EE4206/EE5806 Digital Image Processing: 2D DFT : Symmetry Properties

EE4206/EE5806 Digital Image Processing: 2D DFT : Symmetry Properties
2D DFT : Symmetry Properties : even() + odd() = 0

1. Any real function or complex function w(x,y) can be expressed as the sum of an even and an odd part ( each of which can be real or complex ).

2.Even functions are said to be symmetric and odd functions are antisymmetric.

3. the product of two even or two odd functions is even, and that the product of an even and an odd function is odd.

4. the ONLY way that a discrete function can be odd is if ALL its samples sum to zero.

excerpted from: Digital Image Processing, 3rd ed. by Gonzalez and Woods, ch.4 p.261-262.