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:
- 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)]
- Calculate the minimum sampling frequencies needed for a perfect
reconstruction for the above image I(x,y).
- 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)}
- Print the results.
- 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...)?