class TSpectrumTransform: public TNamed

        ONE-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:
        source-pointer to the vector of source spectrum, its length should
             be size except for inverse FOURIER, FOUR-WALSH, FOUR-HAAR
             transform. These need 2*size length to supply real and
             imaginary coefficients.
        destVector-pointer to the vector of dest data, its length should be
             size except for direct FOURIER, FOUR-WALSH, FOUR-HAAR. These
             need 2*size length to store real and imaginary coefficients

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 TSpectrumTransform::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 functions.

 

Member variables of TSpectrumTransform class:

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

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

        fSize-basic length of the source and dest spectrum. It should be power of 2.

fType-type of transform

            Classic transforms:

                        kTransformHaar

                        kTransformWalsh

                        kTransformCos

                        kTransformSin

                        kTransformFourier

                        kTransformHartey

            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  – script Transform.c:

Fig. 1 Original gamma-ray spectrum

 

Fig. 2 Transformed spectrum from Fig. 1 using Cosine transform

 

Script:

// Example to illustrate Transform function (class TSpectrumTransform).

// To execute this example, do

// root > .x Transform.C

  

#include <TSpectrum>

#include <TSpectrumTransform>

 

void Transform() {

   Int_t i;

   Double_t nbins = 4096;

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbins;

   Float_t * source = new float[nbins];

   Float_t * dest = new float[nbins];  

   TH1F *h = new TH1F("h","Transformed spectrum using Cosine transform",nbins,xmin,xmax);

   TFile *f = new TFile("spectra\\TSpectrum.root");

   h=(TH1F*) f->Get("transform1;1");  

   for (i = 0; i < nbins; i++) source[i]=h->GetBinContent(i + 1);        

   TCanvas *Transform1 = gROOT->GetListOfCanvases()->FindObject("Transform1");

   if (!Transform1) Transform1 = new TCanvas("Transform","Transform1",10,10,1000,700);

   TSpectrum *s = new TSpectrum();

   TSpectrumTransform *t = new TSpectrumTransform(4096);

   t->SetTransformType(t->kTransformCos,0);

   t->SetDirection(t->kTransformForward);

   t->Transform(source,dest);

   for (i = 0; i < nbins; i++) h->SetBinContent(i + 1,dest[i]);  

   h->SetLineColor(kRed);     

   h->Draw("L");

}

        ONE-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 (fXmin, fXmax) to the given
        fFilterCoeff and transforms it back.
        Filtered data are written into dest spectrum.

        Function parameters:
        source-pointer to the vector of source spectrum, its length should
             be size except for inverse FOURIER, FOUR-WALSH, FOUR-HAAR
             transform. These need 2*size length to supply real and
             imaginary coefficients.
        destVector-pointer to the vector of dest data, its length should be
           size except for direct FOURIER, FOUR-WALSH, FOUR-HAAR. These
           need 2*size length to store real and imaginary coefficients

Example of zonal filtering

 

Function:

void TSpectrumTransform::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 Filter.c:

Fig. 1 Original spectrum (black line) and filtered spectrum (red line) using Cosine transform and zonal filtration (channels 2048-4095 were set to 0)

 

Script:

// Example to illustrate FilterZonal function (class TSpectrumTransform).

// To execute this example, do

// root > .x Filter.C

  

#include <TSpectrum>

#include <TSpectrumTransform>

 

void Filter() {

   Int_t i;

   Double_t nbins = 4096;

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbins;

   Float_t * source = new float[nbins];

   Float_t * dest = new float[nbins];  

   TH1F *h = new TH1F("h","Zonal filtering using Cosine transform",nbins,xmin,xmax);

   TH1F *d = new TH1F("d","",nbins,xmin,xmax);        

   TFile *f = new TFile("spectra\\TSpectrum.root");

   h=(TH1F*) f->Get("transform1;1");  

   for (i = 0; i < nbins; i++) source[i]=h->GetBinContent(i + 1);    

   TCanvas *Transform1 = gROOT->GetListOfCanvases()->FindObject("Transform1");

   if (!Transform1) Transform1 = new TCanvas("Transform","Transform1",10,10,1000,700);

   h->SetAxisRange(700,1024);  

   h->Draw("L");  

   TSpectrum *s = new TSpectrum();

   TSpectrumTransform *t = new TSpectrumTransform(4096);

   t->SetTransformType(t->kTransformCos,0);

   t->SetRegion(2048, 4095);

   t->FilterZonal(source,dest);    

   for (i = 0; i < nbins; i++) d->SetBinContent(i + 1,dest[i]);

   d->SetLineColor(kRed);  

   d->Draw("SAME L");

}

        ONE-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 (fXmin, fXmax) by the given
      fEnhanceCoeff and transforms it back
        Processed data are written into dest spectrum.

        Function parameters:
        source-pointer to the vector of source spectrum, its length should
             be size except for inverse FOURIER, FOUR-WALSh, FOUR-HAAR
             transform. These need 2*size length to supply real and
             imaginary coefficients.
        destVector-pointer to the vector of dest data, its length should be
           size except for direct FOURIER, FOUR-WALSh, FOUR-HAAR. These
           need 2*size length to store real and imaginary coefficients

Example of enhancement

 

Function:

void TSpectrumTransform::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) by the given fEnhancCoeff and transforms it back. Enhanced data are written into dest spectrum.

 

Example  – script Enhance.c:

 

Fig. 1 Original spectrum (black line) and enhanced spectrum (red line) using Cosine transform (channels 0-1024 were multiplied by 2)

 

Script:

 

// Example to illustrate Enhance function (class TSpectrumTransform).

// To execute this example, do

// root > .x Enhance.C

 

void Enhance() {

   Int_t i;

   Double_t nbins = 4096;

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbins;

   Float_t * source = new float[nbins];

   Float_t * dest = new float[nbins];  

   TH1F *h = new TH1F("h","Enhancement using Cosine transform",nbins,xmin,xmax);

   TH1F *d = new TH1F("d","",nbins,xmin,xmax);        

   TFile *f = new TFile("spectra\\TSpectrum.root");

   h=(TH1F*) f->Get("transform1;1");  

   for (i = 0; i < nbins; i++) source[i]=h->GetBinContent(i + 1);    

   TCanvas *Transform1 = gROOT->GetListOfCanvases()->FindObject("Transform1");

   if (!Transform1) Transform1 = new TCanvas("Transform","Transform1",10,10,1000,700);

   h->SetAxisRange(700,1024);  

   h->Draw("L");  

   TSpectrum *s = new TSpectrum();

   TSpectrumTransform *t = new TSpectrumTransform(4096);

   t->SetTransformType(t->kTransformCos,0);

   t->SetRegion(0, 1024);

   t->SetEnhanceCoeff(2);

   t->Enhance(source,dest);       

   for (i = 0; i < nbins; i++) d->SetBinContent(i + 1,dest[i]);

   d->SetLineColor(kRed);  

   d->Draw("SAME L");

}