1. 2D Fourier transform is separable

2. Visualisation
Amplitude
Phase

3. Basis functions of 2D FT
Real part, u=v

4. Rectangular pulse in 2D

5. 5

6. 6

7. Other important functions

8. ... holds for periodic convolution only!
Discrete convolution theorem
... holds for periodic convolution only! 8

9. Discrete convolution via FT
Zero padding to the same size
DFT calculation of both
Multiplication of the spectra
Inverse DFT

10. Filtering in the Fourier domain=
high pass
Gaussian high pass
band pass
low pass
Gaussian low pass
directional

12. Discrete shift theorem

13. What is more
important?
Amplitude or phase?

14. Image whitening
original image “whitened” image