4 ECTS credits
100 u studietijd
Aanbieding 1 met studiegidsnummer 4019802EER voor alle studenten in het 1e semester met een verdiepend master niveau.
This course aims to deliver the theoretical foundations for our modern communication society: the study of signals for communication purposes and an introduction to information theory to be able to measure the amount of information within the signals.
The course starts with a brief introduction on Information theory and how this forms the basis of modern communication techniques. The work of Shannon is therefore used as main reference and reworked such that it is easier digestible for master students.
Chapter 2 studies discrete information sources, namely sources which can only produce a finite number of possible values. The concept of entropy is introduced and illustrated with various examples. Afterwards, possible correlation between the information is introduced through a Markov process. Next, entropy measures between transmitted and received signal are discussed to measure the mutual information. Afterwards, transducers are introduced to enable the protection of the channel against communication errors. Finally, the famous Shannon theorem is stated, showing that there exists a coding system such that the output of the source can be transmitted over the channel with an arbitrarily small frequency of errors.
Chapter 3 extends the results of Chapter 2 towards continuous information sources, implying that a continuous range of real values are allowed. It also determines the distributions which maximize the entropy of the source under various conditions.
Chapter 4 introduces the time dependency of the signal in the continuous time domain. The chapter also revises some import telecommunication filters (such as the root-cosine filter) and modulation schemes (from BPSK to QAM modulation) to more easily introduce practical examples in a later stage.
Chapter 5 introduces the Shannon-Hartley theorem to determine the channel capacity in both the single channel and the multiple channel case. This will lead to various examples and optimization problems such as the optimal power distribution when using independent parallel channels.
Chapter 6 deals with optimal binary encoding, providing the foundation of a large number of data compression techniques and algorithms. The chapter concludes by determining Shannon's fundamental source coding theorem.
Chapter 7 studies the properties of the continuous time signals (generated by the data sources) and introduces concepts such as (wide-sense) stationary and ergodicity. Using these concepts, it becomes possible to study the power spectra of the random messages/signals using the Wiener-Kinchin theorem. This theory is developed in Chapter 8 and illustrated using a large number of practical examples (including power spectra of NRZ signals, 1/f noise and power spectra of modulated signals).
Chapter 9 discusses the Karhunen-Loève expansion and illustrates how this enables the approximation of a continuous time random signal using the least possible number of coefficients to transmit. Chapter 10 and 11 finally discuss the Wiener filter, which determines the filter that maximizes the signal to noise ratio, and the Matched filter, which aims to detect a particular signal when it is buried in the noise.
Course notes are available in pdf format and will be distributed using the canvas platform and the ELEC website http://vubirelec.be/
Reference handbooks, proceedings, journals etc. are also available in the library from the department ELEC where students can consult the material.
This course is an introduction to signal theory, detection theory, information theory and modulation. It is based on general concepts of mathematical analysis and algebra, statistics and probability theory. The fundamental theorems are proven and illustrated by practical applications in the technology. The student will be able to treat signals statically and he/she will be able to apply the fundamental theories in practice.
De beoordeling bestaat uit volgende opdrachtcategorieën:
Examen Andere bepaalt 100% van het eindcijfer
Binnen de categorie Examen Andere dient men volgende opdrachten af te werken:
During the oral exam covers all levels of leaning outcome, from remembering, over insight, and up to the application of the knowledge. The oral exam is composed out of three parts:
Deze aanbieding maakt deel uit van de volgende studieplannen:
Master of Electrical Engineering: Standaard traject BRUFACE J (enkel aangeboden in het Engels)
Educatieve master in de wetenschappen en technologie: ingenieurswetenschappen (120 ECTS, Etterbeek)