Fourier Transform

In the two following labs, we will put hands on the Fourier Transform.

In the first part, we will show the spectrum of common 2D signals (constant, harmonic, square, circ, Gaussian, and optionally Gabor). You will implement a parametric generator of 2D signals and a procedure which will visualize the magnitude spectrum. Then, we will see the spectrum of a real photo and show that important information is carried by the phase spectrum. Next task will demonstrate how the magnitude spectrum changes when the image is translated and rotated. Finally, we will use the Fourier transform to attenuate certain frequencies and observe the impact on the image. See the template and our results here: part1.

In the second part, we will demonstrate the Sampling Theorem, demonstrate the aliasing effect, and a way to avoid aliasing when subsampling an image containing high frequencies. See the template and our results here: part2.

Download all Matlab templates, and all input images here: cv_fourier.zip.

When you are done, upload the complete ZIP-archive containing all m-files (and input images):
  • cv_fourier.m,
  • cv_fourier2.m,
  • image_generator.m,
  • show_spectrum.m,
  • all input images (A_black.png, A_black_45.png, Lenna.png, start-chart.png). This is for automatic execution of your scripts on our server.

Please make sure, that your script always finishes. In case you decide not to make an optional task, set the required output to zero, in order your script does not crash when executed by the BRUTE system.