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| ELEN0070-1 | Signal Processing
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
| Bachelor in engineering sciences, civil engineer orientation (Bachelor in engineering sciences, civil engineer orientation), 3rd year | | First semester | | 5 |
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| Master in Electrical Engineering, in-depth approach, 1st year | | First semester | | 5 |
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| Master of science in computer science and engineering, in-depth approach, 1st year | | First semester | | 5 |
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| Master in Computer science, Research Focus, 2nd year | | First semester | | 6 |
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| Master in Engineering Physics, in-depth approach, 1st year | | First semester | | 5 |
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| Master en ingénieur civil électricien, à finalité spécialisée en technologies durables en automobile, 1st year | | First semester | | 5 |
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| Master in Electrical Engineering, specialized approach, 1st year | | First semester | | 5 |
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| Master of science in computer science and engineering, professional focus in management, 1st year | | First semester | | 5 |
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| Master in Engineering Physics, specialized approach, 1st year | | First semester | | 5 |
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| Lecturer : | Jacques Verly |
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Language(s) of instruction :
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| French language |
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Course contents :
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| The course is an advanced introduction to the fundamental elements of signal processing. Since signals are often "processed" through "systems", the course also touches upon some elements of the theory of systems. However, the course is more oriented towards signals than towards systems. The course considers mainly signals that are functions of time, but it emphasizes the applicability of the concepts and results to functions of other types of independent variables, such as space/position. Occasional references are made to the extension from one-dimensional (1D) signals to multidimensional signals, in particular 2D. The course covers both analog and digital signals, also called continuous-time (CT) signals and discrete-time (DT) signals. An effort is made to maintain a maximum of parallelism between the CT and DT cases. The CT and DT convolutions are covered, and the fundamental importance of convolution is explained, especially in the context of linear, time-invariant (LTI) systems. The course covers in great detail the two most important signals of signal processing, i.e. the complex exponential and the Dirac impulse. These signals directly lead to the key notions of impulse response, and of transfer function and frequency response. A significant part of the course is dedicated to the "spectrum" of signals, and thus to the Fourier series (FS) for periodic signals and to the Fourier transform (FT) for arbirtrary signals (including periodic ones). The course emphasizes the CTFT and DTFT, and tends to view the CTFS and DTFS as particular cases. The concept of "signal-transform pair" is emphasized and exploited throughout. The course covers sampling theory as a simple application of Fourier transforms. Because of the emphasis on FTs (and FSs), the course can be viewed both as a signal processing course and as a course on the Fourier transform and its applications. The course is taught at an advanced level. In particular, most developments are made directly for complex-valued signals, and Dirac impulses are discussed both as limits of ordinary functions and as distributions.
The course has 3 features :
- abundant use of graphs for signals and their spectra.
- frequent historical references to those who made significant contributions (Euler, Fourier,...)
- shows how the theory and principles discussed are immediately applicable to applications.
Main topics :
- What signals are. Why deal with complex signals from the start. Examples of signals in daily life. DT and CT. Operations on the independent variable (e.g. time) and the dependent variable (i.e. the amplitude). The not-so-trivial definition of periodicity.
- Complex exponentials and their multiple interpretations.
- Convolution, introduced as an accumulation of "things" over time. Interpretations. How to compute convolutions.
- CT impulses, i.e. Dirac impulses, mainly viewed as limits. DT impulses. Introduction to distributions. Properties of impulses. Representation of signals. Bed-of-nails functions.
- Fourier series (FS), introduced via musical instruments, and more specifically via the plucked-string problem.
- CT Fourier transform (CTFT). Properties and theorems. Importance of duality. Power of thinking in terms of CTFT pairs. Special case of periodic signals and relation to CTFS. Sampling and sampling theorem as direct, amazing results from properties of CTFT. Methods for computing CTFTs, with emphasis on exploiting other CTFT pairs.
- DT Fourier transform (DTFT), presented by preserving a maximum of parallelism with CTFT. Properties and theorems. Special nature of duality. Power of thinking in terms of DTFT pairs. Special case of periodic signals and relation to DTFS. DT sampling and DT sampling theorem as direct, amazing results from properties of DTFT. Methods for computing DTFTs, with emphasis on exploiting other DTFT pairs.
- Connection with scientific and engineering applications.
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Learning outcomes of the course :
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| The student will understand and be able to use the key concepts in the topics listed above. He/she will understand the mathematical and theoretical underpinnings of these concepts. He will have both a precise mathematical understanding and a highly visual and intuitive view of all the concepts.
The student will understand the concepts of complex exponentials and of impulses. He will understand - and perhaps discover - why the integral often used in connection with Dirac impulses is just a notation and not a real integral. He will understand the need for treating impulses in a special way, i.e. more by what they do, than by what they are. He will develop the reflex of treating a carrier wave as a periodic complex exponential (in telecommunications), and a calcification as a Dirac impulse (in medical imaging).
The student will be able to compute key "quantities" such as convolutions and Fourier transforms (CTFT, DTFT, CTFS, and DTFS). He will juggle with all the properties and theorems of these transforms, and the relations between them. He will adopt the mindset of thinking in terms of FT pairs. He will not hesitate to go back and forth between the time domain and the frequency domain. He will understand the power of combining previously-derived FT pairs and FT properties and theorems to obtain new results.
The student will discover that some familiar physical devices do FTs instantly ... without worrying about whether the FTs converge!
Most importantly, the student will become friend with the convolution, all the forms of FTs, and Dirac impulses. He will no longer be afraid of them! He will have a highly visual and intuitive view of them. He will have fun manipulating these concepts. He will not hesitate to put these concepts to use in applications. He may become highly creative in using them.
Through the laboratories, the student will have created, processed, and visualized signals and their spectra using computers.
The student will have a chance to revisit mathematical concepts that may have become rusty, such as the true nature of complex numbers, complex-valued functions of complex variables, analytic/holomorphic functions, and integration in the complex plane.
The laboratory sessions in small groups will help the student to develop new skills, such as team work, problem solving, capacity to apply theoretical concepts to real data, critical analysis of results, writing-up of reports.
Since the recommended references and the optional course notes are in English, the student will enhance his capacity at reading the technical literature written in English.
The student will learn to dig into the recommended references to find complementary information and to identify the problems/exercices that relate to the material covered in class.
The students will learn - hopefully early on - that mastering the course material requires a lot of practice in solving problems.
Due to the fact that the instructor makes extensive use of the blackboard and rarely uses slides, and that the lectures are highly dynamic and interactive, the learning outcomes will be greatly increased if the student attends the classes. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| The course requires a basic understanding of complex numbers. For some limited parts of the course, the student will find it necessary to have a basic understanding of complex-valued functions of complex variables, and of integration in the complex plane.
The student will find in the course SYST002, "Modeling and analysis of systems", an interesting, complementary view of some of the material covered in the present course. The course notes from SYST002 may also be useful.
Since all course materials are mainly in English, proficiency in reading technical material in English will be useful. |
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Planned learning activities and teaching methods :
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| The course consists of
- "ex-cathedra" lectures (mostly by the instructor),
- occasional review/problem sessions on specific topics (by the teaching assistant),
- laboratories (in small groups),
- possibly one or more written midterm tests (announced ahead of time),
- a written final exam.
The lectures are given mostly by the instructor, who makes intensive use of the blackboard. While the optional course notes follow quite closely what is taught in class, these notes cannot possibly reflect precisely the "spirit" that is communicated in class, and the dynamics and interactivity of the class. It is thus highly recommended that the student attend classes. The lectures present a mix of theoretical concepts and of exercices. Therefore, except for the occasional review/problem sessions, the student should not expect the class on a given day to be clearly divided into a theoretical part and an exercise part. The instructor uses the time in a flexible way, which allows him to address the specific needs of the students.
"Laboratory" refers to an activity done by small groups of students. The students in each group can do a laboratory at any time before the corresponding deadline, possibly at home. One laboratory consists of reading, experimenting on the computer, and writing a report (one per group). There are 3 to 4 laboratories. The laboratories are not always synchronized with the topics covered in class.
The possible midterm tests are announced ahead of time.
Normally, the instructor teaches the class in French, but he simultaneously writes on the blackoard in English. He periodically asks the students whether they want the class to be taught in French, or English, or both. The optional course notes are in English. All the recommended references are in English. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face. |
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Recommended or required readings :
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| Reading:
The recommended references are:
- Signal & Systems, Second edition, by Alan V. Oppenheim and
Alan S. Willsky, Prentice Hall, 1997.
- The Fourier Transform and its Applications, Third edition, by
Ronald N. Bracewell, McGraw Hill, 2000.
These classical references are in English.
The course does not follow any of these references closely. However, much of the material covered in class is found in these references. Bracewell's book is particularly recommended for the CTFT, the Dirac impulse, and the pictorial dictionary of CTFT pairs.
Both books contain excellent problems/exercises. Many of these problems, or variations thereof, appear on the written tests and final exam.
Course notes:
The instuctor uses personal, handwritten
course notes during class. Before or after each class, the intructor gives
copies of most of these course notes, possibly modified, to a representative of
the students. Each student is free to use these copies to make his own copies.
The course notes are thus optional. These personal course notes are not, and
cannot be, placed online.
Laboratories: Appropriate information will be made available near the beginning of the course. The optional course notes made available to the students are for their personal use only, and these notes are hereby protected by copyright. They cannot be further distributed. Any unauthorized use may constitute a violation of copyright laws and of other laws. |
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Assessment methods and criteria :
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| The final grade for the course is based on the grades for the written final exam, one or more written midterm tests, and the laboratories. Between 75% and 80% of the final grade is determined by the final exam, and the balance is determined by the midterm test(s) and laboratories. During the year, the instructor may offer to the students that the test(s) be taken into consideration only if these tests increase their final grades; the same rule is then applied to all students.
The (writtent) final exam is "open notes". This means that the student can have his own notes, as well as copies of the optional course notes provided by the instructor. No other document or textbook can be used. Thus, the laboratory reports cannot be used.
The final exam consists mainly of a set of problems to be solved. Some problems are likely to come, with or without modifications, from the recommended references. It is thus important that the student learn to find and solve as many relevant problems as possible. The instructor may provide a list of relevant problems in the first recommended reference. The final exam may include questions about the laboratories. The questions may be written in French or English (as in the recommended references), or in a mix thereof.
The test may be "open notes" or "closed notes".
All the laboratories must be done. However, the instructor and/or the teaching assistant may decide to evaluate only one laboratory, and they may decide to take into account how many of the laboratories were turned in by each group of students. Although all the students in a group normally receive the same grade for a given laboratory, the instructor reserves the right to take into account the specific contribution of each student. It is therefore very important for each group to turn in the reports for all the laboratories, and for each member of a group to participate actively. |
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Organizational remarks :
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| The course is taught during the first semester of the academic year.
Detailed course information is available from http://intelsig.montefiore.ulg.ac.be/~ries/ or from the Montefiore Institute website http://www.montefiore.ulg.ac.be/
under the name of Verly Jacques. |
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Contacts :
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| Instructor:
Prof. Jacques G. Verly
Tel: 04 366 4994
jacques.verly@ulg.ac.be
Teaching assistant:
Cédric André
R 138 (B28)
Tel: 04 366 5942
c.andre@ulg.ac.be |
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