
Properties 
A few interesting properties of the 2D DFT.


As with the one dimensional DFT, there are many properties of the
transformation that give insight into the content of the frequency
domain representation of a signal and allow us to manipulate singals
in one domain or the other.
Shift Property

See an example

As in one dimension, there is a simple relationship that can be
derived for shifting an image in one domain or the other. Since
both the space and frequency domains are considered periodic for the
purposes of the transforms, shifting means rotating around the
boundaries. The equations describing this are:



Scale Property

See an example

Just as in one dimension, shrinking in one domain causes expansion in the other for the 2D DFT. This means that as an object grows in an image, the corresponding features in the frequency domain will expand. The equation governing this is:



Rotation Property

See an example

This is a property of the 2D DFT that has no analog in one
dimension. Becuase of the seperability of the transform equations,
the content in the frequency domain is positioned based on the
spatial location of the content in the space domain. This means
that rotating the spatial domain contents rotates the frequency
domain contents. This can be formally described by the following
relationship:



