HW #4

ECE 178 WINTER 2003

DUE: February 7, 2003

In this (programming) assignment we will explore the 2D sampling theorem. You will find at this link the Matlab code necessary to carry out the experiments. Note that the computations are quite intensive and memory consuming, so... be patient! Here is what you are supposed to do:
  1. First of all browse through the code and understand how it works. Pay particular attention to the approach we use to "simulate" an image defined on a continuous set and to the procedure used to recover the original image starting from its samples. Note that the code generates an image defined by the function:

    I(x,y) = sin[2 pi (u x + v y)]

  2. Calculate the minimum sampling frequencies needed for a perfect reconstruction for the above image I(x,y).
  3. In the MATLAB code, the variables that contain the spatial sampling frequencies are us and vs. Run the code trying the following set of values:

    (us, vs) = {(13, 15), (10, 12), (7, 6), (5, 4)}

  4. Print the results.
  5. Do they agree with what is stated in the sampling theorem? In which case do you have aliasing? What can you notice in the images sampled with a frequency which satisfies the Nyquist constraint (pay attention to the phase...)? The reconstruction formula given by the sampling theorem requires an infinite number of samples, but in our implementation we are forced to use a finite number of samples: how is the reconstruction affected (pay attention to the quality of the reconstructed image near the boundaries...)?