Digital Signal Processing Using Matlab

14.3. Exercises

EXERCISE 14.7.

Compare the compression performed using the DCT and the KLT for the image “flower”, which can be found in the file “imdemos” of the image processing toolbox. Use the MATLAB codes provided in the first two solved exercises. Consider successively image block partitions of 4×4, 8×8 and 16×16 pixels.

Comment on the effect of the block size on the compression effectiveness and calculation time.

EXERCISE 14.8.

Perform the wavelet packet based compression of a sinusoid having the frequency 1 kHz, sampled at 100 kHz, represented on 512 points and exhibiting random phase discontinuities at the zero-crossing instants. Perform the compression of the same signal using the DCT. In the two cases, preserve 99.5% of the initial signal energy. Comment on the results obtained.

EXERCISE 14.9.

a. Run the algorithm “K-means”, provided in exercise 14.5, for 4 clusters centered on: (0, 0), (0, 10), (10, 0), (10, 10), and for a number of code vectors equal to 4, then to 5. Comment on the solution obtained.

b. Consider a random initialization of the code vectors and repeat the training process several times. What do you conclude?

EXERCISE 14.10.

Train a Kohonen map to compress the image “Saturn”, which can be found in the file “imdemos” of the image processing toolbox. Consider successively image block partitions of 2×1, 2×2 and 4×4 pixels. For each case, plot the compression result using 16, 32 and 64 code vectors. Use a Manhattan distance and then a Euclidian distance based ...