step of the lifting scheme.

Parameters:

i	index of the step to get (0 <= i < steps()).

Referenced by invLift(), lift(), and operator==().

bool bwave::Wavelet::normalized ( ) const

Query if wavelet and scaling coefficients are normalized after lifting.

Returns:: true if normS() and normD() both equal 1, false if not.

double bwave::Wavelet::normD ( ) const [inline]

Get the normalization factor for the wavelet coefficients.

See also:: normS().

Referenced by operator==().

double bwave::Wavelet::normS ( ) const [inline]

Get the normalization factor for the scaling coefficients.

Wavelet and scaling coefficients are not automatically normalized after lifting, otherwise integer applications would not be possible.

Referenced by operator==().

bool bwave::Wavelet::operator== ( const Wavelet & w ) const

Compare with another wavelet.

Parameters:

w	the wavelet to compare with.

Returns:: true if the wavelets are equal, false if not.

References equals(), liftingStep(), normD(), normS(), and steps().

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

/home/pclz-02/oschulz/Data/Science/Projects/Gerda/Software/blitzwave/src/Wavelet.h
/home/pclz-02/oschulz/Data/Science/Projects/Gerda/Software/blitzwave/src/Wavelet.cxx

Classes

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation