TFFT2D< ComplexTraits > Class Template Reference
[Fast Fourier Transforms]

A class to perform Fast Fourier Transforms and inverse Fast Fourier Transforms on regularly spaced two dimensional data. More...

#include <FFT2D.h>

Inheritance diagram for TFFT2D< ComplexTraits >:

List of all members.

Public Types
typedef std::complex< typename ComplexTraits::ComplexPrecision >	Complex
typedef TRegularData2D< std::complex< typename ComplexTraits::ComplexPrecision > >	ComplexVector
Public Member Functions
void	doFFT () throw ()
	Perform a single fast fourier transform on the data.
void	doiFFT () throw ()
	Perform a single inverse fourier transform on the data.
bool	translate (const Vector2 &trans_origin) throw ()
	Translate the origin in physical space about {trans_origin}, i.e.
bool	setPhysStepWidth (double new_width_x, double new_width_y) throw ()
	Set the step width in physical space to {new_width_x, new_width_y}.
double	getPhysStepWidthX () const throw ()
	Returns the step width in physical space in X direction.
double	getPhysStepWidthY () const throw ()
	Returns the step width in physical space in Y direction.
double	getFourierStepWidthX () const throw ()
	Returns the step width in fourier space in X direction.
double	getFourierStepWidthY () const throw ()
	Returns the step width in fourier space in Y direction.
double	getPhysSpaceMinX () const throw ()
	Returns the minimal position of the grid in physical space in X direction.
double	getPhysSpaceMinY () const throw ()
	Returns the minimal position of the grid in physical space in Y direction.
double	getPhysSpaceMaxX () const throw ()
	Returns the maximal position of the grid in physical space in X direction.
double	getPhysSpaceMaxY () const throw ()
	Returns the maximal position of the grid in physical space in Y direction.
double	getFourierSpaceMinX () const throw ()
	Returns the minimal position of the grid in fourier space in X direction.
double	getFourierSpaceMinY () const throw ()
	Returns the minimal position of the grid in fourier space in Y direction.
double	getFourierSpaceMaxX () const throw ()
	Returns the maximal position of the grid in fourier space in X direction.
double	getFourierSpaceMaxY () const throw ()
	Returns the maximal position of the grid in fourier space in Y direction.
Size	getMaxXIndex () const throw ()
	AR: Return the largest grid position for the x direction.
Size	getMaxYIndex () const throw ()
	AR: Return the largest grid position for the y direction.
Size	getNumberOfInverseTransforms () const throw ()
	AR: Return the number of inverse transforms that have been carried out using this class.
Vector2	getGridCoordinates (Position position) const throw ()
	AR: Returns the grid coordinate corresponding to the position.
Complex	getData (const Vector2 &pos) const throw (Exception::OutOfGrid)
	Returns the data at the grid position closest to pos , and automatically includes the correct phase factor and (symmetric) normalization.
Complex	getInterpolatedValue (const Vector2 &pos) const throw (Exception::OutOfGrid)
	Returns the data at point pos.
void	setData (const Vector2 &pos, Complex val) throw (Exception::OutOfGrid)
	Sets the data point at the grid position closest to pos to the value val , and -- if called in fourier space -- automatically includes the correct phase factor and (symmetric) normalization.
Complex &	operator[] (const Vector2 &pos) throw (Exception::OutOfGrid)
	Access the data at the grid position closest to pos .
const Complex &	operator[] (const Vector2 &pos) const throw (Exception::OutOfGrid)
	Access the data at the grid position closest to pos .
Complex &	operator[] (const Position &pos) throw (Exception::OutOfGrid)
	AR: Access the (raw) data at Position pos.
const Complex &	operator[] (const Position &pos) const throw (Exception::OutOfGrid)
	AR: Access the (raw) data at Position pos.
void	setNumberOfFFTTransforms (Size num)
void	setNumberOfiFFTTransforms (Size num)
Complex	phase (const Vector2 &pos) const throw ()
	This computes the phase factor in fourier space that results if the origin of the coordinate system in physical space is not in the "lower left corner".
bool	isInFourierSpace () const throw ()
	AR: Returns true if the data is considered to be in Fourier space, false otherwise.
Constructors and Destructors
	throw ()
	Default constructor.
	throw ()
	Copy constructor.
	TFFT2D (Size ldnX, Size ldnY, double stepPhysX=1., double stepPhysY=1., Vector2 origin=Vector2(0., 0.), bool inFourierSpace=false) throw ()
	Detailed constructor.
virtual	~TFFT2D () throw ()
	Destructor.
Assignment
const TFFT2D &	operator= (const TFFT2D &fft_2d) throw ()
	Assignment operator.
virtual void	clear () throw ()
	Clear the contents.
virtual void	destroy () throw ()
	Clear the contents and reset all attributes.
Predicates
bool	operator== (const TFFT2D &fft_2d) const throw ()
	Equality operator.
Protected Attributes
Size	lengthX_
Size	lengthY_
bool	inFourierSpace_
Size	numPhysToFourier_
Size	numFourierToPhys_
Vector2	origin_
	Origin of the grid (offset).
double	stepPhysX_
double	stepPhysY_
double	stepFourierX_
double	stepFourierY_
Vector2	minPhys_
Vector2	maxPhys_
Vector2	minFourier_
Vector2	maxFourier_
ComplexTraits::FftwPlan	planForward_
ComplexTraits::FftwPlan	planBackward_
Size	dataLength_
Complex *	dataAdress_
bool	planCalculated_

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Detailed Description

template<typename ComplexTraits>
class TFFT2D< ComplexTraits >

A class to perform Fast Fourier Transforms and inverse Fast Fourier Transforms on regularly spaced two dimensional data.

This class makes use of the freely available library FFTW, which can be found at http://www.fftw.org coordinate system can be handled automatically. The normaliztion is chosen symmetrically.

S/TFFT2D.h

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Constructor & Destructor Documentation

template<typename ComplexTraits> TFFT2D< ComplexTraits >::TFFT2D (  Size  ldnX, Size  ldnY, double  stepPhysX = 1., double  stepPhysY = 1., Vector2  origin = Vector2(0., 0.), bool  inFourierSpace = false )  throw ()

Detailed constructor. Parameters: ldnX  The binary logarithm of the number of grid points in X direction (we use the logarithm to ensure that the number of points is a power of two, which is important for the FFT) ldnY  The binary logarithm of the number of grid points in Y direction stepPhysX  The step width in X direction in physical space stepPhysY  The step width in Y direction in physical space origin  The origin of the coordinate system inFourierSpace  Flag to decide whether the data is assumed to be in physical or fourier space

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Member Function Documentation

template<typename ComplexTraits> virtual void TFFT2D< ComplexTraits >::clear (   )  throw () [virtual]

Clear the contents. Reimplemented from TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > >.

template<typename ComplexTraits> virtual void TFFT2D< ComplexTraits >::destroy (   )  throw () [virtual]

Clear the contents and reset all attributes.

template<typename ComplexTraits> void TFFT2D< ComplexTraits >::doFFT (   )  throw ()

Perform a single fast fourier transform on the data.

template<typename ComplexTraits> void TFFT2D< ComplexTraits >::doiFFT (   )  throw ()

Perform a single inverse fourier transform on the data.

template<typename ComplexTraits> TFFT2D< ComplexTraits >::Complex TFFT2D< ComplexTraits >::getData (  const Vector2 &  pos  )  const throw (Exception::OutOfGrid)

Returns the data at the grid position closest to pos , and automatically includes the correct phase factor and (symmetric) normalization.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getFourierSpaceMaxX (   )  const throw ()

Returns the maximal position of the grid in fourier space in X direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getFourierSpaceMaxY (   )  const throw ()

Returns the maximal position of the grid in fourier space in Y direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getFourierSpaceMinX (   )  const throw ()

Returns the minimal position of the grid in fourier space in X direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getFourierSpaceMinY (   )  const throw ()

Returns the minimal position of the grid in fourier space in Y direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getFourierStepWidthX (   )  const throw ()

Returns the step width in fourier space in X direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getFourierStepWidthY (   )  const throw ()

Returns the step width in fourier space in Y direction.

template<typename ComplexTraits> Vector2 TFFT2D< ComplexTraits >::getGridCoordinates (  Position  position  )  const throw ()

AR: Returns the grid coordinate corresponding to the position.

template<typename ComplexTraits> TFFT2D< ComplexTraits >::Complex TFFT2D< ComplexTraits >::getInterpolatedValue (  const Vector2 &  pos  )  const throw (Exception::OutOfGrid)

Returns the data at point pos. If pos is not a point on the grid, the data is linearly interpolated. This method automatically includes the correct phase factor and (symmetric) normalization.

template<typename ComplexTraits> Size TFFT2D< ComplexTraits >::getMaxXIndex (   )  const throw ()

AR: Return the largest grid position for the x direction. This method returns the maximum position allowed in the grid. As the point in the origin has the indices (0, 0), this method returns the number of points in X direction minus one.

template<typename ComplexTraits> Size TFFT2D< ComplexTraits >::getMaxYIndex (   )  const throw ()

AR: Return the largest grid position for the y direction. This method returns the maximum position allowed in the grid. As the point in the origin has the indices (0, 0), this method returns the number of points in Y direction minus one.

template<typename ComplexTraits> Size TFFT2D< ComplexTraits >::getNumberOfInverseTransforms (   )  const throw ()

AR: Return the number of inverse transforms that have been carried out using this class. This is an important factor for the normalization of the data.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getPhysSpaceMaxX (   )  const throw ()

Returns the maximal position of the grid in physical space in X direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getPhysSpaceMaxY (   )  const throw ()

Returns the maximal position of the grid in physical space in Y direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getPhysSpaceMinX (   )  const throw ()

Returns the minimal position of the grid in physical space in X direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getPhysSpaceMinY (   )  const throw ()

Returns the minimal position of the grid in physical space in Y direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getPhysStepWidthX (   )  const throw ()

Returns the step width in physical space in X direction.

template<typename ComplexTraits> double TFFT2D< ComplexTraits >::getPhysStepWidthY (   )  const throw ()

Returns the step width in physical space in Y direction.

template<typename ComplexTraits> bool TFFT2D< ComplexTraits >::isInFourierSpace (   )  const throw ()

AR: Returns true if the data is considered to be in Fourier space, false otherwise.

template<typename ComplexTraits> bool TFFT2D< ComplexTraits >::operator== (  const TFFT2D< ComplexTraits > &  fft_2d  )  const throw ()

Equality operator.

template<typename ComplexTraits> const Complex& TFFT2D< ComplexTraits >::operator[] (  const Position &  pos  )  const throw (Exception::OutOfGrid)

AR: Access the (raw) data at Position pos. Const method.

template<typename ComplexTraits> Complex& TFFT2D< ComplexTraits >::operator[] (  const Position &  pos  )  throw (Exception::OutOfGrid)

AR: Access the (raw) data at Position pos.

template<typename ComplexTraits> const TFFT2D< ComplexTraits >::Complex & TFFT2D< ComplexTraits >::operator[] (  const Vector2 &  pos  )  const throw (Exception::OutOfGrid)

Access the data at the grid position closest to pos . This function returns the "raw" data at that position.

template<typename ComplexTraits> TFFT2D< ComplexTraits >::Complex & TFFT2D< ComplexTraits >::operator[] (  const Vector2 &  pos  )  throw (Exception::OutOfGrid)

Access the data at the grid position closest to pos . This function returns the "raw" data at that position.

template<typename ComplexTraits> TFFT2D< ComplexTraits >::Complex TFFT2D< ComplexTraits >::phase (  const Vector2 &  pos  )  const throw ()

This computes the phase factor in fourier space that results if the origin of the coordinate system in physical space is not in the "lower left corner".

template<typename ComplexTraits> void TFFT2D< ComplexTraits >::setData (  const Vector2 &  pos, Complex  val )  throw (Exception::OutOfGrid)

Sets the data point at the grid position closest to pos to the value val , and -- if called in fourier space -- automatically includes the correct phase factor and (symmetric) normalization.

template<typename ComplexTraits> bool TFFT2D< ComplexTraits >::setPhysStepWidth (  double  new_width_x, double  new_width_y )  throw ()

Set the step width in physical space to {new_width_x, new_width_y}. The step width in fourier space is automatically adjusted accordingly. {new_width_x and new_width_y} must be positive, otherwise the function does nothing and retuns false .

template<typename ComplexTraits> bool TFFT2D< ComplexTraits >::translate (  const Vector2 &  trans_origin  )  throw ()

Translate the origin in physical space about {trans_origin}, i.e. the new origin will be located at the former position {trans_origin}. If the result is out of bounds, the function does nothing and returns false .