class TSpectrum2Transform: public TObject

TWO-DIMENSIONAL TRANSFORM FUNCTION
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 analyze 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

 

Function:

void TSpectrumTransform2::Transform(const float **fSource, float **fDest)

 

This function transforms the source spectrum according to the given input parameters. Transformed data are written into dest spectrum. Before the Transform 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 funcions:

 

Member variables of TSpectrumTransform2 class:

fSource-pointer to the matrix of source spectrum. Its lengths should be equal to the “fSizex, fSizey” parameters except for inverse FOURIER, FOUR-WALSH, FOUR-HAAR transforms. These need “2*fSizex*fSizey” length to supply real and imaginary coefficients.                   

fDest-pointer to the matrix of destination spectrum. Its lengths should be equal to the “fSizex, fSizey” parameters except for inverse FOURIER, FOUR-WALSH, FOUR-HAAR transforms. These need “2*fSizex*fSizey” length to store real and imaginary coefficients.

        fSizeX,fSizeY-basic lengths of the source and dest spectra. They should be power  

      of 2.

fType-type of transform

            Classic transforms:

                        kTransformHaar

                        kTransformWalsh

                        kTransformCos

                        kTransformSin

                        kTransformFourier

                        kTransformHartley

            Mixed transforms:

                        kTransformFourierWalsh

                        kTransformFourierHaar

                        kTransformWalshHaar

                        kTransformCosWalsh

                        kTransformCosHaar

                        kTransformSinWalsh

                        kTransformSinHaar

fDirection-direction-transform direction (forward, inverse)

                        kTransformForward

                        kTransformInverse

fDegree-applies only for mixed transforms [2], [3], [4].

                  Allowed range  .

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

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

[4] Morháč M., Matoušek 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 trasnsformed 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;

   Float_t ** source = new float *[nbinsx];  

   Float_t ** dest = new float *[nbinsx];     

   for (i=0;i<nbinsx;i++)

                                                source[i]=new float[nbinsy];

   for (i=0;i<nbinsx;i++)

                                                dest[i]=new float[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","Illustation 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");     

}

TWO-DIMENSIONAL FILTER ZONAL FUNCTION
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

 

Function:

void TSpectrumTransform2::FilterZonal(const float **fSource, float **fDest)

 

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 funcions. 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;

   Float_t ** source = new float *[nbinsx];  

   Float_t ** dest = new float *[nbinsx];     

   for (i=0;i<nbinsx;i++)

                                                source[i]=new float[nbinsy];

   for (i=0;i<nbinsx;i++)

                                                dest[i]=new float[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","Illustation 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");    

}

TWO-DIMENSIONAL ENHANCE ZONAL FUNCTION
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

 

Function:

void TSpectrumTransform2::Enhance(const float **fSource, float **fDest)

 

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 funcions. 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;

   Float_t ** source = new float *[nbinsx];  

   Float_t ** dest = new float *[nbinsx];     

   for (i=0;i<nbinsx;i++)

                                                source[i]=new float[nbinsy];

   for (i=0;i<nbinsx;i++)

                                                dest[i]=new float[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","Illustation 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");    

}