Hi, I have problems working with FFTW (www.fftw.org). I need to transform a 2-dimensional array into its fourier spectrum, modify some of the coefficients and invert it back. It is part of a watermarking algorithm for images that works in the fourier spectrum. My code: const int IMG_SIZE = 1024; fftw_plan p; fftw_complex *in, *out, *out2; in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * IMG_SIZE * IMG_SIZE); out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * IMG_SIZE * IMG_SIZE); out2 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * IMG_SIZE * IMG_SIZE); // fill the input array 'in' with values ... // do the FFT p = fftw_plan_dft_2d(IMG_SIZE, IMG_SIZE, in, out, FFTW_FORWARD, FFTW_MEASURE); fftw_execute(p); fftw_destroy_plan(p); // modify very few of 'out''s real and imaginary values ... // invert FFT p = fftw_plan_dft_2d(IMG_SIZE, IMG_SIZE, out, out2, FFTW_BACKWARD, FFTW_MEASURE); fftw_execute(p); fftw_destroy_plan(p); fftw_free(in); fftw_free(out); fftw_free(out2); The values of 'in' are integers between 0 and 255 (the brightness of an image's pixels). The results in 'out2' are very small values, not the original values. I know that they are scaled in a way, but I have no idea how to transform them to be between 0 and 255 again. I read something about diving them by the array size (IMG_SIZE * IMG_SIZE, in my case 1024*1024). But this does not help, they seem to be scaled everything but linear. An example: Input values: 26, 28, 32, 29, 19, 12 Output values (after inverse FFT): -51441664, -52130816, -51351351, -52323270, -53409792, -52888576 Even without manipulating the values they turn this way... Any help would be appreciated :)

# Scaling inverse result of FFT with FFTW

Started by ●January 18, 2007

Reply by ●January 18, 20072007-01-18

floppes@gmx.de wrote:> The values of 'in' are integers between 0 and 255 (the brightness of an > image's pixels). The results in 'out2' are very small values, not the > original values. I know that they are scaled in a way, but I have no > idea how to transform them to be between 0 and 255 again. I read > something about diving them by the array size (IMG_SIZE * IMG_SIZE, in > my case 1024*1024). But this does not help, they seem to be scaled > everything but linear.As described in the FFTW manual and FAQ, you do indeed have to divide by the IMG_SIZE^2 to get the inverse. If this is not working for you, probably you are initializing or reading the array incorrectly. Note also that you have to initialize the input array *after* creating the plan if you use FFTW_MEASURE, as explained in the manual and the FAQ. (However, if you are only computing the transform once, FFTW_MEASURE is not worth it and you should just use FFTW_ESTIMATE.)

Reply by ●January 18, 20072007-01-18

stev...@alum.mit.edu schrieb:> Note also that you have to initialize the input array *after* creating > the plan if you use FFTW_MEASURE, as explained in the manual and the > FAQ. (However, if you are only computing the transform once, > FFTW_MEASURE is not worth it and you should just use FFTW_ESTIMATE.)Changing FFTW_MEASURE to FFTW_ESTIMATE did the trick :) Now I can divide the values by 1024^2 and get the correct results. Thanks a lot! Florian