Tutorial 1

• Prove the shift theorem in DFT.
• Demo of visualization of Fourier transform magnitude for an image
• Demo of finding the translation between two images efficiently using Fourier transforms: see here.
• Demo for displaying Fourier bases: see here and here.
• Demo for rotation theorem: see here.

Tutorial 2

• Analysis of Fourier transform of filters such as [0 1/4 0; 1/4 0 1/4; 0 1/4 0], laplacian [0 1 0; 1 -4 1; 0 1 0] and [-1 -1 -1; -1 8 -1; -1 -1 -1]
• Effect of zero-padding on the Fourier transform of an image
• Effect of adding a sinusoidal wave pattern A sin(ax + by) on the Fourier transform of an image.
• A nice application of Wiener filtering from an old exam. See here.