Signals and Transforms
Syllabus, Bachelor's level, 1TE746
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Technology G2F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 5 March 2019
- Responsible department
- Department of Electrical Engineering
60 credits within Science and Technology, including Imperative and Object-Oriented Programming Methodology, Single Variable Calculus as well as Linear Algebra and Geometry. Numerical Methods and Simulations as well as Digital Technology and Electronics should have been attended.
On completion of the course the student shall be able to:
- explain the following transform definitions and characteristics: Laplace transform, z-transform, Fourier transform,
- apply transform rules to calculate transforms of simple functions and use tables to calculate inverse transforms,
- account for basic analysis of signal processing systems using transforms,
- account for basic theory of linear, time-invariant systems and their characteristics, such as linearity, time invariability, stability and causality,
- analyse and synthesize simple analog systems,
- explain basic principles for sampling time-continuous signals including the sampling criterion and signal reconstruction,
- analyse and synthesize simple digital filters,
- use transform methods within any of the application areas of the educational programs and in this context implement and present the results of a smaller project.
Basic theory and characteristics of Fourier series, Fourier, Laplace and Z transform of discrete and continuous signals and systems: linearity, delay, attenuation and scaling, behavior during derivation and integration. Convolution. Start and final value theorem. Applications for differential and difference equations.
Discrete and continuous linear time-invariant systems: causality and time invariance. Stability condistions.
Ohms and Kirchhoff's laws in a complex form and the concept of impedance. Operational Amplifier. Passive and active analogue filters and the terms transfer function, poles, zeroes, magnitude surfaces, cut-off frequency and Bode diagams.
The sampling theorem. Analysis and synthesis of analogue and digital filters. Examples of applications.
A project aimed at deepening the understanding of the properties of transforms and their use in relevant applications.
Lectures, lessons, exercises. Laboratory work may be part of the special project. Assignments during the course as instructed at the start of the course.
Written tests combined with a complementary written exam (6 credits), oral and written presentation of project (2 credits), assignments (2 credits).
If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.