[Insight-users] FFT Confusion

[David Doria]

> This is the "normal" FFT -- a real image produces a complex image, but there is
> complex conjugate symmetry of the first half of the transform because
>
> sin(-x) = - sin(x) (odd)
> cos(-x) = cos(x)   (even)
>
> exp(ix) = cos(x) + isin(x)
>
> This complex conjugate symmetry is sometimes called Hermitian symmetry, but I
> have been told that is an incorrect term.
>
> Regards,
> Matt

Thanks Matt. Maybe you could explain this in the documentation of the
class (right now it is basically empty)? (and explain the choice of
the name of the class too - i.e. why not just VnlFFTImageFilter? ).

Also, should I just use UnaryFunctorImageFilter to compute the complex
conjugate of the resulting image? I'm surprised not to find a
ConjugateImageFilter or similar. For a normalized correlation of
images A and B in the frequency domain, I believe you are supposed to
do

FFT(A) * conj(FFT(B))

Thanks,

David