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fft.h
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fft.h
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// Forward and inverse FFT code
// Hacked by D. Crandall
//
// Compute 2D Discrete Fourier Transform (DFT) using the Fast Fourier
// Transform (FFT) algorithm.
// dir: 1 for forward transform, 0 for inverse
// real and imag buffers are *overwritten*
//
#include <math.h>
using namespace std;
void FFT_1D(short int dir,long m,double *x,double *y);
SDoublePlane transpose(const SDoublePlane &in)
{
SDoublePlane result(in.cols(), in.rows());
double *in_cp = in[0];
for(int i=0; i<in.rows(); i++)
{
for(int j=0; j<in.cols(); j++)
result[j][i] = *(in_cp++);
}
return result;
}
void swap_quadrants(SDoublePlane &real, SDoublePlane &imag)
{
for(int i=0; i<real.rows()/2; i++)
{
for(int j=0; j<real.cols()/2; j++)
{
swap(real[i][j], real[ i+real.rows()/2][j+real.cols()/2]);
swap(imag[i][j], imag[ i+imag.rows()/2][j+imag.cols()/2]);
}
for(int j=real.cols()/2; j<real.cols(); j++)
{
swap(real[i][j], real[ i+real.rows()/2][j-real.cols()/2]);
swap(imag[i][j], imag[ i+imag.rows()/2][j-imag.cols()/2]);
}
}
}
void FFT_2D(short int dir, SDoublePlane & real, SDoublePlane &imag)
{
// check squareness and powers of two
if(real.rows() != real.cols() || (real.rows() & (real.rows()-1)))
throw string("In fft, image isn't square and/or size isn't a power of 2!");
// figure exponent k
int k = int(round(log2(real.rows())));
if(!dir)
swap_quadrants(real, imag);
// 1d transform on rows
for(int j=0; j<real.rows(); j++)
FFT_1D(dir, k, real[j], imag[j]);
// 1d transform on cols
real = transpose(real); imag = transpose(imag);
for(int j=0; j<real.rows(); j++)
FFT_1D(dir, k, real[j], imag[j]);
real = transpose(real); imag = transpose(imag);
if(dir)
swap_quadrants(real, imag);
}
// This function is from
// http://paulbourke.net/miscellaneous/dft/
//
void FFT_1D(short int dir,long m,double *x,double *y)
{
long n,i,i1,j,k,i2,l,l1,l2;
double c1,c2,tx,ty,t1,t2,u1,u2,z;
/* Calculate the number of points */
n = 1;
for (i=0;i<m;i++)
n *= 2;
/* Do the bit reversal */
i2 = n >> 1;
j = 0;
for (i=0;i<n-1;i++) {
if (i < j) {
tx = x[i];
ty = y[i];
x[i] = x[j];
y[i] = y[j];
x[j] = tx;
y[j] = ty;
}
k = i2;
while (k <= j) {
j -= k;
k >>= 1;
}
j += k;
}
/* Compute the FFT */
c1 = -1.0;
c2 = 0.0;
l2 = 1;
for (l=0;l<m;l++) {
l1 = l2;
l2 <<= 1;
u1 = 1.0;
u2 = 0.0;
for (j=0;j<l1;j++) {
for (i=j;i<n;i+=l2) {
i1 = i + l1;
t1 = u1 * x[i1] - u2 * y[i1];
t2 = u1 * y[i1] + u2 * x[i1];
x[i1] = x[i] - t1;
y[i1] = y[i] - t2;
x[i] += t1;
y[i] += t2;
}
z = u1 * c1 - u2 * c2;
u2 = u1 * c2 + u2 * c1;
u1 = z;
}
c2 = sqrt((1.0 - c1) / 2.0);
if (dir == 1)
c2 = -c2;
c1 = sqrt((1.0 + c1) / 2.0);
}
/* Scaling for forward transform */
if (dir == 1) {
for (i=0;i<n;i++) {
x[i] /= n;
y[i] /= n;
}
}
}