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 fourier_shift.m on google drive.
• Demo for displaying Fourier bases: see fourier2.m and dft_plots.m on google drive.
• Demo for rotation theorem: see fourier_rotation.m on google drive.

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.

Tutorial 3

• Determining the 2D-DCT of the signal 4 cos ((2x+1) pi/N) + 5 sin ((2y+1) 3pi/N) + cos ((2x+1)5 pi/N) sin ((2y+1) 7 pi/N), and other such similar signals
• Estimating an image given multiple blurred versions of the image, each respectively associated with a different blur kernel.
• Fourier transform of exp(-(x^2+y^2)) exp (j 2\pi (3x + 5y)/N) and its potential applications