// @(#)root/spectrum:$Id$
// Author: Miroslav Morhac 25/09/06
//__________________________________________________________________________
// THIS CLASS CONTAINS ORTHOGONAL TRANSFORM FUNCTIONS. //
// //
// These functions were written by: //
// Miroslav Morhac //
// Institute of Physics //
// Slovak Academy of Sciences //
// Dubravska cesta 9, 842 28 BRATISLAVA //
// SLOVAKIA //
// //
// email:fyzimiro@savba.sk, fax:+421 7 54772479 //
// //
// The original code in C has been repackaged as a C++ class by R.Brun //
// //
// The algorithms in this class have been published in the following //
// 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., Matousek V., New adaptive Cosine-Walsh transform and //
// its application to nuclear data compression, IEEE Transactions on //
// Signal Processing 48 (2000) 2693. //
// [3] Morhac M., Matousek V., Data compression using new fast adaptive //
// Cosine-Haar transforms, Digital Signal Processing 8 (1998) 63. //
// [4] Morhac M., Matousek V.: Multidimensional nuclear data compression //
// using fast adaptive Walsh-Haar transform. Acta Physica Slovaca 51 //
// (2001) 307. //
//____________________________________________________________________________
#include "TSpectrumTransform.h"
#include "TMath.h"
ClassImp(TSpectrumTransform)
//____________________________________________________________________________
TSpectrumTransform::TSpectrumTransform()
{
//default constructor
fSize=0;
fTransformType=kTransformCos;
fDegree=0;
fDirection=kTransformForward;
fXmin=0;
fXmax=0;
fFilterCoeff=0;
fEnhanceCoeff=0.5;
}
//____________________________________________________________________________
TSpectrumTransform::TSpectrumTransform(Int_t size):TNamed("SpectrumTransform", "Miroslav Morhac transformer")
{
//the constructor creates TSpectrumTransform object. Its size 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.
Int_t j,n;
if (size <= 0){
Error ("TSpectrumTransform","Invalid length, must be > than 0");
return;
}
j = 0;
n = 1;
for (; n < size;) {
j += 1;
n = n * 2;
}
if (n != size){
Error ("TSpectrumTransform","Invalid length, must be power of 2");
return;
}
fSize=size;
fTransformType=kTransformCos;
fDegree=0;
fDirection=kTransformForward;
fXmin=size/4;
fXmax=size-1;
fFilterCoeff=0;
fEnhanceCoeff=0.5;
}
//______________________________________________________________________________
TSpectrumTransform::~TSpectrumTransform()
{
//destructor
}
//_____________________________________________________________________________
void TSpectrumTransform::Haar(float *working_space, int num, int direction)
{
//////////////////////////////////////////////////////////////////////////////////
// AUXILIARY FUNCION //
// //
// 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 //
// //
//////////////////////////////////////////////////////////////////////////////////
int i, ii, li, l2, l3, j, jj, jj1, lj, iter, m, jmin, jmax;
double a, b, c, wlk;
float val;
for (i = 0; i < num; i++)
working_space[i + num] = 0;
i = num;
iter = 0;
for (; i > 1;) {
iter += 1;
i = i / 2;
}
if (direction == kTransformForward) {
for (m = 1; m <= iter; m++) {
li = iter + 1 - m;
l2 = (int) TMath::Power(2, li - 1);
for (i = 0; i < (2 * l2); i++) {
working_space[num + i] = working_space[i];
}
for (j = 0; j < l2; j++) {
l3 = l2 + j;
jj = 2 * j;
val = working_space[jj + num] + working_space[jj + 1 + num];
working_space[j] = val;
val = working_space[jj + num] - working_space[jj + 1 + num];
working_space[l3] = val;
}
}
}
val = working_space[0];
val = val / TMath::Sqrt(TMath::Power(2, iter));
working_space[0] = val;
val = working_space[1];
val = val / TMath::Sqrt(TMath::Power(2, iter));
working_space[1] = val;
for (ii = 2; ii <= iter; ii++) {
i = ii - 1;
wlk = 1 / TMath::Sqrt(TMath::Power(2, iter - i));
jmin = (int) TMath::Power(2, i);
jmax = (int) TMath::Power(2, ii) - 1;
for (j = jmin; j <= jmax; j++) {
val = working_space[j];
a = val;
a = a * wlk;
val = a;
working_space[j] = val;
}
}
if (direction == kTransformInverse) {
for (m = 1; m <= iter; m++) {
a = 2;
b = m - 1;
c = TMath::Power(a, b);
li = (int) c;
for (i = 0; i < (2 * li); i++) {
working_space[i + num] = working_space[i];
}
for (j = 0; j < li; j++) {
lj = li + j;
jj = 2 * (j + 1) - 1;
jj1 = jj - 1;
val = working_space[j + num] - working_space[lj + num];
working_space[jj] = val;
val = working_space[j + num] + working_space[lj + num];
working_space[jj1] = val;
}
}
}
return;
}
//____________________________________________________________________________
void TSpectrumTransform::Walsh(float *working_space, int num)
{
//////////////////////////////////////////////////////////////////////////////////
// AUXILIARY FUNCION //
// //
// 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 //
// //
//////////////////////////////////////////////////////////////////////////////////
int i, m, nump = 1, mnum, mnum2, mp, ib, mp2, mnum21, iba, iter;
double a;
float val1, val2;
for (i = 0; i < num; i++)
working_space[i + num] = 0;
i = num;
iter = 0;
for (; i > 1;) {
iter += 1;
i = i / 2;
}
for (m = 1; m <= iter; m++) {
if (m == 1)
nump = 1;
else
nump = nump * 2;
mnum = num / nump;
mnum2 = mnum / 2;
for (mp = 0; mp < nump; mp++) {
ib = mp * mnum;
for (mp2 = 0; mp2 < mnum2; mp2++) {
mnum21 = mnum2 + mp2 + ib;
iba = ib + mp2;
val1 = working_space[iba];
val2 = working_space[mnum21];
working_space[iba + num] = val1 + val2;
working_space[mnum21 + num] = val1 - val2;
}
}
for (i = 0; i < num; i++) {
working_space[i] = working_space[i + num];
}
}
a = num;
a = TMath::Sqrt(a);
val2 = a;
for (i = 0; i < num; i++) {
val1 = working_space[i];
val1 = val1 / val2;
working_space[i] = val1;
}
return;
}
//____________________________________________________________________________
void TSpectrumTransform::BitReverse(float *working_space, int num)
{
//////////////////////////////////////////////////////////////////////////////////
// AUXILIARY FUNCION //
// //
// This function carries out bir-reverse reordering of data //
// Function parameters: //
// -working_space-pointer to vector of processed data //
// -num-length of processed data //
// //
//////////////////////////////////////////////////////////////////////////////////
int ipower[26];
int i, ib, il, ibd, ip, ifac, i1;
for (i = 0; i < num; i++) {
working_space[i + num] = working_space[i];
}
for (i = 1; i <= num; i++) {
ib = i - 1;
il = 1;
lab9:ibd = ib / 2;
ipower[il - 1] = 1;
if (ib == (ibd * 2))
ipower[il - 1] = 0;
if (ibd == 0)
goto lab10;
ib = ibd;
il = il + 1;
goto lab9;
lab10:ip = 1;
ifac = num;
for (i1 = 1; i1 <= il; i1++) {
ifac = ifac / 2;
ip = ip + ifac * ipower[i1 - 1];
}
working_space[ip - 1] = working_space[i - 1 + num];
}
return;
}
//____________________________________________________________________________
void TSpectrumTransform::Fourier(float *working_space, int num, int hartley,
int direction, int zt_clear)
{
//////////////////////////////////////////////////////////////////////////////////
// AUXILIARY FUNCION //
// //
// 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 othewise //
// -direction-forward or inverse transform //
// //
//////////////////////////////////////////////////////////////////////////////////
int nxp2, nxp, i, j, k, m, iter, mxp, j1, j2, n1, n2, it;
double a, b, c, d, sign, wpwr, arg, wr, wi, tr, ti, pi =
3.14159265358979323846;
float val1, val2, val3, val4;
if (direction == kTransformForward && zt_clear == 0) {
for (i = 0; i < num; i++)
working_space[i + num] = 0;
}
i = num;
iter = 0;
for (; i > 1;) {
iter += 1;
i = i / 2;
}
sign = -1;
if (direction == kTransformInverse)
sign = 1;
nxp2 = num;
for (it = 1; it <= iter; it++) {
nxp = nxp2;
nxp2 = nxp / 2;
a = nxp2;
wpwr = pi / a;
for (m = 1; m <= nxp2; m++) {
a = m - 1;
arg = a * wpwr;
wr = TMath::Cos(arg);
wi = sign * TMath::Sin(arg);
for (mxp = nxp; mxp <= num; mxp += nxp) {
j1 = mxp - nxp + m;
j2 = j1 + nxp2;
val1 = working_space[j1 - 1];
val2 = working_space[j2 - 1];
val3 = working_space[j1 - 1 + num];
val4 = working_space[j2 - 1 + num];
a = val1;
b = val2;
c = val3;
d = val4;
tr = a - b;
ti = c - d;
a = a + b;
val1 = a;
working_space[j1 - 1] = val1;
c = c + d;
val1 = c;
working_space[j1 - 1 + num] = val1;
a = tr * wr - ti * wi;
val1 = a;
working_space[j2 - 1] = val1;
a = ti * wr + tr * wi;
val1 = a;
working_space[j2 - 1 + num] = val1;
}
}
}
n2 = num / 2;
n1 = num - 1;
j = 1;
for (i = 1; i <= n1; i++) {
if (i >= j)
goto lab55;
val1 = working_space[j - 1];
val2 = working_space[j - 1 + num];
val3 = working_space[i - 1];
working_space[j - 1] = val3;
working_space[j - 1 + num] = working_space[i - 1 + num];
working_space[i - 1] = val1;
working_space[i - 1 + num] = val2;
lab55: k = n2;
lab60: if (k >= j) goto lab65;
j = j - k;
k = k / 2;
goto lab60;
lab65: j = j + k;
}
a = num;
a = TMath::Sqrt(a);
for (i = 0; i < num; i++) {
if (hartley == 0) {
val1 = working_space[i];
b = val1;
b = b / a;
val1 = b;
working_space[i] = val1;
b = working_space[i + num];
b = b / a;
working_space[i + num] = b;
}
else {
b = working_space[i];
c = working_space[i + num];
b = (b + c) / a;
working_space[i] = b;
working_space[i + num] = 0;
}
}
if (hartley == 1 && direction == kTransformInverse) {
for (i = 1; i < num; i++)
working_space[num - i + num] = working_space[i];
working_space[0 + num] = working_space[0];
for (i = 0; i < num; i++) {
working_space[i] = working_space[i + num];
working_space[i + num] = 0;
}
}
return;
}
//____________________________________________________________________________
void TSpectrumTransform::BitReverseHaar(float *working_space, int shift, int num,
int start)
{
//////////////////////////////////////////////////////////////////////////////////
// AUXILIARY FUNCION //
// //
// This function carries out bir-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 //
// //
//////////////////////////////////////////////////////////////////////////////////
int ipower[26];
int i, ib, il, ibd, ip, ifac, i1;
for (i = 0; i < num; i++) {
working_space[i + shift + start] = working_space[i + start];
working_space[i + shift + start + 2 * shift] =
working_space[i + start + 2 * shift];
}
for (i = 1; i <= num; i++) {
ib = i - 1;
il = 1;
lab9: ibd = ib / 2;
ipower[il - 1] = 1;
if (ib == (ibd * 2))
ipower[il - 1] = 0;
if (ibd == 0)
goto lab10;
ib = ibd;
il = il + 1;
goto lab9;
lab10: ip = 1;
ifac = num;
for (i1 = 1; i1 <= il; i1++) {
ifac = ifac / 2;
ip = ip + ifac * ipower[i1 - 1];
}
working_space[ip - 1 + start] =
working_space[i - 1 + shift + start];
working_space[ip - 1 + start + 2 * shift] =
working_space[i - 1 + shift + start + 2 * shift];
}
return;
}
//____________________________________________________________________________
int TSpectrumTransform::GeneralExe(float *working_space, int zt_clear, int num,
int degree, int type)
{
//////////////////////////////////////////////////////////////////////////////////
// AUXILIARY FUNCION //
// //
// 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) //
// //
//////////////////////////////////////////////////////////////////////////////////
int i, j, k, m, nump, mnum, mnum2, mp, ib, mp2, mnum21, iba, iter,
mp2step, mppom, ring;
double a, b, c, d, wpwr, arg, wr, wi, tr, ti, pi =
3.14159265358979323846;
float val1, val2, val3, val4, a0oldr = 0, b0oldr = 0, a0r, b0r;
if (zt_clear == 0) {
for (i = 0; i < num; i++)
working_space[i + 2 * num] = 0;
}
i = num;
iter = 0;
for (; i > 1;) {
iter += 1;
i = i / 2;
}
a = num;
wpwr = 2.0 * pi / a;
nump = num;
mp2step = 1;
ring = num;
for (i = 0; i < iter - degree; i++)
ring = ring / 2;
for (m = 1; m <= iter; m++) {
nump = nump / 2;
mnum = num / nump;
mnum2 = mnum / 2;
if (m > degree
&& (type == kTransformFourierHaar
|| type == kTransformWalshHaar
|| type == kTransformCosHaar
|| type == kTransformSinHaar))
mp2step *= 2;
if (ring > 1)
ring = ring / 2;
for (mp = 0; mp < nump; mp++) {
if (type != kTransformWalshHaar) {
mppom = mp;
mppom = mppom % ring;
a = 0;
j = 1;
k = num / 4;
for (i = 0; i < (iter - 1); i++) {
if ((mppom & j) != 0)
a = a + k;
j = j * 2;
k = k / 2;
}
arg = a * wpwr;
wr = TMath::Cos(arg);
wi = TMath::Sin(arg);
}
else {
wr = 1;
wi = 0;
}
ib = mp * mnum;
for (mp2 = 0; mp2 < mnum2; mp2++) {
mnum21 = mnum2 + mp2 + ib;
iba = ib + mp2;
if (mp2 % mp2step == 0) {
a0r = a0oldr;
b0r = b0oldr;
a0r = 1 / TMath::Sqrt(2.0);
b0r = 1 / TMath::Sqrt(2.0);
}
else {
a0r = 1;
b0r = 0;
}
val1 = working_space[iba];
val2 = working_space[mnum21];
val3 = working_space[iba + 2 * num];
val4 = working_space[mnum21 + 2 * num];
a = val1;
b = val2;
c = val3;
d = val4;
tr = a * a0r + b * b0r;
val1 = tr;
working_space[num + iba] = val1;
ti = c * a0r + d * b0r;
val1 = ti;
working_space[num + iba + 2 * num] = val1;
tr =
a * b0r * wr - c * b0r * wi - b * a0r * wr + d * a0r * wi;
val1 = tr;
working_space[num + mnum21] = val1;
ti =
c * b0r * wr + a * b0r * wi - d * a0r * wr - b * a0r * wi;
val1 = ti;
working_space[num + mnum21 + 2 * num] = val1;
}
}
for (i = 0; i < num; i++) {
val1 = working_space[num + i];
working_space[i] = val1;
val1 = working_space[num + i + 2 * num];
working_space[i + 2 * num] = val1;
}
}
return (0);
}
//____________________________________________________________________________
int TSpectrumTransform::GeneralInv(float *working_space, int num, int degree,
int type)
{
//////////////////////////////////////////////////////////////////////////////////
// AUXILIARY FUNCION //
// //
// 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) //
// //
//////////////////////////////////////////////////////////////////////////////////
int i, j, k, m, nump =
1, mnum, mnum2, mp, ib, mp2, mnum21, iba, iter, mp2step, mppom,
ring;
double a, b, c, d, wpwr, arg, wr, wi, tr, ti, pi =
3.14159265358979323846;
float val1, val2, val3, val4, a0oldr = 0, b0oldr = 0, a0r, b0r;
i = num;
iter = 0;
for (; i > 1;) {
iter += 1;
i = i / 2;
}
a = num;
wpwr = 2.0 * pi / a;
mp2step = 1;
if (type == kTransformFourierHaar || type == kTransformWalshHaar
|| type == kTransformCosHaar || type == kTransformSinHaar) {
for (i = 0; i < iter - degree; i++)
mp2step *= 2;
}
ring = 1;
for (m = 1; m <= iter; m++) {
if (m == 1)
nump = 1;
else
nump = nump * 2;
mnum = num / nump;
mnum2 = mnum / 2;
if (m > iter - degree + 1)
ring *= 2;
for (mp = nump - 1; mp >= 0; mp--) {
if (type != kTransformWalshHaar) {
mppom = mp;
mppom = mppom % ring;
a = 0;
j = 1;
k = num / 4;
for (i = 0; i < (iter - 1); i++) {
if ((mppom & j) != 0)
a = a + k;
j = j * 2;
k = k / 2;
}
arg = a * wpwr;
wr = TMath::Cos(arg);
wi = TMath::Sin(arg);
}
else {
wr = 1;
wi = 0;
}
ib = mp * mnum;
for (mp2 = 0; mp2 < mnum2; mp2++) {
mnum21 = mnum2 + mp2 + ib;
iba = ib + mp2;
if (mp2 % mp2step == 0) {
a0r = a0oldr;
b0r = b0oldr;
a0r = 1 / TMath::Sqrt(2.0);
b0r = 1 / TMath::Sqrt(2.0);
}
else {
a0r = 1;
b0r = 0;
}
val1 = working_space[iba];
val2 = working_space[mnum21];
val3 = working_space[iba + 2 * num];
val4 = working_space[mnum21 + 2 * num];
a = val1;
b = val2;
c = val3;
d = val4;
tr = a * a0r + b * wr * b0r + d * wi * b0r;
val1 = tr;
working_space[num + iba] = val1;
ti = c * a0r + d * wr * b0r - b * wi * b0r;
val1 = ti;
working_space[num + iba + 2 * num] = val1;
tr = a * b0r - b * wr * a0r - d * wi * a0r;
val1 = tr;
working_space[num + mnum21] = val1;
ti = c * b0r - d * wr * a0r + b * wi * a0r;
val1 = ti;
working_space[num + mnum21 + 2 * num] = val1;
}
}
if (m <= iter - degree
&& (type == kTransformFourierHaar
|| type == kTransformWalshHaar
|| type == kTransformCosHaar
|| type == kTransformSinHaar))
mp2step /= 2;
for (i = 0; i < num; i++) {
val1 = working_space[num + i];
working_space[i] = val1;
val1 = working_space[num + i + 2 * num];
working_space[i + 2 * num] = val1;
}
}
return (0);
}
//////////END OF AUXILIARY FUNCTIONS FOR TRANSFORM! FUNCTION////////////////////////
//////////TRANSFORM FUNCTION - CALCULATES DIFFERENT 1-D DIRECT AND INVERSE ORTHOGONAL TRANSFORMS//////
//____________________________________________________________________________
void TSpectrumTransform::Transform(const float *source, float *destVector)
{
///////////////////////////////////////////////////////////////////////////////
// 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
//
///////////////////////////////////////////////////////////////////////////////
//Begin_Html
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");
}
End_Html
int i, j=0, k = 1, m, l;
float val;
double a, b, pi = 3.14159265358979323846;
float *working_space = 0;
if (fTransformType >= kTransformFourierWalsh && fTransformType <= kTransformSinHaar) {
if (fTransformType >= kTransformCosWalsh)
fDegree += 1;
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
}
switch (fTransformType) {
case kTransformHaar:
case kTransformWalsh:
working_space = new float[2 * fSize];
break;
case kTransformCos:
case kTransformSin:
case kTransformFourier:
case kTransformHartley:
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
working_space = new float[4 * fSize];
break;
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
working_space = new float[8 * fSize];
break;
}
if (fDirection == kTransformForward) {
switch (fTransformType) {
case kTransformHaar:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Haar(working_space, fSize, fDirection);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformWalsh:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Walsh(working_space, fSize);
BitReverse(working_space, fSize);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformCos:
fSize = 2 * fSize;
for (i = 1; i <= (fSize / 2); i++) {
val = source[i - 1];
working_space[i - 1] = val;
working_space[fSize - i] = val;
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
a = TMath::Cos(a);
b = working_space[i];
a = b / a;
working_space[i] = a;
working_space[i + fSize] = 0;
} working_space[0] = working_space[0] / TMath::Sqrt(2.0);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformSin:
fSize = 2 * fSize;
for (i = 1; i <= (fSize / 2); i++) {
val = source[i - 1];
working_space[i - 1] = val;
working_space[fSize - i] = -val;
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
a = TMath::Sin(a);
b = working_space[i];
if (a != 0)
a = b / a;
working_space[i - 1] = a;
working_space[i + fSize] = 0;
}
working_space[fSize / 2 - 1] =
working_space[fSize / 2] / TMath::Sqrt(2.0);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourier:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
for (i = 0; i < 2 * fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformHartley:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 1, kTransformForward, 0);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
for (i = 0; i < fSize; i++) {
val = source[i];
if (fTransformType == kTransformCosWalsh
|| fTransformType == kTransformCosHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
k = i / j;
k = 2 * k * j;
working_space[k + i % j] = val;
working_space[k + 2 * j - 1 - i % j] = val;
}
else if (fTransformType == kTransformSinWalsh
|| fTransformType == kTransformSinHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
k = i / j;
k = 2 * k * j;
working_space[k + i % j] = val;
working_space[k + 2 * j - 1 - i % j] = -val;
}
else
working_space[i] = val;
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar
|| fTransformType == kTransformWalshHaar) {
for (i = 0; i < j; i++)
BitReverseHaar(working_space, fSize, k, i * k);
GeneralExe(working_space, 0, fSize, fDegree, fTransformType);
}
else if (fTransformType == kTransformCosWalsh
|| fTransformType == kTransformCosHaar) {
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
GeneralExe(working_space, 0, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
a = TMath::Cos(a);
b = working_space[k + i % j];
if (i % j == 0)
a = b / TMath::Sqrt(2.0);
else
a = b / a;
working_space[i] = a;
working_space[i + 2 * fSize] = 0;
}
}
else if (fTransformType == kTransformSinWalsh
|| fTransformType == kTransformSinHaar) {
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
GeneralExe(working_space, 0, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
a = TMath::Cos(a);
b = working_space[j + k + i % j];
if (i % j == 0)
a = b / TMath::Sqrt(2.0);
else
a = b / a;
working_space[j + k / 2 - i % j - 1] = a;
working_space[i + 2 * fSize] = 0;
}
}
if (fTransformType > kTransformWalshHaar)
k = (int) TMath::Power(2, fDegree - 1);
else
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
for (i = 0, l = 0; i < fSize; i++, l = (l + k) % fSize) {
working_space[fSize + i] = working_space[l + i / j];
working_space[fSize + i + 2 * fSize] =
working_space[l + i / j + 2 * fSize];
}
for (i = 0; i < fSize; i++) {
working_space[i] = working_space[fSize + i];
working_space[i + 2 * fSize] =
working_space[fSize + i + 2 * fSize];
}
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar) {
for (i = 0; i < fSize; i++) {
destVector[fSize + i] = working_space[i + 2 * fSize];
}
}
break;
}
}
else if (fDirection == kTransformInverse) {
switch (fTransformType) {
case kTransformHaar:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Haar(working_space, fSize, fDirection);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformWalsh:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
BitReverse(working_space, fSize);
Walsh(working_space, fSize);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformCos:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
fSize = 2 * fSize;
working_space[0] = working_space[0] * TMath::Sqrt(2.0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[i + fSize] = (double) working_space[i] * b;
working_space[i] = (double) working_space[i] * a;
} for (i = 2; i <= (fSize / 2); i++) {
working_space[fSize - i + 1] = working_space[i - 1];
working_space[fSize - i + 1 + fSize] =
-working_space[i - 1 + fSize];
}
working_space[fSize / 2] = 0;
working_space[fSize / 2 + fSize] = 0;
Fourier(working_space, fSize, 0, kTransformInverse, 1);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformSin:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
fSize = 2 * fSize;
working_space[fSize / 2] =
working_space[fSize / 2 - 1] * TMath::Sqrt(2.0);
for (i = fSize / 2 - 1; i > 0; i--) {
a = pi * (double) i / (double) fSize;
working_space[i + fSize] =
-(double) working_space[i - 1] * TMath::Cos(a);
working_space[i] =
(double) working_space[i - 1] * TMath::Sin(a);
} for (i = 2; i <= (fSize / 2); i++) {
working_space[fSize - i + 1] = working_space[i - 1];
working_space[fSize - i + 1 + fSize] =
-working_space[i - 1 + fSize];
}
working_space[0] = 0;
working_space[fSize] = 0;
working_space[fSize / 2 + fSize] = 0;
Fourier(working_space, fSize, 0, kTransformInverse, 0);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourier:
for (i = 0; i < 2 * fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 0, kTransformInverse, 0);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformHartley:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 1, kTransformInverse, 0);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar) {
for (i = 0; i < fSize; i++) {
working_space[i + 2 * fSize] = source[fSize + i];
}
}
if (fTransformType > kTransformWalshHaar)
k = (int) TMath::Power(2, fDegree - 1);
else
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
for (i = 0, l = 0; i < fSize; i++, l = (l + k) % fSize) {
working_space[fSize + l + i / j] = working_space[i];
working_space[fSize + l + i / j + 2 * fSize] =
working_space[i + 2 * fSize];
}
for (i = 0; i < fSize; i++) {
working_space[i] = working_space[fSize + i];
working_space[i + 2 * fSize] =
working_space[fSize + i + 2 * fSize];
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar
|| fTransformType == kTransformWalshHaar) {
GeneralInv(working_space, fSize, fDegree, fTransformType);
for (i = 0; i < j; i++)
BitReverseHaar(working_space, fSize, k, i * k);
}
else if (fTransformType == kTransformCosWalsh
|| fTransformType == kTransformCosHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
if (i % j == 0) {
working_space[2 * fSize + k + i % j] =
working_space[i] * TMath::Sqrt(2.0);
working_space[4 * fSize + 2 * fSize + k + i % j] = 0;
}
else {
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[4 * fSize + 2 * fSize + k + i % j] =
-(double) working_space[i] * b;
working_space[2 * fSize + k + i % j] =
(double) working_space[i] * a;
} } for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
if (i % j == 0) {
working_space[2 * fSize + k + j] = 0;
working_space[4 * fSize + 2 * fSize + k + j] = 0;
}
else {
working_space[2 * fSize + k + 2 * j - i % j] =
working_space[2 * fSize + k + i % j];
working_space[4 * fSize + 2 * fSize + k + 2 * j - i % j] =
-working_space[4 * fSize + 2 * fSize + k + i % j];
}
}
for (i = 0; i < 2 * fSize; i++) {
working_space[i] = working_space[2 * fSize + i];
working_space[4 * fSize + i] =
working_space[4 * fSize + 2 * fSize + i];
}
GeneralInv(working_space, 2 * fSize, fDegree, fTransformType);
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
}
else if (fTransformType == kTransformSinWalsh
|| fTransformType == kTransformSinHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
if (i % j == 0) {
working_space[2 * fSize + k + j + i % j] =
working_space[j + k / 2 - i % j -
1] * TMath::Sqrt(2.0);
working_space[4 * fSize + 2 * fSize + k + j + i % j] = 0;
}
else {
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[4 * fSize + 2 * fSize + k + j + i % j] =
-(double) working_space[j + k / 2 - i % j - 1] * b;
working_space[2 * fSize + k + j + i % j] =
(double) working_space[j + k / 2 - i % j - 1] * a;
} } for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
if (i % j == 0) {
working_space[2 * fSize + k] = 0;
working_space[4 * fSize + 2 * fSize + k] = 0;
}
else {
working_space[2 * fSize + k + i % j] =
working_space[2 * fSize + k + 2 * j - i % j];
working_space[4 * fSize + 2 * fSize + k + i % j] =
-working_space[4 * fSize + 2 * fSize + k + 2 * j -
i % j];
}
}
for (i = 0; i < 2 * fSize; i++) {
working_space[i] = working_space[2 * fSize + i];
working_space[4 * fSize + i] =
working_space[4 * fSize + 2 * fSize + i];
}
GeneralInv(working_space, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
}
for (i = 0; i < fSize; i++) {
if (fTransformType >= kTransformCosWalsh) {
k = i / j;
k = 2 * k * j;
val = working_space[k + i % j];
}
else
val = working_space[i];
destVector[i] = val;
}
break;
}
}
delete[]working_space;
return;
}
//////////FilterZonal FUNCTION - CALCULATES DIFFERENT 1-D ORTHOGONAL TRANSFORMS, SETS GIVEN REGION TO FILTER COEFFICIENT AND TRANSFORMS IT BACK//////
//______________________________________________________________________________
void TSpectrumTransform::FilterZonal(const float *source, float *destVector)
{
////////////////////////////////////////////////////////////////////////////////
// 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
//
////////////////////////////////////////////////////////////////////////////////
//
//Begin_Html
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
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 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");
}
End_Html
int i, j=0, k = 1, m, l;
float val;
float *working_space = 0;
double a, b, pi = 3.14159265358979323846, old_area, new_area;
if (fTransformType >= kTransformFourierWalsh && fTransformType <= kTransformSinHaar) {
if (fTransformType >= kTransformCosWalsh)
fDegree += 1;
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
}
switch (fTransformType) {
case kTransformHaar:
case kTransformWalsh:
working_space = new float[2 * fSize];
break;
case kTransformCos:
case kTransformSin:
case kTransformFourier:
case kTransformHartley:
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
working_space = new float[4 * fSize];
break;
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
working_space = new float[8 * fSize];
break;
}
switch (fTransformType) {
case kTransformHaar:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Haar(working_space, fSize, kTransformForward);
break;
case kTransformWalsh:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Walsh(working_space, fSize);
BitReverse(working_space, fSize);
break;
case kTransformCos:
fSize = 2 * fSize;
for (i = 1; i <= (fSize / 2); i++) {
val = source[i - 1];
working_space[i - 1] = val;
working_space[fSize - i] = val;
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
a = TMath::Cos(a);
b = working_space[i];
a = b / a;
working_space[i] = a;
working_space[i + fSize] = 0;
} working_space[0] = working_space[0] / TMath::Sqrt(2.0);
fSize = fSize / 2;
break;
case kTransformSin:
fSize = 2 * fSize;
for (i = 1; i <= (fSize / 2); i++) {
val = source[i - 1];
working_space[i - 1] = val;
working_space[fSize - i] = -val;
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
a = TMath::Sin(a);
b = working_space[i];
if (a != 0)
a = b / a;
working_space[i - 1] = a;
working_space[i + fSize] = 0;
}
working_space[fSize / 2 - 1] =
working_space[fSize / 2] / TMath::Sqrt(2.0);
fSize = fSize / 2;
break;
case kTransformFourier:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
break;
case kTransformHartley:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 1, kTransformForward, 0);
break;
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
for (i = 0; i < fSize; i++) {
val = source[i];
if (fTransformType == kTransformCosWalsh || fTransformType == kTransformCosHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
k = i / j;
k = 2 * k * j;
working_space[k + i % j] = val;
working_space[k + 2 * j - 1 - i % j] = val;
}
else if (fTransformType == kTransformSinWalsh
|| fTransformType == kTransformSinHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
k = i / j;
k = 2 * k * j;
working_space[k + i % j] = val;
working_space[k + 2 * j - 1 - i % j] = -val;
}
else
working_space[i] = val;
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar
|| fTransformType == kTransformWalshHaar) {
for (i = 0; i < j; i++)
BitReverseHaar(working_space, fSize, k, i * k);
GeneralExe(working_space, 0, fSize, fDegree, fTransformType);
}
else if (fTransformType == kTransformCosWalsh || fTransformType == kTransformCosHaar) {
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
GeneralExe(working_space, 0, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
a = TMath::Cos(a);
b = working_space[k + i % j];
if (i % j == 0)
a = b / TMath::Sqrt(2.0);
else
a = b / a;
working_space[i] = a;
working_space[i + 2 * fSize] = 0;
}
}
else if (fTransformType == kTransformSinWalsh || fTransformType == kTransformSinHaar) {
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
GeneralExe(working_space, 0, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
a = TMath::Cos(a);
b = working_space[j + k + i % j];
if (i % j == 0)
a = b / TMath::Sqrt(2.0);
else
a = b / a;
working_space[j + k / 2 - i % j - 1] = a;
working_space[i + 2 * fSize] = 0;
}
}
if (fTransformType > kTransformWalshHaar)
k = (int) TMath::Power(2, fDegree - 1);
else
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
for (i = 0, l = 0; i < fSize; i++, l = (l + k) % fSize) {
working_space[fSize + i] = working_space[l + i / j];
working_space[fSize + i + 2 * fSize] =
working_space[l + i / j + 2 * fSize];
}
for (i = 0; i < fSize; i++) {
working_space[i] = working_space[fSize + i];
working_space[i + 2 * fSize] = working_space[fSize + i + 2 * fSize];
}
break;
}
if (!working_space) return;
for (i = 0, old_area = 0; i < fSize; i++) {
old_area += working_space[i];
}
for (i = 0, new_area = 0; i < fSize; i++) {
if (i >= fXmin && i <= fXmax)
working_space[i] = fFilterCoeff;
new_area += working_space[i];
}
if (new_area != 0) {
a = old_area / new_area;
for (i = 0; i < fSize; i++) {
working_space[i] *= a;
}
}
if (fTransformType == kTransformFourier) {
for (i = 0, old_area = 0; i < fSize; i++) {
old_area += working_space[i + fSize];
}
for (i = 0, new_area = 0; i < fSize; i++) {
if (i >= fXmin && i <= fXmax)
working_space[i + fSize] = fFilterCoeff;
new_area += working_space[i + fSize];
}
if (new_area != 0) {
a = old_area / new_area;
for (i = 0; i < fSize; i++) {
working_space[i + fSize] *= a;
}
}
}
else if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar) {
for (i = 0, old_area = 0; i < fSize; i++) {
old_area += working_space[i + 2 * fSize];
}
for (i = 0, new_area = 0; i < fSize; i++) {
if (i >= fXmin && i <= fXmax)
working_space[i + 2 * fSize] = fFilterCoeff;
new_area += working_space[i + 2 * fSize];
}
if (new_area != 0) {
a = old_area / new_area;
for (i = 0; i < fSize; i++) {
working_space[i + 2 * fSize] *= a;
}
}
}
switch (fTransformType) {
case kTransformHaar:
Haar(working_space, fSize, kTransformInverse);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformWalsh:
BitReverse(working_space, fSize);
Walsh(working_space, fSize);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformCos:
fSize = 2 * fSize;
working_space[0] = working_space[0] * TMath::Sqrt(2.0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[i + fSize] = (double) working_space[i] * b;
working_space[i] = (double) working_space[i] * a;
} for (i = 2; i <= (fSize / 2); i++) {
working_space[fSize - i + 1] = working_space[i - 1];
working_space[fSize - i + 1 + fSize] =
-working_space[i - 1 + fSize];
}
working_space[fSize / 2] = 0;
working_space[fSize / 2 + fSize] = 0;
Fourier(working_space, fSize, 0, kTransformInverse, 1);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformSin:
fSize = 2 * fSize;
working_space[fSize / 2] =
working_space[fSize / 2 - 1] * TMath::Sqrt(2.0);
for (i = fSize / 2 - 1; i > 0; i--) {
a = pi * (double) i / (double) fSize;
working_space[i + fSize] =
-(double) working_space[i - 1] * TMath::Cos(a);
working_space[i] = (double) working_space[i - 1] * TMath::Sin(a);
} for (i = 2; i <= (fSize / 2); i++) {
working_space[fSize - i + 1] = working_space[i - 1];
working_space[fSize - i + 1 + fSize] =
-working_space[i - 1 + fSize];
}
working_space[0] = 0;
working_space[fSize] = 0;
working_space[fSize / 2 + fSize] = 0;
Fourier(working_space, fSize, 0, kTransformInverse, 0);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourier:
Fourier(working_space, fSize, 0, kTransformInverse, 0);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformHartley:
Fourier(working_space, fSize, 1, kTransformInverse, 0);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
if (fTransformType > kTransformWalshHaar)
k = (int) TMath::Power(2, fDegree - 1);
else
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
for (i = 0, l = 0; i < fSize; i++, l = (l + k) % fSize) {
working_space[fSize + l + i / j] = working_space[i];
working_space[fSize + l + i / j + 2 * fSize] =
working_space[i + 2 * fSize];
}
for (i = 0; i < fSize; i++) {
working_space[i] = working_space[fSize + i];
working_space[i + 2 * fSize] = working_space[fSize + i + 2 * fSize];
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar
|| fTransformType == kTransformWalshHaar) {
GeneralInv(working_space, fSize, fDegree, fTransformType);
for (i = 0; i < j; i++)
BitReverseHaar(working_space, fSize, k, i * k);
}
else if (fTransformType == kTransformCosWalsh || fTransformType == kTransformCosHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
if (i % j == 0) {
working_space[2 * fSize + k + i % j] =
working_space[i] * TMath::Sqrt(2.0);
working_space[4 * fSize + 2 * fSize + k + i % j] = 0;
}
else {
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[4 * fSize + 2 * fSize + k + i % j] =
-(double) working_space[i] * b;
working_space[2 * fSize + k + i % j] =
(double) working_space[i] * a;
} } for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
if (i % j == 0) {
working_space[2 * fSize + k + j] = 0;
working_space[4 * fSize + 2 * fSize + k + j] = 0;
}
else {
working_space[2 * fSize + k + 2 * j - i % j] =
working_space[2 * fSize + k + i % j];
working_space[4 * fSize + 2 * fSize + k + 2 * j - i % j] =
-working_space[4 * fSize + 2 * fSize + k + i % j];
}
}
for (i = 0; i < 2 * fSize; i++) {
working_space[i] = working_space[2 * fSize + i];
working_space[4 * fSize + i] =
working_space[4 * fSize + 2 * fSize + i];
}
GeneralInv(working_space, 2 * fSize, fDegree, fTransformType);
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
}
else if (fTransformType == kTransformSinWalsh || fTransformType == kTransformSinHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
if (i % j == 0) {
working_space[2 * fSize + k + j + i % j] =
working_space[j + k / 2 - i % j - 1] * TMath::Sqrt(2.0);
working_space[4 * fSize + 2 * fSize + k + j + i % j] = 0;
}
else {
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[4 * fSize + 2 * fSize + k + j + i % j] =
-(double) working_space[j + k / 2 - i % j - 1] * b;
working_space[2 * fSize + k + j + i % j] =
(double) working_space[j + k / 2 - i % j - 1] * a;
} } for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
if (i % j == 0) {
working_space[2 * fSize + k] = 0;
working_space[4 * fSize + 2 * fSize + k] = 0;
}
else {
working_space[2 * fSize + k + i % j] =
working_space[2 * fSize + k + 2 * j - i % j];
working_space[4 * fSize + 2 * fSize + k + i % j] =
-working_space[4 * fSize + 2 * fSize + k + 2 * j - i % j];
}
}
for (i = 0; i < 2 * fSize; i++) {
working_space[i] = working_space[2 * fSize + i];
working_space[4 * fSize + i] =
working_space[4 * fSize + 2 * fSize + i];
}
GeneralInv(working_space, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
}
for (i = 0; i < fSize; i++) {
if (fTransformType >= kTransformCosWalsh) {
k = i / j;
k = 2 * k * j;
val = working_space[k + i % j];
}
else
val = working_space[i];
destVector[i] = val;
}
break;
}
delete[]working_space;
return;
}
//////////ENHANCE FUNCTION - CALCULATES DIFFERENT 1-D ORTHOGONAL TRANSFORMS, MULTIPLIES GIVEN REGION BY ENHANCE COEFFICIENT AND TRANSFORMS IT BACK//////
//___________________________________________________________________________
void TSpectrumTransform::Enhance(const float *source, float *destVector)
{
////////////////////////////////////////////////////////////////////////////////
// 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
//
////////////////////////////////////////////////////////////////////////////////
//Begin_Html
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 functions.
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");
}
End_Html
int i, j=0, k = 1, m, l;
float val;
float *working_space = 0;
double a, b, pi = 3.14159265358979323846, old_area, new_area;
if (fTransformType >= kTransformFourierWalsh && fTransformType <= kTransformSinHaar) {
if (fTransformType >= kTransformCosWalsh)
fDegree += 1;
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
}
switch (fTransformType) {
case kTransformHaar:
case kTransformWalsh:
working_space = new float[2 * fSize];
break;
case kTransformCos:
case kTransformSin:
case kTransformFourier:
case kTransformHartley:
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
working_space = new float[4 * fSize];
break;
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
working_space = new float[8 * fSize];
break;
}
switch (fTransformType) {
case kTransformHaar:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Haar(working_space, fSize, kTransformForward);
break;
case kTransformWalsh:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Walsh(working_space, fSize);
BitReverse(working_space, fSize);
break;
case kTransformCos:
fSize = 2 * fSize;
for (i = 1; i <= (fSize / 2); i++) {
val = source[i - 1];
working_space[i - 1] = val;
working_space[fSize - i] = val;
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
a = TMath::Cos(a);
b = working_space[i];
a = b / a;
working_space[i] = a;
working_space[i + fSize] = 0;
} working_space[0] = working_space[0] / TMath::Sqrt(2.0);
fSize = fSize / 2;
break;
case kTransformSin:
fSize = 2 * fSize;
for (i = 1; i <= (fSize / 2); i++) {
val = source[i - 1];
working_space[i - 1] = val;
working_space[fSize - i] = -val;
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
a = TMath::Sin(a);
b = working_space[i];
if (a != 0)
a = b / a;
working_space[i - 1] = a;
working_space[i + fSize] = 0;
}
working_space[fSize / 2 - 1] =
working_space[fSize / 2] / TMath::Sqrt(2.0);
fSize = fSize / 2;
break;
case kTransformFourier:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 0, kTransformForward, 0);
break;
case kTransformHartley:
for (i = 0; i < fSize; i++) {
working_space[i] = source[i];
}
Fourier(working_space, fSize, 1, kTransformForward, 0);
break;
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
for (i = 0; i < fSize; i++) {
val = source[i];
if (fTransformType == kTransformCosWalsh || fTransformType == kTransformCosHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
k = i / j;
k = 2 * k * j;
working_space[k + i % j] = val;
working_space[k + 2 * j - 1 - i % j] = val;
}
else if (fTransformType == kTransformSinWalsh
|| fTransformType == kTransformSinHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
k = i / j;
k = 2 * k * j;
working_space[k + i % j] = val;
working_space[k + 2 * j - 1 - i % j] = -val;
}
else
working_space[i] = val;
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar
|| fTransformType == kTransformWalshHaar) {
for (i = 0; i < j; i++)
BitReverseHaar(working_space, fSize, k, i * k);
GeneralExe(working_space, 0, fSize, fDegree, fTransformType);
}
else if (fTransformType == kTransformCosWalsh || fTransformType == kTransformCosHaar) {
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
GeneralExe(working_space, 0, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
a = TMath::Cos(a);
b = working_space[k + i % j];
if (i % j == 0)
a = b / TMath::Sqrt(2.0);
else
a = b / a;
working_space[i] = a;
working_space[i + 2 * fSize] = 0;
}
}
else if (fTransformType == kTransformSinWalsh || fTransformType == kTransformSinHaar) {
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
GeneralExe(working_space, 0, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
a = TMath::Cos(a);
b = working_space[j + k + i % j];
if (i % j == 0)
a = b / TMath::Sqrt(2.0);
else
a = b / a;
working_space[j + k / 2 - i % j - 1] = a;
working_space[i + 2 * fSize] = 0;
}
}
if (fTransformType > kTransformWalshHaar)
k = (int) TMath::Power(2, fDegree - 1);
else
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
for (i = 0, l = 0; i < fSize; i++, l = (l + k) % fSize) {
working_space[fSize + i] = working_space[l + i / j];
working_space[fSize + i + 2 * fSize] =
working_space[l + i / j + 2 * fSize];
}
for (i = 0; i < fSize; i++) {
working_space[i] = working_space[fSize + i];
working_space[i + 2 * fSize] = working_space[fSize + i + 2 * fSize];
}
break;
}
if (!working_space) return;
for (i = 0, old_area = 0; i < fSize; i++) {
old_area += working_space[i];
}
for (i = 0, new_area = 0; i < fSize; i++) {
if (i >= fXmin && i <= fXmax)
working_space[i] *= fEnhanceCoeff;
new_area += working_space[i];
}
if (new_area != 0) {
a = old_area / new_area;
for (i = 0; i < fSize; i++) {
working_space[i] *= a;
}
}
if (fTransformType == kTransformFourier) {
for (i = 0, old_area = 0; i < fSize; i++) {
old_area += working_space[i + fSize];
}
for (i = 0, new_area = 0; i < fSize; i++) {
if (i >= fXmin && i <= fXmax)
working_space[i + fSize] *= fEnhanceCoeff;
new_area += working_space[i + fSize];
}
if (new_area != 0) {
a = old_area / new_area;
for (i = 0; i < fSize; i++) {
working_space[i + fSize] *= a;
}
}
}
else if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar) {
for (i = 0, old_area = 0; i < fSize; i++) {
old_area += working_space[i + 2 * fSize];
}
for (i = 0, new_area = 0; i < fSize; i++) {
if (i >= fXmin && i <= fXmax)
working_space[i + 2 * fSize] *= fEnhanceCoeff;
new_area += working_space[i + 2 * fSize];
}
if (new_area != 0) {
a = old_area / new_area;
for (i = 0; i < fSize; i++) {
working_space[i + 2 * fSize] *= a;
}
}
}
switch (fTransformType) {
case kTransformHaar:
Haar(working_space, fSize, kTransformInverse);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformWalsh:
BitReverse(working_space, fSize);
Walsh(working_space, fSize);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformCos:
fSize = 2 * fSize;
working_space[0] = working_space[0] * TMath::Sqrt(2.0);
for (i = 0; i < fSize / 2; i++) {
a = pi * (double) i / (double) fSize;
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[i + fSize] = (double) working_space[i] * b;
working_space[i] = (double) working_space[i] * a;
} for (i = 2; i <= (fSize / 2); i++) {
working_space[fSize - i + 1] = working_space[i - 1];
working_space[fSize - i + 1 + fSize] =
-working_space[i - 1 + fSize];
}
working_space[fSize / 2] = 0;
working_space[fSize / 2 + fSize] = 0;
Fourier(working_space, fSize, 0, kTransformInverse, 1);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformSin:
fSize = 2 * fSize;
working_space[fSize / 2] =
working_space[fSize / 2 - 1] * TMath::Sqrt(2.0);
for (i = fSize / 2 - 1; i > 0; i--) {
a = pi * (double) i / (double) fSize;
working_space[i + fSize] =
-(double) working_space[i - 1] * TMath::Cos(a);
working_space[i] = (double) working_space[i - 1] * TMath::Sin(a);
} for (i = 2; i <= (fSize / 2); i++) {
working_space[fSize - i + 1] = working_space[i - 1];
working_space[fSize - i + 1 + fSize] =
-working_space[i - 1 + fSize];
}
working_space[0] = 0;
working_space[fSize] = 0;
working_space[fSize / 2 + fSize] = 0;
Fourier(working_space, fSize, 0, kTransformInverse, 0);
for (i = 0; i < fSize / 2; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourier:
Fourier(working_space, fSize, 0, kTransformInverse, 0);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformHartley:
Fourier(working_space, fSize, 1, kTransformInverse, 0);
for (i = 0; i < fSize; i++) {
destVector[i] = working_space[i];
}
break;
case kTransformFourierWalsh:
case kTransformFourierHaar:
case kTransformWalshHaar:
case kTransformCosWalsh:
case kTransformCosHaar:
case kTransformSinWalsh:
case kTransformSinHaar:
if (fTransformType > kTransformWalshHaar)
k = (int) TMath::Power(2, fDegree - 1);
else
k = (int) TMath::Power(2, fDegree);
j = fSize / k;
for (i = 0, l = 0; i < fSize; i++, l = (l + k) % fSize) {
working_space[fSize + l + i / j] = working_space[i];
working_space[fSize + l + i / j + 2 * fSize] =
working_space[i + 2 * fSize];
}
for (i = 0; i < fSize; i++) {
working_space[i] = working_space[fSize + i];
working_space[i + 2 * fSize] = working_space[fSize + i + 2 * fSize];
}
if (fTransformType == kTransformFourierWalsh
|| fTransformType == kTransformFourierHaar
|| fTransformType == kTransformWalshHaar) {
GeneralInv(working_space, fSize, fDegree, fTransformType);
for (i = 0; i < j; i++)
BitReverseHaar(working_space, fSize, k, i * k);
}
else if (fTransformType == kTransformCosWalsh || fTransformType == kTransformCosHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
if (i % j == 0) {
working_space[2 * fSize + k + i % j] =
working_space[i] * TMath::Sqrt(2.0);
working_space[4 * fSize + 2 * fSize + k + i % j] = 0;
}
else {
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[4 * fSize + 2 * fSize + k + i % j] =
-(double) working_space[i] * b;
working_space[2 * fSize + k + i % j] =
(double) working_space[i] * a;
} } for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
if (i % j == 0) {
working_space[2 * fSize + k + j] = 0;
working_space[4 * fSize + 2 * fSize + k + j] = 0;
}
else {
working_space[2 * fSize + k + 2 * j - i % j] =
working_space[2 * fSize + k + i % j];
working_space[4 * fSize + 2 * fSize + k + 2 * j - i % j] =
-working_space[4 * fSize + 2 * fSize + k + i % j];
}
}
for (i = 0; i < 2 * fSize; i++) {
working_space[i] = working_space[2 * fSize + i];
working_space[4 * fSize + i] =
working_space[4 * fSize + 2 * fSize + i];
}
GeneralInv(working_space, 2 * fSize, fDegree, fTransformType);
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
}
else if (fTransformType == kTransformSinWalsh || fTransformType == kTransformSinHaar) {
j = (int) TMath::Power(2, fDegree) / 2;
m = (int) TMath::Power(2, fDegree);
l = 2 * fSize / m;
for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
a = pi * (double) (i % j) / (double) (2 * j);
if (i % j == 0) {
working_space[2 * fSize + k + j + i % j] =
working_space[j + k / 2 - i % j - 1] * TMath::Sqrt(2.0);
working_space[4 * fSize + 2 * fSize + k + j + i % j] = 0;
}
else {
b = TMath::Sin(a);
a = TMath::Cos(a);
working_space[4 * fSize + 2 * fSize + k + j + i % j] =
-(double) working_space[j + k / 2 - i % j - 1] * b;
working_space[2 * fSize + k + j + i % j] =
(double) working_space[j + k / 2 - i % j - 1] * a;
} } for (i = 0; i < fSize; i++) {
k = i / j;
k = 2 * k * j;
if (i % j == 0) {
working_space[2 * fSize + k] = 0;
working_space[4 * fSize + 2 * fSize + k] = 0;
}
else {
working_space[2 * fSize + k + i % j] =
working_space[2 * fSize + k + 2 * j - i % j];
working_space[4 * fSize + 2 * fSize + k + i % j] =
-working_space[4 * fSize + 2 * fSize + k + 2 * j - i % j];
}
}
for (i = 0; i < 2 * fSize; i++) {
working_space[i] = working_space[2 * fSize + i];
working_space[4 * fSize + i] =
working_space[4 * fSize + 2 * fSize + i];
}
GeneralInv(working_space, 2 * fSize, fDegree, fTransformType);
for (i = 0; i < l; i++)
BitReverseHaar(working_space, 2 * fSize, m, i * m);
}
for (i = 0; i < fSize; i++) {
if (fTransformType >= kTransformCosWalsh) {
k = i / j;
k = 2 * k * j;
val = working_space[k + i % j];
}
else
val = working_space[i];
destVector[i] = val;
}
break;
}
delete[]working_space;
return;
}
//___________________________________________________________________________
void TSpectrumTransform::SetTransformType(Int_t transType, Int_t degree)
{
//////////////////////////////////////////////////////////////////////////////
// SETTER FUNCION
//
// 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
//////////////////////////////////////////////////////////////////////////////
Int_t j, n;
j = 0;
n = 1;
for (; n < fSize;) {
j += 1;
n = n * 2;
}
if (transType < kTransformHaar || transType > kTransformSinHaar){
Error ("TSpectrumTransform","Invalid type of transform");
return;
}
if (transType >= kTransformFourierWalsh && transType <= kTransformSinHaar) {
if (degree > j || degree < 1){
Error ("TSpectrumTransform","Invalid degree of mixed transform");
return;
}
}
fTransformType=transType;
fDegree=degree;
}
//___________________________________________________________________________
void TSpectrumTransform::SetRegion(Int_t xmin, Int_t xmax)
{
//////////////////////////////////////////////////////////////////////////////
// SETTER FUNCION
//
// This function sets the filtering or enhancement region:
// -xmin, xmax
//////////////////////////////////////////////////////////////////////////////
if(xmin<0 || xmax < xmin || xmax >= fSize){
Error("TSpectrumTransform", "Wrong range");
return;
}
fXmin = xmin;
fXmax = xmax;
}
//___________________________________________________________________________
void TSpectrumTransform::SetDirection(Int_t direction)
{
//////////////////////////////////////////////////////////////////////////////
// SETTER FUNCION
//
// This function sets the direction of the transform:
// -direction (forward or inverse)
//////////////////////////////////////////////////////////////////////////////
if(direction != kTransformForward && direction != kTransformInverse){
Error("TSpectrumTransform", "Wrong direction");
return;
}
fDirection = direction;
}
//___________________________________________________________________________
void TSpectrumTransform::SetFilterCoeff(Float_t filterCoeff)
{
//////////////////////////////////////////////////////////////////////////////
// SETTER FUNCION
//
// This function sets the filter coefficient:
// -filterCoeff - after the transform the filtered region (xmin, xmax) is replaced by this coefficient. Applies only for filtereng operation.
//////////////////////////////////////////////////////////////////////////////
fFilterCoeff = filterCoeff;
}
//___________________________________________________________________________
void TSpectrumTransform::SetEnhanceCoeff(Float_t enhanceCoeff)
{
//////////////////////////////////////////////////////////////////////////////
// SETTER FUNCION
//
// This function sets the enhancement coefficient:
// -enhanceCoeff - after the transform the enhanced region (xmin, xmax) is multiplied by this coefficient. Applies only for enhancement operation.
//////////////////////////////////////////////////////////////////////////////
fEnhanceCoeff = enhanceCoeff;
}