Imagine, you would like to preserve the music of your favorite band on a CD. What does it take to put music on a CD? You would use a microphone to transform the acoustic waves into an electrical signal. Now you are faced with your first challenge. The electrical signal is continuous in time but all you can store on a CD are bits (zeros and ones)! The first step therefore is to sample the signal, transforming the continuous waveform in a sequence of samples (numbers). Quite suprisingly, if done correctly, this step entails no loss of quality and you can reconstruct the original continuous waveform perfectly from the discrete set of samples. As a next step you will represent the samples (numbers) as sequence of bits (zeros and ones) and if possible compress this sequence of bits, i.e., represent the information contained therein in a more compact way. It is not unusual that you can achieve a compression by a factor ten or more without any essential loss in quality (just think of long pauses or repetitive patterns in the music). This second step is called source coding. You can now store the information on a CD. This is done by storing the sequence of bits are as a sequence of flat regions versus bumps on the surface of the CD, changing the reflectivity of the surface. Since the physical dimensions of each “bump” are tiny (less than a million-th of a meter), even small impurities (fingerprints, dust, …) on the surface of the CD can cause lots of bits to be “erased” if you try to read the data back. Therefore, it is important that before storing your data you add some redundancy to your data. This will ensure that you can retrieve it correctly even if some of the data is lost or corrupted. This is called error correction coding. As a final step you might want to protect your data from unauthorized access by encrypting it.

The final grade is determined as follows:

Exam Rules: closed book, no calculator, no mobile phone, no friend, no cheat sheet, no formula book; only you and your brain

There are 4 graded homeworks, one for each module. Although you will receive some points that count towards your final grade, these homeworks are really designed for you to see if you can solve problems on your own. Use this chance.

For each graded homework it would therefore be best for you to solve it completely on your own.

But if you have trouble YOU CAN: (i) ask us in class if you do not know how to solve it, (ii) discuss with your colleagues; YOU CANNOT: (i) copy a solution from a friend (and neither from an enemy);

After any discussion you might have had, write down the solutions in your own words and independently from your colleagues.

IF WE FIND SIMILARITIES IN SOLUTIONS THAT GO BEYOND RANDOM, ALL INVOLVED SOLUTIONS WILL RECEIVE 0 POINTS, REGARDLESS OF WHO COPIED FROM WHOM.

Lecture Notes - Chapter 1 (English)
Notes de Cours - Chapitre 1 (Francais)
Notes de Cours - Chapitre 2 (Francais)
Lecture Notes - Chapter 3 (English)
Notes de Cours - Chapitre 3 (Francais)
Lecture Notes - Chapter 4 (English)
Notes de Cours - Chapitre 4 (Francais)

The following is a set of links that contain some useful information. Some contain applets, some contain recommendations for further reading.

• demo 1 for the sampling theorem
• demo 2 for the sampling theorem
• demo 3 for the sampling theorem