According to the conjugate symmetry property of Fourier transform, shouldn't the following command not return 1 (=true):
x=imread('cameraman.tif');
ishermitian(fft2(x))
However it does not (returns 0).
Is it due to some rounding error? Something else? Otherwise, how would you check that it is (avoiding to write a painful code with for loops etc)?
In the 2D (continuous) Fourier domain, the Hermitian symmetry (for functions) writes (conjugate symmetric with respect to the origin):
$$F(-u,-v) = \overline{F}(u,v)\,.$$
For matrix $A_{i,j}$, we should have:
$$ a_{i,j} = \overline{a}_{j,i}$$
which means that the diagonal is real. As you can see, Hermitian matrices and Hermitian functions are slightly different. There is something in the diagonal that needs a center. But diagonals of matrices are real.
Plus, the FFT output matrix is not straightforwardly organized like the (continuous) Fourier transform. Friday night here, I am coming back later on FFT symmetries.
