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Multidimensional Signal Analysis, 6 credits
Multidimensionell signalanalys, 6 hp
TSBB06
Main field of study
Electrical EngineeringCourse level
Second cycleCourse type
Programme courseExaminer
Klas NordbergDirector of studies or equivalent
Klas NordbergEducation components
Preliminary scheduled hours: 68 hRecommended self-study hours: 92 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Electrical EngineeringCourse level
Second cycleAdvancement level
A1XCourse offered for
- Computer Science and Engineering, M Sc in Engineering
- Industrial Engineering and Management - International, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Information Technology, M Sc in Engineering
- Biomedical Engineering, M Sc in Engineering
- Computer Science and Software Engineering, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Biomedical Engineering, Master's programme
- Mathematics, Master's programme
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Basic Linear Algebra: vector spaces, bases, scalar product, least squares problem, eigenvalue problems. Basic signal processing (corresponding to Linear Systems): sampling, convolution and Fourier transform of one-variable signals. Basic skills in Matlab is recommended.Intended learning outcomes
Passing the course means that the student is able to use concepts and methods in signal and image processing that are based on linear algebra. The student is then able to:
- Use homogeneous coordinates for the Euclidean geometry of two and three dimensions. This includes points and lines in two dimensions, points, planes, and lines in three dimensions, homographies and camera projections.
- Estimate geometric objects based on various types of least sqaures techniques.
- Use linear representations: bases, subspace bases, and frames for signals.
- Apply linear signal representations on practical problems, such as filter optimization, normalized convolution, over-sampling, PCA, wavelet-transform and filter banks.
Course content
Signal spaces and signal bases, dual bases. Least squares problem, filteroptimering, normalized convolution. Eigenvalue and singular value analysis. Principal component analysis. Frames. Wavelet transform and filterbanks. Projective spaces, homogeneous coordinates, homographies, camera projections. Representation and estimation of various types of geometric objects.
Teaching and working methods
The course has lectures that present basic concepts and theory, accompanied by lessons that exemplify some of the calculations. In a set of mandatory computer exercises, each participant must demonstrate the ability to carry out more complex calculation and answer related questions. The course runs over the entire autumn semester.
Examination
| KTR1 | Optional Written Test | 0 credits | U, G |
| LAB1 | Laboratory Work | 3 credits | U, G |
| TEN2 | Written Examination | 3 credits | U, 3, 4, 5 |
The written examination is divided into four parts that correspond to the four course objectives, and in order to pass the examination a certain level is required for each of the four parts. A failed examination can be completed if at least three of the parts are passed and if it is done as specified in the current course information.
The optional test covers the first half of the course and its result can be used in the first written examination after the course.
Some assignments of the laboratory work may include a small written exam that must be passed by the student before the rest of the assignment can be completed.
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Computer Vision, Image and Audio Coding, Medical Image Analysis, Neural Networks and Learning Systems, Image Sensors
Department
Institutionen för systemteknikDirector of Studies or equivalent
Klas NordbergExaminer
Klas NordbergCourse website and other links
https://www.cvl.isy.liu.se/education/undergraduateEducation components
Preliminary scheduled hours: 68 hRecommended self-study hours: 92 h
Course literature
Additional literature
Compendia
- Prerequisites for studies at advanced level in Image Science at Linköping University
A supplementary compendium, describes prerequisites for the course. In addition to these, articles and exerpts from book and compendiums are used, in accordance with the course information at the start of the course. - Klas Nordberg, Introduction to Representations and Estimation in Geometry
Covers the geometry part of the course.
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| KTR1 | Optional Written Test | 0 credits | U, G |
| LAB1 | Laboratory Work | 3 credits | U, G |
| TEN2 | Written Examination | 3 credits | U, 3, 4, 5 |
The written examination is divided into four parts that correspond to the four course objectives, and in order to pass the examination a certain level is required for each of the four parts. A failed examination can be completed if at least three of the parts are passed and if it is done as specified in the current course information.
The optional test covers the first half of the course and its result can be used in the first written examination after the course.
Some assignments of the laboratory work may include a small written exam that must be passed by the student before the rest of the assignment can be completed.
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Compendia
Prerequisites for studies at advanced level in Image Science at Linköping University
A supplementary compendium, describes prerequisites for the course. In addition to these, articles and exerpts from book and compendiums are used, in accordance with the course information at the start of the course.
Klas Nordberg, Introduction to Representations and Estimation in Geometry
Covers the geometry part of the course.
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
X
|
X
|
X
|
LAB1
TEN2
|
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| 1.2 Fundamental engineering knowledge (G1X level) |
|
|
X
|
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
X
|
X
|
|
LAB1
TEN2
|
||
| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
|
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
|
|
X
|
LAB1
|
||
| 2.2 Experimentation, investigation, and knowledge discovery |
|
X
|
X
|
LAB1
|
||
| 2.3 System thinking |
|
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| 2.4 Attitudes, thought, and learning |
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| 2.5 Ethics, equity, and other responsibilities |
X
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X
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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