I want to compute the autocorrelation of a 3D array using FFTW (2 dimensions are periodic). The file is very large (dimension 256*256*49995, double precision, 25GB).
1 : Is padding necessary for periodic dimensions?
2 : Is it possible to avoid zero-padding to limit memory usage? (fftw++ seems to answer yes)
3 : From the 3d FFT of the non-padded signal, is it possible to compute the cross-correlation using a Discrete Cosine Transform?
Cross-correlation = DCT[ FFT(signal)*Conjugate(FFT(signal)) ]
EDIT - 4 : Is it mandatory to use a mask?