In practical image processing one considers finite signals, ie, functions
defined on finitely many discrete points, Fk for k
ranging from 0 to N-1. Such F can be considered as a periodic
signal with period N.
The Fourier transform of F is
The convolution of finite signals is
If F is real it has N independent components (degrees of freedom), its Fourier transform is complex but it satisfies
F^0 | is real |
F^N/2 | is real |
F^v | for intermediate v is complex |
These symmetries are also present for the 2-dim Fourier transforms.
Marco Corvi - Page hosted by geocities.com.