2D Discrete Fourier Transform
Tomas Svoboda
Abstract:
This is assistant text for Signal and Image Processing subject. It
reminds some properties of 2-D Discrete Fourier Transform and
discrete convolution. It probably helps to solve problem of motion
blur removing.
The discrete Fourier transform pair is
|
(1) |
remind that
|
(2) |
Suppose discrete function
defined as
|
(3) |
DFT is computed using
|
(4) |
Note discrete nature of
and
.
Using
(3) the equation (4) can be simplified to
|
(5) |
This summation gives the same value for each .
The Fourier
transform of the step function (3) is a periodic function
with the period
|
(6) |
Figure:
1D discrete function.
|
Figure 2:
Shifted amplitude of DFT of the function from the figure above.
|
1999-05-13