Advanced 2-dimensional orthogonal transform functions.

Author: Miroslav Morhac

Legacy Code

TSpectrum2Transform is a legacy interface: there will be no bug fixes nor new developments. Therefore it is not recommended to use it in new long-term production code. But, depending on the context, using TSpectrum2Transform might still be a valid solution. For modeling a spectrum fitting and estimating the background one can use RooFit while for deconvolution and unfolding one can use TUnfold.

Class to carry out transforms of 2D spectra, its filtering and enhancement. It allows to calculate classic Fourier, Cosine, Sin, Hartley, Walsh, Haar transforms as well as mixed transforms (Fourier- Walsh, Fourier-Haar, Walsh-Haar, Cosine-Walsh, Cosine-Haar, Sin-Walsh and Sin-Haar). All the transforms are fast.

The algorithms in this class have been published in the following references:

C.V. Hampton, B. Lian, Wm. C. McHarris: Fast-Fourier-transform spectral enhancement techniques for gamma-ray spectroscopy.NIM A353 (1994) 280-284.
Morhac M., Matousek V., New adaptive Cosine-Walsh transform and its application to nuclear data compression, IEEE Transactions on Signal Processing 48 (2000) 2693.
Morhac M., Matousek V., Data compression using new fast adaptive Cosine-Haar transforms, Digital Signal Processing 8 (1998) 63.
Morhac M., Matousek V.: Multidimensional nuclear data compression using fast adaptive Walsh-Haar transform. Acta Physica Slovaca 51 (2001) 307.

Definition at line 16 of file TSpectrum2Transform.h.

Public Types
enum	{ kTransformHaar =0 , kTransformWalsh =1 , kTransformCos =2 , kTransformSin =3 , kTransformFourier =4 , kTransformHartley =5 , kTransformFourierWalsh =6 , kTransformFourierHaar =7 , kTransformWalshHaar =8 , kTransformCosWalsh =9 , kTransformCosHaar =10 , kTransformSinWalsh =11 , kTransformSinHaar =12 , kTransformForward =0 , kTransformInverse =1 }

Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

enum	{ kSingleKey = (1ULL << ( 0 )) , kOverwrite = (1ULL << ( 1 )) , kWriteDelete = (1ULL << ( 2 )) }

enum	EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }

enum	EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) }

Public Member Functions
	TSpectrum2Transform ()
	Default constructor.

	TSpectrum2Transform (Int_t sizeX, Int_t sizeY)
	The constructor creates TSpectrum2Transform object.

	~TSpectrum2Transform () override
	Destructor.

void	Enhance (const Double_t fSource, Double_t fDest)
	This function transforms the source spectrum.

void	FilterZonal (const Double_t fSource, Double_t fDest)
	This function transforms the source spectrum.

TClass *	IsA () const override

void	SetDirection (Int_t direction)
	This function sets the direction of the transform:

void	SetEnhanceCoeff (Double_t enhanceCoeff)
	This function sets the enhancement coefficient:

void	SetFilterCoeff (Double_t filterCoeff)
	This function sets the filter coefficient:

void	SetRegion (Int_t xmin, Int_t xmax, Int_t ymin, Int_t ymax)
	This function sets the filtering or enhancement region:

void	SetTransformType (Int_t transType, Int_t degree)
	This function sets the following parameters for transform:

void	Streamer (TBuffer &) override
	Stream an object of class TObject.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

void	Transform (const Double_t fSource, Double_t fDest)
	This function transforms the source spectrum.

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.

	TObject (const TObject &object)
	TObject copy ctor.

virtual	~TObject ()
	TObject destructor.

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract.

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad.

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action.

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.

virtual const char *	ClassName () const
	Returns name of class to which the object belongs.

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility.

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method.

virtual void	Copy (TObject &object) const
	Copy this to obj.

virtual void	Delete (Option_t *option="")
	Delete this object.

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object.

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects.

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs.

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad with: `gROOT->SetSelectedPad(c1)`.

virtual void	Dump () const
	Dump contents of object on stdout.

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message.

virtual void	Execute (const char method, const char params, Int_t *error=nullptr)
	Execute method on this object with the given parameter string, e.g.

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=nullptr)
	Execute method on this object with parameters stored in the TObjArray.

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py).

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message.

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes.

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object.

virtual const char *	GetIconName () const
	Returns mime type name of object.

virtual const char *	GetName () const
	Returns name of object.

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py).

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const
	Returns title of object.

virtual UInt_t	GetUniqueID () const
	Return the unique object id.

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out.

virtual ULong_t	Hash () const
	Return hash value for this object.

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message.

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname".

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl.

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas.

void	InvertBit (UInt_t f)

Bool_t	IsDestructed () const
	IsDestructed.

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory).

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

virtual Bool_t	IsSortable () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout.

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary).

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification (the base implementation is no-op).

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete.

void	operator delete (void *ptr)
	Operator delete.

void	operator delete (void ptr, void vp)
	Only called by placement new when throwing an exception.

void	operator delete[] (void *ptr)
	Operator delete [].

void	operator delete[] (void ptr, void vp)
	Only called by placement new[] when throwing an exception.

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator.

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself.

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list.

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself.

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory.

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list.

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename.

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out".

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f.

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object.

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message.

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message.

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory.

Static Public Member Functions
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TObject
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Longptr_t	GetDtorOnly ()
	Return destructor only flag.

static Bool_t	GetObjectStat ()
	Get status of object stat flag.

static void	SetDtorOnly (void *obj)
	Set destructor only flag.

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable.

Protected Member Functions
void	BitReverse (Double_t *working_space, Int_t num)
	This function carries out bit-reverse reordering of data.

void	BitReverseHaar (Double_t *working_space, Int_t shift, Int_t num, Int_t start)
	This function carries out bit-reverse reordering for Haar transform.

void	FourCos2 (Double_t *working_matrix, Double_t working_vector, Int_t numx, Int_t numy, Int_t direction, Int_t type)
	This function calculates 2D Fourier based transforms Function parameters:

void	Fourier (Double_t *working_space, Int_t num, Int_t hartley, Int_t direction, Int_t zt_clear)
	This function calculates Fourier based transform of a part of data.

void	General2 (Double_t *working_matrix, Double_t working_vector, Int_t numx, Int_t numy, Int_t direction, Int_t type, Int_t degree)
	This function calculates generalized (mixed) 2D transforms Function parameters:

Int_t	GeneralExe (Double_t *working_space, Int_t zt_clear, Int_t num, Int_t degree, Int_t type)
	This function calculates generalized (mixed) transforms of different degrees.

Int_t	GeneralInv (Double_t *working_space, Int_t num, Int_t degree, Int_t type)
	This function calculates inverse generalized (mixed) transforms Function parameters:

void	Haar (Double_t *working_space, Int_t num, Int_t direction)
	This function calculates Haar transform of a part of data.

void	HaarWalsh2 (Double_t *working_matrix, Double_t working_vector, Int_t numx, Int_t numy, Int_t direction, Int_t type)
	This function calculates 2D Haar and Walsh transforms Function parameters:

void	Walsh (Double_t *working_space, Int_t num)
	This function calculates Walsh transform of a part of data.

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected).

void	MakeZombie ()

Protected Attributes
Int_t	fDegree
	degree of mixed transform, applies only for Fourier-Walsh, Fourier-Haar, Walsh-Haar, Cosine-Walsh, Cosine-Haar, Sine-Walsh, Sine-Haar transforms

Int_t	fDirection
	forward or inverse transform

Double_t	fEnhanceCoeff
	multiplication coefficient applied in enhanced region;

Double_t	fFilterCoeff
	value set in the filtered region

Int_t	fSizeX
	x length of transformed data

Int_t	fSizeY
	y length of transformed data

Int_t	fTransformType
	type of transformation (Haar, Walsh, Cosine, Sine, Fourier, Hartley, Fourier-Walsh, Fourier-Haar, Walsh-Haar, Cosine-Walsh, Cosine-Haar, Sine-Walsh, Sine-Haar)

Int_t	fXmax
	last channel x of filtered or enhanced region

Int_t	fXmin
	first channel x of filtered or enhanced region

Int_t	fYmax
	last channel y of filtered or enhanced region

Int_t	fYmin
	first channel y of filtered or enhanced region

Additional Inherited Members
Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }

#include <TSpectrum2Transform.h>

Inheritance diagram for TSpectrum2Transform:

[legend]

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
kTransformHaar
kTransformWalsh
kTransformCos
kTransformSin
kTransformFourier
kTransformHartley
kTransformFourierWalsh
kTransformFourierHaar
kTransformWalshHaar
kTransformCosWalsh
kTransformCosHaar
kTransformSinWalsh
kTransformSinHaar
kTransformForward
kTransformInverse

Definition at line 30 of file TSpectrum2Transform.h.

Constructor & Destructor Documentation

◆ TSpectrum2Transform() [1/2]

TSpectrum2Transform::TSpectrum2Transform ( )

Default constructor.

Definition at line 41 of file TSpectrum2Transform.cxx.

◆ TSpectrum2Transform() [2/2]

TSpectrum2Transform::TSpectrum2Transform	(	Int_t	sizeX,
		Int_t	sizeY
	)

The constructor creates TSpectrum2Transform object.

Its sizes must be > than zero and must be power of 2. It sets default transform type to be Cosine transform. Transform parameters can be changed using setter functions.

Definition at line 59 of file TSpectrum2Transform.cxx.

◆ ~TSpectrum2Transform()

TSpectrum2Transform::~TSpectrum2Transform ( )

override

Destructor.

Definition at line 97 of file TSpectrum2Transform.cxx.

Member Function Documentation

◆ BitReverse()

void TSpectrum2Transform::BitReverse	(	Double_t *	working_space,
		Int_t	num
	)

protected

This function carries out bit-reverse reordering of data.

Function parameters:

working_space-pointer to vector of processed data
num-length of processed data

Definition at line 242 of file TSpectrum2Transform.cxx.

◆ BitReverseHaar()

void TSpectrum2Transform::BitReverseHaar	(	Double_t *	working_space,
		Int_t	shift,
		Int_t	num,
		Int_t	start
	)

protected

This function carries out bit-reverse reordering for Haar transform.

Function parameters:

working_space-pointer to vector of processed data
shift-shift of position of processing
start-initial position of processed data
num-length of processed data

Definition at line 403 of file TSpectrum2Transform.cxx.

◆ Class()

static TClass * TSpectrum2Transform::Class ( )

static

Returns: TClass describing this class

◆ Class_Name()

static const char * TSpectrum2Transform::Class_Name ( )

static

Returns: Name of this class

◆ Class_Version()

static constexpr Version_t TSpectrum2Transform::Class_Version ( )

inlinestaticconstexpr

Returns: Version of this class

Definition at line 73 of file TSpectrum2Transform.h.

◆ DeclFileName()

static const char * TSpectrum2Transform::DeclFileName ( )

inlinestatic

Returns: Name of the file containing the class declaration

Definition at line 73 of file TSpectrum2Transform.h.

◆ Enhance()

void TSpectrum2Transform::Enhance	(	const Double_t **	fSource,
		Double_t **	fDest
	)

This function transforms the source spectrum.

The calling program should fill in input parameters. Then it multiplies transformed coefficients in the given region by the given enhance_coeff and transforms it back

Function parameters:

fSource-pointer to the matrix of source spectrum, its size should be fSizeX*fSizeY
fDest-pointer to the matrix of destination data, its size should be fSizeX*fSizeY

Example of enhancement

This function transforms the source spectrum (for details see Transform function). Before the Enhance function is called the class must be created by constructor and the type of the transform as well as some other parameters must be set using a set of setter functions. The Enhance function multiplies transformed coefficients in the given region (fXmin, fXmax, fYmin, fYmax) by the given fEnhancCoeff and transforms it back. Enhanced data are written into dest spectrum.

Example - script Enhance2.c:

Fig. 1 Original two-dimensional noisy spectrum

Fig. 2 Enhanced spectrum of the data from Fig. 1 using Cosine transform (channels in region (0-63)x(0-63) were multiplied by 5)

Script:

Example to illustrate enhancement (class TSpectrumTransform2). To execute this example, do

root > .x Enhance2.C

void Enhance2() {
   Int_t i, j;
   Int_t nbinsx = 256;
   Int_t nbinsy = 256;
   Int_t xmin = 0;
   Int_t xmax = nbinsx;
   Int_t ymin = 0;
   Int_t ymax = nbinsy;
   Double_t ** source = new Double_t *[nbinsx];
   Double_t ** dest = new Double_t *[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]= new Double_t[nbinsy];
   for (i=0;i<nbinsx;i++)
      dest[i]= new Double_t[nbinsy];
   TH2F *trans = new TH2F("trans","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("TSpectrum2.root");
   trans=(TH2F*)f->Get("back3;1");
   TCanvas *Tr = new TCanvas("Transform","Illustration of transform function",10,10,1000,700);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = trans->GetBinContent(i + 1,j + 1);
      }
   }
   TSpectrumTransform2 *t = new TSpectrumTransform2(256,256);
   t->SetTransformType(t->kTransformCos,0);
   t->SetRegion(0,63,0,63);
   t->SetEnhanceCoeff(5);
   t->Enhance(source,dest);
   trans->Draw("SURF");
}

Definition at line 2439 of file TSpectrum2Transform.cxx.

◆ FilterZonal()

void TSpectrum2Transform::FilterZonal	(	const Double_t **	fSource,
		Double_t **	fDest
	)

This function transforms the source spectrum.

The calling program should fill in input parameters. Then it sets transformed coefficients in the given region to the given filter_coeff and transforms it back Filtered data are written into dest spectrum.

Function parameters:

fSource-pointer to the matrix of source spectrum, its size should be fSizeX*fSizeY
fDest-pointer to the matrix of destination data, its size should be fSizeX*fSizeY

Example of zonal filtering

This function transforms the source spectrum (for details see Transform function). Before the FilterZonal function is called the class must be created by constructor and the type of the transform as well as some other parameters must be set using a set of setter functions. The FilterZonal function sets transformed coefficients in the given region (fXmin, fXmax) to the given fFilterCoeff and transforms it back. Filtered data are written into dest spectrum.

Example - script Fitler2.c:

Fig. 1 Original two-dimensional noisy spectrum

Fig. 2 Filtered spectrum using Cosine transform and zonal filtration (channels in regions (128-255)x(0-255) and (0-255)x(128-255) were set to 0).

Script:

Example to illustrate zonal filtration (class TSpectrumTransform2). To execute this example, do

root > .x Filter2.C

void Filter2() {
   Int_t i, j;
   Int_t nbinsx = 256;
   Int_t nbinsy = 256;
   Int_t xmin = 0;
   Int_t xmax = nbinsx;
   Int_t ymin = 0;
   Int_t ymax = nbinsy;
   Double_t ** source = new Double_t *[nbinsx];
   Double_t ** dest = new Double_t *[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i] = new Double_t[nbinsy];
   for (i=0;i<nbinsx;i++)
      dest[i]= new Double_t[nbinsy];
   TH2F *trans = new TH2F("trans","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("TSpectrum2.root");
   trans=(TH2F*)f->Get("back3;1");
   TCanvas *Tr = new TCanvas("Transform","Illustration of transform function",10,10,1000,700);
   for (i = 0; i < nbinsx;i++){
      for (j = 0; j <nbinsy; j++){
         source[i][j] = trans->GetBinContent(i + 1,j+ 1);
      }
   }
   TSpectrumTransform2 *t = new TSpectrumTransform2(256,256);
   t->SetTransformType(t->kTransformCos,0);
   t->SetRegion(0,255,128,255);
   t->FilterZonal(source,dest);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j <nbinsy; j++){
         source[i][j] = dest[i][j];
      }
   }
   t->SetRegion(128,255,0,255);
   t->FilterZonal(source,dest);
   trans->Draw("SURF");
}

Definition at line 2108 of file TSpectrum2Transform.cxx.

◆ FourCos2()

void TSpectrum2Transform::FourCos2	(	Double_t **	working_matrix,
		Double_t *	working_vector,
		Int_t	numx,
		Int_t	numy,
		Int_t	direction,
		Int_t	type
	)

protected

This function calculates 2D Fourier based transforms Function parameters:

working_matrix-pointer to matrix of transformed data
working_vector-pointer to vector where the data are processed
numx,numy-lengths of processed data
direction-forward or inverse
type-type of transform (see manual)

Definition at line 776 of file TSpectrum2Transform.cxx.

◆ Fourier()

void TSpectrum2Transform::Fourier	(	Double_t *	working_space,
		Int_t	num,
		Int_t	hartley,
		Int_t	direction,
		Int_t	zt_clear
	)

protected

This function calculates Fourier based transform of a part of data.

Function parameters:

working_space-pointer to vector of transformed data
num-length of processed data
hartley-1 if it is Hartley transform, 0 otherwise
direction-forward or inverse transform

Definition at line 281 of file TSpectrum2Transform.cxx.

◆ General2()

void TSpectrum2Transform::General2	(	Double_t **	working_matrix,
		Double_t *	working_vector,
		Int_t	numx,
		Int_t	numy,
		Int_t	direction,
		Int_t	type,
		Int_t	degree
	)

protected

This function calculates generalized (mixed) 2D transforms Function parameters:

working_matrix-pointer to matrix of transformed data
working_vector-pointer to vector where the data are processed
numx,numy-lengths of processed data
direction-forward or inverse
type-type of transform (see manual)
degree-degree of transform (see manual)

Definition at line 1040 of file TSpectrum2Transform.cxx.

◆ GeneralExe()

Int_t TSpectrum2Transform::GeneralExe	(	Double_t *	working_space,
		Int_t	zt_clear,
		Int_t	num,
		Int_t	degree,
		Int_t	type
	)

protected

This function calculates generalized (mixed) transforms of different degrees.

Function parameters:

working_space-pointer to vector of transformed data
zt_clear-flag to clear imaginary data before staring
num-length of processed data
degree-degree of transform (see manual)
type-type of mixed transform (see manual)

Definition at line 449 of file TSpectrum2Transform.cxx.

◆ GeneralInv()

Int_t TSpectrum2Transform::GeneralInv	(	Double_t *	working_space,
		Int_t	num,
		Int_t	degree,
		Int_t	type
	)

protected

This function calculates inverse generalized (mixed) transforms Function parameters:

working_space-pointer to vector of transformed data
num-length of processed data
degree-degree of transform (see manual)
type-type of mixed transform (see manual)

Definition at line 566 of file TSpectrum2Transform.cxx.

◆ Haar()

void TSpectrum2Transform::Haar	(	Double_t *	working_space,
		Int_t	num,
		Int_t	direction
	)

protected

This function calculates Haar transform of a part of data.

Function parameters:

working_space-pointer to vector of transformed data
num-length of processed data
direction-forward or inverse transform

Definition at line 109 of file TSpectrum2Transform.cxx.

◆ HaarWalsh2()

void TSpectrum2Transform::HaarWalsh2	(	Double_t **	working_matrix,
		Double_t *	working_vector,
		Int_t	numx,
		Int_t	numy,
		Int_t	direction,
		Int_t	type
	)

protected

This function calculates 2D Haar and Walsh transforms Function parameters:

working_matrix-pointer to matrix of transformed data
working_vector-pointer to vector where the data are processed
numx,numy-lengths of processed data
direction-forward or inverse
type-type of transform (see manual)

Definition at line 685 of file TSpectrum2Transform.cxx.

◆ IsA()

TClass * TSpectrum2Transform::IsA ( ) const

inlineoverridevirtual

Returns: TClass describing current object

Reimplemented from TObject.

Definition at line 73 of file TSpectrum2Transform.h.

◆ SetDirection()

void TSpectrum2Transform::SetDirection ( Int_t direction )

This function sets the direction of the transform:

direction (forward or inverse)

Definition at line 2762 of file TSpectrum2Transform.cxx.

◆ SetEnhanceCoeff()

void TSpectrum2Transform::SetEnhanceCoeff ( Double_t enhanceCoeff )

This function sets the enhancement coefficient:

enhanceCoeff - after the transform the enhanced region (xmin, xmax, ymin, ymax) is multiplied by this coefficient. Applies only for enhancement operation.

Definition at line 2784 of file TSpectrum2Transform.cxx.

◆ SetFilterCoeff()

void TSpectrum2Transform::SetFilterCoeff ( Double_t filterCoeff )

This function sets the filter coefficient:

filterCoeff - after the transform the filtered region (xmin, xmax, ymin, ymax) is replaced by this coefficient. Applies only for filtereng operation.

Definition at line 2775 of file TSpectrum2Transform.cxx.

◆ SetRegion()

void TSpectrum2Transform::SetRegion	(	Int_t	xmin,
		Int_t	xmax,
		Int_t	ymin,
		Int_t	ymax
	)

This function sets the filtering or enhancement region:

xmin, xmax, ymin, ymax

Definition at line 2742 of file TSpectrum2Transform.cxx.

◆ SetTransformType()

void TSpectrum2Transform::SetTransformType	(	Int_t	transType,
		Int_t	degree
	)

This function sets the following parameters for transform:

transType - type of transform (Haar, Walsh, Cosine, Sine, Fourier, Hartley, Fourier-Walsh, Fourier-Haar, Walsh-Haar, Cosine-Walsh, Cosine-Haar, Sine-Walsh, Sine-Haar)
degree - degree of mixed transform, applies only for Fourier-Walsh, Fourier-Haar, Walsh-Haar, Cosine-Walsh, Cosine-Haar, Sine-Walsh, Sine-Haar transforms

Definition at line 2709 of file TSpectrum2Transform.cxx.

◆ Streamer()

void TSpectrum2Transform::Streamer ( TBuffer & R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TObject.

◆ StreamerNVirtual()

void TSpectrum2Transform::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )

inline

Definition at line 73 of file TSpectrum2Transform.h.

◆ Transform()

void TSpectrum2Transform::Transform	(	const Double_t **	fSource,
		Double_t **	fDest
	)

This function transforms the source spectrum.

The calling program should fill in input parameters. Transformed data are written into dest spectrum.

Function parameters:

fSource-pointer to the matrix of source spectrum, its size should be fSizex*fSizey except for inverse FOURIER, FOUR-WALSH, FOUR-HAAR transform. These need fSizex*2*fSizey length to supply real and imaginary coefficients.
fDest-pointer to the matrix of destination data, its size should be fSizex*fSizey except for direct FOURIER, FOUR-WALSh, FOUR-HAAR. These need fSizex*2*fSizey length to store real and imaginary coefficients
fSizex,fSizey-basic dimensions of source and dest spectra

Transform methods

Goal: to analyse experimental data using orthogonal transforms

orthogonal transforms can be successfully used for the processing of nuclear spectra (not only)
they can be used to remove high frequency noise, to increase signal-to-background ratio as well as to enhance low intensity components [1], to carry out e.g. Fourier analysis etc.
- we have implemented the function for the calculation of the commonly used orthogonal transforms as well as functions for the filtration and enhancement of experimental data

References:

[1] C.V. Hampton, B. Lian, Wm. C. McHarris: Fast-Fourier-transform spectral enhancement techniques for gamma-ray spectroscopy. NIM A353 (1994) 280-284.

[2] Morhac M., Matouoek V., New adaptive Cosine-Walsh transform and its application to nuclear data compression, IEEE Transactions on Signal Processing 48 (2000) 2693.

[3] Morhac M., Matouoek V., Data compression using new fast adaptive Cosine-Haar transforms, Digital Signal Processing 8 (1998) 63.

[4] Morhac M., Matouoek V.: Multidimensional nuclear data compression using fast adaptive Walsh-Haar transform. Acta Physica Slovaca 51 (2001) 307.

Example 1 - script Transform2.c:

Fig. 1 Original two-dimensional noisy spectrum

Fig. 2 Transformed spectrum from Fig. 1 using Cosine transform. Energy of the transformed data is concentrated around the beginning of the coordinate system

Script:

Example to illustrate Transform function (class TSpectrumTransform2). To execute this example, do

root > .x Transform2.C

void Transform2() {
   Int_t i, j;
   Int_t nbinsx = 256;
   Int_t nbinsy = 256;
   Int_t xmin = 0;
   Int_t xmax = nbinsx;
   Int_t ymin = 0;
   Int_t ymax = nbinsy;
   Double_t ** source = new Double_t *[nbinsx];
   Double_t ** dest = new Double_t *[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=newDouble_t[nbinsy];
   for (i=0;i<nbinsx;i++)
      dest[i]=newDouble_t[nbinsy];
   TH2F *trans = newTH2F("trans","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("TSpectrum2.root");
   trans=(TH2F*)f->Get("back3;1");
   TCanvas *Tr = new TCanvas("Transform","Illustration of transform function",10,10,1000,700);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = trans->GetBinContent(i + 1,j + 1);
      }
   }
   TSpectrumTransform2 *t = new TSpectrumTransform2(256,256);
   t->SetTransformType(t->kTransformCos,0);
   t->SetDirection(t->kTransformForward);
   t->Transform(source,dest);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         trans->SetBinContent(i+ 1, j + 1,dest[i][j]);
      }
   }
   trans->Draw("SURF");
}

Definition at line 1748 of file TSpectrum2Transform.cxx.

◆ Walsh()

void TSpectrum2Transform::Walsh	(	Double_t *	working_space,
		Int_t	num
	)

protected

This function calculates Walsh transform of a part of data.

Function parameters:

working_space-pointer to vector of transformed data
num-length of processed data

Definition at line 188 of file TSpectrum2Transform.cxx.

Member Data Documentation

◆ fDegree

Int_t TSpectrum2Transform::fDegree

protected

degree of mixed transform, applies only for Fourier-Walsh, Fourier-Haar, Walsh-Haar, Cosine-Walsh, Cosine-Haar, Sine-Walsh, Sine-Haar transforms

Definition at line 21 of file TSpectrum2Transform.h.

◆ fDirection

Int_t TSpectrum2Transform::fDirection

protected

forward or inverse transform

Definition at line 22 of file TSpectrum2Transform.h.

◆ fEnhanceCoeff

Double_t TSpectrum2Transform::fEnhanceCoeff

protected

multiplication coefficient applied in enhanced region;

Definition at line 28 of file TSpectrum2Transform.h.

◆ fFilterCoeff

Double_t TSpectrum2Transform::fFilterCoeff

protected

value set in the filtered region

Definition at line 27 of file TSpectrum2Transform.h.

◆ fSizeX

Int_t TSpectrum2Transform::fSizeX

protected

x length of transformed data

Definition at line 18 of file TSpectrum2Transform.h.

◆ fSizeY

Int_t TSpectrum2Transform::fSizeY

protected

y length of transformed data

Definition at line 19 of file TSpectrum2Transform.h.

◆ fTransformType

Int_t TSpectrum2Transform::fTransformType

protected

type of transformation (Haar, Walsh, Cosine, Sine, Fourier, Hartley, Fourier-Walsh, Fourier-Haar, Walsh-Haar, Cosine-Walsh, Cosine-Haar, Sine-Walsh, Sine-Haar)

Definition at line 20 of file TSpectrum2Transform.h.

◆ fXmax

Int_t TSpectrum2Transform::fXmax

protected

last channel x of filtered or enhanced region

Definition at line 24 of file TSpectrum2Transform.h.

◆ fXmin

Int_t TSpectrum2Transform::fXmin

protected

first channel x of filtered or enhanced region

Definition at line 23 of file TSpectrum2Transform.h.

◆ fYmax

Int_t TSpectrum2Transform::fYmax

protected

last channel y of filtered or enhanced region

Definition at line 26 of file TSpectrum2Transform.h.

◆ fYmin

Int_t TSpectrum2Transform::fYmin

protected

first channel y of filtered or enhanced region

Definition at line 25 of file TSpectrum2Transform.h.

Libraries for TSpectrum2Transform:

[legend]

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

hist/spectrum/inc/TSpectrum2Transform.h
hist/spectrum/src/TSpectrum2Transform.cxx

Legacy Code

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ TSpectrum2Transform() [1/2]

◆ TSpectrum2Transform() [2/2]

◆ ~TSpectrum2Transform()

Member Function Documentation

◆ BitReverse()

◆ BitReverseHaar()

◆ Class()

◆ Class_Name()

◆ Class_Version()

◆ DeclFileName()

◆ Enhance()

Example of enhancement

Example - script Enhance2.c:

Script:

◆ FilterZonal()

Example of zonal filtering

Example - script Fitler2.c:

Script:

◆ FourCos2()

◆ Fourier()

◆ General2()

◆ GeneralExe()

◆ GeneralInv()

◆ Haar()

◆ HaarWalsh2()

◆ IsA()

◆ SetDirection()

◆ SetEnhanceCoeff()

◆ SetFilterCoeff()

◆ SetRegion()

◆ SetTransformType()

◆ Streamer()

◆ StreamerNVirtual()

◆ Transform()

Transform methods

References:

Example 1 - script Transform2.c:

Script:

◆ Walsh()

Member Data Documentation

◆ fDegree

◆ fDirection

◆ fEnhanceCoeff

◆ fFilterCoeff

◆ fSizeX

◆ fSizeY

◆ fTransformType

◆ fXmax

◆ fXmin

◆ fYmax

◆ fYmin