Signals and Systems, and Transform Theory, 8 credits
Signaler och system samt transformer, 8 hp
TSDT84
Main field of study
Applied Mathematics Electrical EngineeringCourse level
First cycleCourse type
Programme courseExaminer
Lasse AlfredssonDirector of studies or equivalent
Lasse AlfredssonEducation components
Preliminary scheduled hours: 76 hRecommended self-study hours: 137 h
Main field of study
Applied Mathematics, Electrical EngineeringCourse level
First cycleAdvancement level
G2XCourse offered for
- Master of Science in Computer Science and Engineering
- Master of Science in Industrial Engineering and Management - International
- Master of Science in Industrial Engineering and Management
Prerequisites
Calculus, Linear Algebra, Basic Electronics.Intended learning outcomes
This course will give basic knowledge about analysis and synthesis of continuous-time and discrete-time linear systems, primarily through the use of mathematical tools from transform theory. Students who pass the course are expected to:
- Define and interpret system properties such as linearity, time invariance, causality, and stability, as well as manage the consequences of those associated with problem solving.
- Interpret and mathematically manage time and frequency characteristics of deterministic continuous-time and discrete-time signals and linear time invariant (LTI) systems.
- Sketch the Bode plot of an LTI system and analyze how it is influenced by the positions of the poles and zeros of the transfer function.
- Calculate the output signal for given LTI systems, both in the time domain and in the frequency/transform domain - in the latter case, by means of appropriate transformations.
- Model problems from different application areas (such as electrical engineering, mechanical engineering, biotechnology, economics, and more) via LTI system models and analyze these models, both in the time domain and the frequency/transform domain.
- Describe the sampling theorem and its consequences, and use this theorem in problem solving and to design and analyze simple sampled systems.
- Give a well structured and logically coherent account - using adequate terminology - of the connections between different concepts in the course, both in Swedish and in English.
Course content
- About signals and systems.
- Fundamental transform theory - Fourier series, the Fourier transform, the Laplace transform, the z-transform.
- System properties - in particular linearity, time invariance, causality and stability.
- Impulse response and step response. Convolution.
- Differential and difference equation description of linear continuous-time and discrete-time systems, respectively.
- Frequency analysis of signals and systems. Frequency spectrum, amplitude and phase spectrum. Frequency response. Magnitude and phase characteristics.
- About passive frequency selective filters.
- Laplace transform and z-transform analysis of signals and systems. The transfer function. Pole-zero diagrams.
- Cascade couplings and feedback.
- Sampling and reconstruction - time properties and spectral relations. The Poisson summation formula, the sampling theorem and pulse amplitude modulation.
- Application examples.
Teaching and working methods
Lectures, lessons, and laboratory work using Matlab.
Some of the lectures are given in the form of "flipped classroom", where the students are expected to have watch related videos before the lectures.
Examination
KTR1 | Written test | 2 credits | U, G |
LAB1 | Laboratory work | 1 credits | U, G |
TEN3 | Written examination | 5 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Subsequent courses in areas such as signal and image processing, telecommunications, electronics, control engineering, biomedical engineering, etc.
About teaching and examination language
The teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows:
- If teaching language is Swedish, the course as a whole or in large parts, is taught in Swedish. Please note that although teaching language is Swedish, parts of the course could be given in English. Examination language is Swedish.
- If teaching language is Swedish/English, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English (depending on teaching language).
- If teaching language is English, the course as a whole is taught in English. Examination language is English.
Other
The course is conducted in a manner where both men's and women's experience and knowledge are made visible and developed.
The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point.
Department
Institutionen för systemteknikDirector of Studies or equivalent
Lasse AlfredssonExaminer
Lasse AlfredssonCourse website and other links
http://www.cvl.isy.liu.se/education/undergraduate/TSDT84Education components
Preliminary scheduled hours: 76 hRecommended self-study hours: 137 h
Course literature
Books
Other
Choose one of the books that are suggested as suitable course books on the course web page. The lectures are primarily formed according to "Linear Systems and Signals", 2nd Edition, B. P. Lathi, Oxford Univ. Press.
Code | Name | Scope | Grading scale |
---|---|---|---|
KTR1 | Written test | 2 credits | U, G |
LAB1 | Laboratory work | 1 credits | U, G |
TEN3 | Written examination | 5 credits | U, 3, 4, 5 |
Course syllabus
A syllabus must be established for each course. The syllabus specifies the aim and contents of the course, and the prior knowledge that a student must have in order to be able to benefit from the course.
Timetabling
Courses are timetabled after a decision has been made for this course concerning its assignment to a timetable module.
Interrupting a course
The vice-chancellor’s decision concerning regulations for registration, deregistration and reporting results (Dnr LiU-2015-01241) states that interruptions in study are to be recorded in Ladok. Thus, all students who do not participate in a course for which they have registered must record the interruption, such that the registration on the course can be removed. Deregistration from a course is carried out using a web-based form: https://www.lith.liu.se/for-studenter/kurskomplettering?l=en.
Cancelled courses
Courses with few participants (fewer than 10) may be cancelled or organised in a manner that differs from that stated in the course syllabus. The Dean is to deliberate and decide whether a course is to be cancelled or changed from the course syllabus.
Guidelines relating to examinations and examiners
For details, see Guidelines for education and examination for first-cycle and second-cycle education at Linköping University, Dnr LiU-2019-00920 (http://styrdokument.liu.se/Regelsamling/VisaBeslut/917592).
An examiner must be employed as a teacher at LiU according to the LiU Regulations for Appointments, Dnr LiU-2017-03931 (https://styrdokument.liu.se/Regelsamling/VisaBeslut/622784). For courses in second-cycle, the following teachers can be appointed as examiner: Professor (including Adjunct and Visiting Professor), Associate Professor (including Adjunct), Senior Lecturer (including Adjunct and Visiting Senior Lecturer), Research Fellow, or Postdoc. For courses in first-cycle, Assistant Lecturer (including Adjunct and Visiting Assistant Lecturer) can also be appointed as examiner in addition to those listed for second-cycle courses. In exceptional cases, a Part-time Lecturer can also be appointed as an examiner at both first- and second cycle, see Delegation of authority for the Board of Faculty of Science and Engineering.
Forms of examination
Principles for examination
Written and oral examinations and digital and computer-based examinations are held at least three times a year: once immediately after the end of the course, once in August, and once (usually) in one of the re-examination periods. Examinations held at other times are to follow a decision of the board of studies.
Principles for examination scheduling for courses that follow the study periods:
- courses given in VT1 are examined for the first time in March, with re-examination in June and August
- courses given in VT2 are examined for the first time in May, with re-examination in August and October
- courses given in HT1 are examined for the first time in October, with re-examination in January and August
- courses given in HT2 are examined for the first time in January, with re-examination in March and in August.
The examination schedule is based on the structure of timetable modules, but there may be deviations from this, mainly in the case of courses that are studied and examined for several programmes and in lower grades (i.e. 1 and 2).
Examinations for courses that the board of studies has decided are to be held in alternate years are held three times during the school year in which the course is given according to the principles stated above.
Examinations for courses that are cancelled or rescheduled such that they are not given in one or several years are held three times during the year that immediately follows the course, with examination scheduling that corresponds to the scheduling that was in force before the course was cancelled or rescheduled.
When a course is given for the last time, the regular examination and two re-examinations will be offered. Thereafter, examinations are phased out by offering three examinations during the following academic year at the same times as the examinations in any substitute course. If there is no substitute course, three examinations will be offered during re-examination periods during the following academic year. Other examination times are decided by the board of studies. In all cases above, the examination is also offered one more time during the academic year after the following, unless the board of studies decides otherwise.
If a course is given during several periods of the year (for programmes, or on different occasions for different programmes) the board or boards of studies determine together the scheduling and frequency of re-examination occasions.
Retakes of other forms of examination
Regulations concerning retakes of other forms of examination than written examinations and digital and computer-based examinations are given in the LiU guidelines for examinations and examiners, http://styrdokument.liu.se/Regelsamling/VisaBeslut/917592.
Registration for examination
Until January 31 2021, the following applies according to previous guidelines: In order to take an written, digital or computer-based examination student must register in advance at the Student Portal during the registration period, which opens 30 days before the date of the examination and closes 10 days before it. Candidates are informed of the location of the examination by email, four days in advance. Students who have not registered for an examination run the risk of being refused admittance to the examination, if space is not available.
From February 1 2021, new guidelines applies for registration for written, digital or computer-based examination, Dnr LiU-2020-02033 (https://styrdokument.liu.se/Regelsamling/VisaBeslut/622682).
Symbols used in the examination registration system:
** denotes that the examination is being given for the penultimate time.
* denotes that the examination is being given for the last time.
Code of conduct for students during examinations
Details are given in a decision in the university’s rule book: http://styrdokument.liu.se/Regelsamling/VisaBeslut/622682.
Retakes for higher grade
Students at the Institute of Technology at LiU have the right to retake written examinations and digital and computer-based examinations in an attempt to achieve a higher grade. This is valid for all examination components with code “TEN”, “DIT” and "DAT". The same right may not be exercised for other examination components, unless otherwise specified in the course syllabus.
A retake is not possible on courses that are included in an issued degree diploma.
Grades
The grades that are preferably to be used are Fail (U), Pass (3), Pass not without distinction (4) and Pass with distinction (5).
- Grades U, 3, 4, 5 are to be awarded for courses that have written or digital examinations.
- Grades Fail (U) and Pass (G) may be awarded for courses with a large degree of practical components such as laboratory work, project work and group work.
- Grades Fail (U) and Pass (G) are to be used for degree projects and other independent work.
Examination components
The following examination components and associated module codes are used at the Faculty of Science and Engineering:
- Grades U, 3, 4, 5 are to be awarded for written examinations (TEN) and digital examinations (DIT).
- Examination components for which the grades Fail (U) and Pass (G) may be awarded are laboratory work (LAB), project work (PRA), preparatory written examination (KTR), digital preparatory written examination (DIK), oral examination (MUN), computer-based examination (DAT), home assignment (HEM), and assignment (UPG).
- Students receive grades either Fail (U) or Pass (G) for other examination components in which the examination criteria are satisfied principally through active attendance such as tutorial group (BAS) or examination item (MOM).
- Grades Fail (U) and Pass (G) are to be used for the examination components Opposition (OPPO) and Attendance at thesis presentation (AUSK) (i.e. part of the degree project).
In general, the following applies:
- Mandatory course components must be scored and given a module code.
- Examination components that are not scored, cannot be mandatory. Hence, it is voluntary to participate in these examinations, and the voluntariness must be clearly stated. Additionally, if there are any associated conditions to the examination component, these must be clearly stated as well.
- For courses with more than one examination component with grades U,3,4,5, it shall be clearly stated how the final grade is weighted.
For mandatory components, the following applies: If special circumstances prevail, and if it is possible with consideration of the nature of the compulsory component, the examiner may decide to replace the compulsory component with another equivalent component. (In accordance with the LiU Guidelines for education and examination for first-cycle and second-cycle education at Linköping University, http://styrdokument.liu.se/Regelsamling/VisaBeslut/917592).
For written examinations, the following applies: If the LiU coordinator for students with disabilities has granted a student the right to an adapted examination for a written examination in an examination hall, the student has the right to it. If the coordinator has instead recommended for the student an adapted examination or alternative form of examination, the examiner may grant this if the examiner assesses that it is possible, based on consideration of the course objectives. (In accordance with the LiU Guidelines for education and examination for first-cycle and second-cycle education at Linköping University, http://styrdokument.liu.se/Regelsamling/VisaBeslut/917592).
Reporting of examination results
The examination results for a student are reported at the relevant department.
Plagiarism
For examinations that involve the writing of reports, in cases in which it can be assumed that the student has had access to other sources (such as during project work, writing essays, etc.), the material submitted must be prepared in accordance with principles for acceptable practice when referring to sources (references or quotations for which the source is specified) when the text, images, ideas, data, etc. of other people are used. It is also to be made clear whether the author has reused his or her own text, images, ideas, data, etc. from previous examinations, such as degree projects, project reports, etc. (this is sometimes known as “self-plagiarism”).
A failure to specify such sources may be regarded as attempted deception during examination.
Attempts to cheat
In the event of a suspected attempt by a student to cheat during an examination, or when study performance is to be assessed as specified in Chapter 10 of the Higher Education Ordinance, the examiner is to report this to the disciplinary board of the university. Possible consequences for the student are suspension from study and a formal warning. More information is available at https://www.student.liu.se/studenttjanster/lagar-regler-rattigheter?l=en.
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.
Books
Other
Choose one of the books that are suggested as suitable course books on the course web page. The lectures are primarily formed according to "Linear Systems and Signals", 2nd Edition, B. P. Lathi, Oxford Univ. Press.
Note: The course matrix might contain more information in Swedish.
I | U | A | Modules | Comment | ||
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1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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A: Calculus, Linear algebra. A,U: Transform theory as a mathematical tool. |
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1.2 Fundamental engineering knowledge (G1X level) |
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X
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X
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LAB1
TEN3
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A: Electronics/Electric circuits. U: Continuous time and discrete time signals and linear systems. |
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1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
X
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Relates the course material to continuation courses and applications. |
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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 |
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X
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X
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LAB1
TEN3
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U,A: Modelling and solving formulated problems, including plausibility assessment of the solutions. |
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2.2 Experimentation, investigation, and knowledge discovery |
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2.3 System thinking |
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X
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LAB1
TEN3
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Modelling and analysis of linear systems. |
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2.4 Attitudes, thought, and learning |
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X
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X
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TEN3
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U,A: Individual problem solution. A: Ability to plan your time and your resources; to work towards a deadline. |
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2.5 Ethics, equity, and other responsibilities |
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3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
3.1 Teamwork |
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X
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LAB1
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Labs in smaller groups. Examination of the ability, to some extent, via the quality of the lab presentation. |
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3.2 Communications |
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X
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LAB1
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Lab presentation. The ability to communicate mathematical-technical reasoning in a logical and structured way. |
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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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X
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LAB1
TEN3
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Simple linear systems: Handling of demands, synthesis/modelling and evaluation of linear systems. |
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4.4 Designing |
X
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X
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LAB1
TEN3
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Filter synthesis methods. |
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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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