FFTW forward and back ward yield in different results why? - c++

Question

I am trying to FFT an image using the library from http://www.fftw.org/. basically i want to do a forward transform and then the backward transform to get the input image i have chosen. Then I would like to get my input back with the backward FFT, but it doesn't work. Here is my code :
double n[w][h][2];
double im[w][h][2];
const int Lx = w;
const int Lt = h;
int var_x;
int var_t;
fftw_complex *in, *out, *result;
fftw_plan p;
fftw_plan inv_p;
in = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*Lx*Lt);
out = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*Lx*Lt);
result = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) *Lx *Lt);
p = fftw_plan_dft_2d(Lx, Lt, in, out, FFTW_FORWARD, FFTW_MEASURE);
for (int x = 0; x < Lx; x++)
{
for (int t = 0; t < Lt; t++)
{
in[t + Lt*x][0] = n[x][t][0];
in[t + Lt*x][1] = 0;
}
}
fftw_execute(p);
for (int x = 0; x < Lx; x++)
{
for (int t = 0; t < Lt; t++)
{
n[x][t][0] = out[t + Lt*x][0];
n[x][t][1] = out[t + Lt*x][1];
}
}
inv_p = fftw_plan_dft_2d(Lx, Lt, out, result, FFTW_BACKWARD, FFTW_MEASURE);
fftw_execute(inv_p);
for (int x = 0; x < Lx; x++)
{
for (int t = 0; t < Lt; t++)
{
im[x][t][0] = result[t + Lt*x][0];
im[x][t][1] = result[t + Lt*x][1];
std::cout<<im[x][t][0]<<std::endl;
}
}
fftw_destroy_plan(p);
fftw_free(in);
fftw_free(out);
As you can see, I just try to perform a normal FFT, then to reverse it. The problem is that my output 'im' is just full of 0, instead of 1 and 0...
So what's wrong with my code ?
Thank you :)

Answer 1

Your original image and transform matrices are declared as int. Try defining them as double:
double n[w][h][2];
double im[w][h][2];
The line below, for example, is destroying data because result[i][j] is of type double (as of fftw_complex definition). So that if result[i][j] == 0.99, it'll be converted to 0.
im[x][t][0] = result[t + Lt*x][0]; //A value of 0.99 may be converted to 0

Answer 2

This is the corrected version of the code which is now working - thank you to everybody who helped me to fix all the problems.
double n[w][h][2];
double im[w][h][2];
const int Lx = w;
const int Lt = h;
int var_x;
int var_t;
fftw_complex *in, *out, *result;
fftw_plan p;
fftw_plan inv_p;
in = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*Lx*Lt);
out = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*Lx*Lt);
result = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) *Lx *Lt);
p = fftw_plan_dft_2d(Lx, Lt, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
for (int x = 0; x < Lx; x++)
{
for (int t = 0; t < Lt; t++)
{
in[t + Lt*x][0] = n[x][t][0];
in[t + Lt*x][1] = 0;
}
}
fftw_execute(p);
for (int x = 0; x < Lx; x++)
{
for (int t = 0; t < Lt; t++)
{
n[x][t][0] = out[t + Lt*x][0];
n[x][t][1] = out[t + Lt*x][1];
}
}
inv_p = fftw_plan_dft_2d(Lx, Lt, out, result, FFTW_BACKWARD, FFTW_ESTIMATE);
fftw_execute(inv_p);
for (int x = 0; x < Lx; x++)
{
for (int t = 0; t < Lt; t++)
{
im[x][t][0] = result[t + Lt*x][0];
im[x][t][1] = result[t + Lt*x][1];
std::cout<<im[x][t][0]<<std::endl;
}
}
fftw_destroy_plan(p);
fftw_destroy_plan(inv_p);
fftw_free(in);
fftw_free(out);
fftw_free(result);