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/*
-----------------------------------------------------------------------
Copyright: 2010-2015, iMinds-Vision Lab, University of Antwerp
2014-2015, CWI, Amsterdam
Contact: astra@uantwerpen.be
Website: http://sf.net/projects/astra-toolbox
This file is part of the ASTRA Toolbox.
The ASTRA Toolbox is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
The ASTRA Toolbox is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with the ASTRA Toolbox. If not, see <http://www.gnu.org/licenses/>.
-----------------------------------------------------------------------
$Id$
*/
#include "astra/Fourier.h"
namespace astra {
void discreteFourierTransform1D(unsigned int iLength,
const float32* pfRealIn,
const float32* pfImaginaryIn,
float32* pfRealOut,
float32* pfImaginaryOut,
unsigned int iStrideIn,
unsigned int iStrideOut,
bool inverse)
{
for (unsigned int w = 0; w < iLength; w++)
{
pfRealOut[iStrideOut*w] = pfImaginaryOut[iStrideOut*w] = 0;
for (unsigned int y = 0; y < iLength; y++)
{
float32 a = 2 * PI * w * y / float32(iLength);
if (!inverse)
a = -a;
float32 ca = cos(a);
float32 sa = sin(a);
pfRealOut[iStrideOut*w] += pfRealIn[iStrideIn*y] * ca - pfImaginaryIn[iStrideIn*y] * sa;
pfImaginaryOut[iStrideOut*w] += pfRealIn[iStrideIn*y] * sa + pfImaginaryIn[iStrideIn*y] * ca;
}
}
if (inverse) {
for (unsigned int x = 0; x < iLength; ++x) {
pfRealOut[iStrideOut*x] /= iLength;
pfImaginaryOut[iStrideOut*x] /= iLength;
}
}
}
void discreteFourierTransform2D(unsigned int iHeight, unsigned int iWidth,
const float32* pfRealIn,
const float32* pfImaginaryIn,
float32* pfRealOut,
float32* pfImaginaryOut,
bool inverse)
{
float32* reTemp = new float32[iWidth * iHeight];
float32* imTemp = new float32[iWidth * iHeight];
//calculate the fourier transform of the columns
for (unsigned int x = 0; x < iWidth; x++)
{
discreteFourierTransform1D(iHeight, pfRealIn+x, pfImaginaryIn+x,
reTemp+x, imTemp+x,
iWidth, iWidth, inverse);
}
//calculate the fourier transform of the rows
for(unsigned int y = 0; y < iHeight; y++)
{
discreteFourierTransform1D(iWidth,
reTemp+y*iWidth,
imTemp+y*iWidth,
pfRealOut+y*iWidth,
pfImaginaryOut+y*iWidth,
1, 1, inverse);
}
delete[] reTemp;
delete[] imTemp;
}
/** permute the entries from pfDataIn into pfDataOut to prepare for an
* in-place FFT. pfDataIn may be equal to pfDataOut.
*/
static void bitReverse(unsigned int iLength,
const float32* pfDataIn, float32* pfDataOut,
unsigned int iStrideShiftIn,
unsigned int iStrideShiftOut)
{
if (pfDataIn == pfDataOut) {
assert(iStrideShiftIn == iStrideShiftOut);
float32 t;
unsigned int j = 0;
for(unsigned int i = 0; i < iLength - 1; i++) {
if (i < j) {
t = pfDataOut[i<<iStrideShiftOut];
pfDataOut[i<<iStrideShiftOut] = pfDataOut[j<<iStrideShiftOut];
pfDataOut[j<<iStrideShiftOut] = t;
}
unsigned int k = iLength / 2;
while (k <= j) {
j -= k;
k /= 2;
}
j += k;
}
} else {
unsigned int j = 0;
for(unsigned int i = 0; i < iLength - 1; i++) {
pfDataOut[i<<iStrideShiftOut] = pfDataIn[j<<iStrideShiftIn];
unsigned int k = iLength / 2;
while (k <= j) {
j -= k;
k /= 2;
}
j += k;
}
pfDataOut[(iLength-1)<<iStrideShiftOut] = pfDataIn[(iLength-1)<<iStrideShiftOut];
}
}
static unsigned int log2(unsigned int n)
{
unsigned int l = 0;
while (n > 1) {
n /= 2;
++l;
}
return l;
}
/** perform 1D FFT. iLength, iStrideIn, iStrideOut must be powers of two. */
void fastTwoPowerFourierTransform1D(unsigned int iLength,
const float32* pfRealIn,
const float32* pfImaginaryIn,
float32* pfRealOut,
float32* pfImaginaryOut,
unsigned int iStrideIn,
unsigned int iStrideOut,
bool inverse)
{
unsigned int iStrideShiftIn = log2(iStrideIn);
unsigned int iStrideShiftOut = log2(iStrideOut);
unsigned int iLogLength = log2(iLength);
bitReverse(iLength, pfRealIn, pfRealOut, iStrideShiftIn, iStrideShiftOut);
bitReverse(iLength, pfImaginaryIn, pfImaginaryOut, iStrideShiftIn, iStrideShiftOut);
float32 ca = -1.0;
float32 sa = 0.0;
unsigned int l1 = 1, l2 = 1;
for(unsigned int l=0; l < iLogLength; ++l)
{
l1 = l2;
l2 *= 2;
float32 u1 = 1.0;
float32 u2 = 0.0;
for(unsigned int j = 0; j < l1; j++)
{
for(unsigned int i = j; i < iLength; i += l2)
{
unsigned int i1 = i + l1;
float32 t1 = u1 * pfRealOut[i1<<iStrideShiftOut] - u2 * pfImaginaryOut[i1<<iStrideShiftOut];
float32 t2 = u1 * pfImaginaryOut[i1<<iStrideShiftOut] + u2 * pfRealOut[i1<<iStrideShiftOut];
pfRealOut[i1<<iStrideShiftOut] = pfRealOut[i<<iStrideShiftOut] - t1;
pfImaginaryOut[i1<<iStrideShiftOut] = pfImaginaryOut[i<<iStrideShiftOut] - t2;
pfRealOut[i<<iStrideShiftOut] += t1;
pfImaginaryOut[i<<iStrideShiftOut] += t2;
}
float32 z = u1 * ca - u2 * sa;
u2 = u1 * sa + u2 * ca;
u1 = z;
}
sa = sqrt((1.0 - ca) / 2.0);
if (!inverse)
sa = -sa;
ca = sqrt((1.0 + ca) / 2.0);
}
if (inverse) {
for (unsigned int i = 0; i < iLength; ++i) {
pfRealOut[i<<iStrideShiftOut] /= iLength;
pfImaginaryOut[i<<iStrideShiftOut] /= iLength;
}
}
}
void fastTwoPowerFourierTransform2D(unsigned int iHeight,
unsigned int iWidth,
const float32* pfRealIn,
const float32* pfImaginaryIn,
float32* pfRealOut,
float32* pfImaginaryOut,
bool inverse)
{
//calculate the fourier transform of the columns
for (unsigned int x = 0; x < iWidth; x++)
{
fastTwoPowerFourierTransform1D(iHeight, pfRealIn+x, pfImaginaryIn+x,
pfRealOut+x, pfImaginaryOut+x,
iWidth, iWidth, inverse);
}
//calculate the fourier transform of the rows
for (unsigned int y = 0; y < iHeight; y++)
{
fastTwoPowerFourierTransform1D(iWidth,
pfRealOut+y*iWidth,
pfImaginaryOut+y*iWidth,
pfRealOut+y*iWidth,
pfImaginaryOut+y*iWidth,
1, 1, inverse);
}
}
}
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