[Insight-users] FFT Confusion

[Matt McCormick]

Hi David,

> 
> VnlFFTRealToComplexConjugateImageFilter
> 
> Am I interpreting the name correctly by:
> 
> It takes a "Real" valued image and produces the "ComplexConjugate" of
> the FFT as the output? If that is correct, is there instead a way to
> produce the "normal" FFT (instead of the conjugate)? Or is there an
> easy way to take the conjugate of a complex valued image?
> 

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