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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "fft.h"
static void
do_fft (complex_t *buffer, int n, complex_t principal, int is_inverse)
{
complex_t *temp, *even, *odd;
complex_t alpha;
complex_t p2;
int i;
double inv;
if (n == 1)
return;
temp = malloc (n * sizeof (complex_t));
even = temp;
odd = temp + n/2;
for (i = 0; i < n/2; ++i)
{
even[i] = buffer[2 * i];
odd[i] = buffer[2 * i + 1];
}
p2 = complex_mul (principal, principal);
do_fft (even, n/2, p2, FALSE);
do_fft (odd, n/2, p2, FALSE);
alpha.re = 1.0;
alpha.im = 0;
if (is_inverse)
inv = 1.0 / n;
for (i = 0; i < n/2; ++i)
{
buffer[i] = complex_add (even[i], complex_mul (alpha, odd[i]));
buffer[i + n/2] = complex_sub (even[i], complex_mul (alpha, odd[i]));
if (is_inverse)
{
buffer[i].re *= inv;
buffer[i].im *= inv;
buffer[i + n/2].re *= inv;
buffer[i + n/2].im *= inv;
}
alpha = complex_mul (alpha, principal);
}
free (temp);
}
void
fft (complex_t *buffer, int n)
{
complex_t p;
p.re = cos (2 * M_PI / n);
p.im = sin (2 * M_PI / n);
do_fft (buffer, n, p, FALSE);
}
void
ifft (complex_t *buffer, int n)
{
complex_t p;
p.re = cos (- (2 * M_PI / n));
p.im = sin (- (2 * M_PI / n));
do_fft (buffer, n, p, TRUE);
}
void
shift (complex_t *buffer, int n)
{
int i;
for (i = 0; i < n/2; ++i)
{
complex_t tmp = buffer[i];
buffer[i] = buffer[i + n/2];
buffer[i + n/2] = tmp;
}
}
typedef void (* fft_1d_t) (complex_t *buffer, int n);
static void
do_fft_2d (complex_t *buffer, int n, fft_1d_t func1d)
{
int i;
/* Transform all the rows */
for (i = 0; i < n; ++i)
{
complex_t *b = buffer + i * n;
func1d (b, n);
}
/* Then the columns */
for (i = 0; i < n; ++i)
{
int j;
complex_t *tmp = malloc (n * sizeof (complex_t));
for (j = 0; j < n; ++j)
tmp[j] = buffer[j * n + i];
func1d (tmp, n);
for (j = 0; j < n; ++j)
buffer[j * n + i] = tmp[j];
free (tmp);
}
}
void
fft_2d (complex_t *buffer, int n)
{
do_fft_2d (buffer, n, fft);
}
void
ifft_2d (complex_t *buffer, int n)
{
do_fft_2d (buffer, n, ifft);
}
void
shift_2d (complex_t *buffer, int n)
{
int i, j;
/* Swap quadrant 0 with quadrant 3 */
for (i = 0; i < n/2; ++i)
{
for (j = 0; j < n/2; ++j)
{
complex_t tmp;
tmp = buffer[i * n + j];
buffer[i * n + j] = buffer[((n/2) + i) * n + (j + n/2)];
buffer[((n/2) + i) * n + (j + n/2)] = tmp;
}
}
/* Swap quadrant 1 with quadrant 2 */
for (i = 0; i < n/2; ++i)
{
for (j = 0; j < n/2; ++j)
{
complex_t tmp;
tmp = buffer[i * n + j + n/2];
buffer[i * n + j + n/2] = buffer[(i + n/2) * n + j];
buffer[(i + n/2) * n + j] = tmp;
}
}
}
void
fft_shift_2d (complex_t *buffer, int n)
{
fft_2d (buffer, n);
shift_2d (buffer, n);
}
void
ifft_shift_2d (complex_t *buffer, int n)
{
shift_2d (buffer, n);
ifft_2d (buffer, n);
}
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