Course syllabus for Linear systems and transforms

Course syllabus adopted 2021-02-10 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjära system och transformer
  • CodeTMA982
  • Credits7.5 Credits
  • OwnerTKELT
  • Education cycleFirst-cycle
  • Main field of studyElectrical Engineering, Biomedical engineering
  • DepartmentELECTRICAL ENGINEERING
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 50114
  • Maximum participants200
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0111 Laboratory 2.5 c
Grading: UG		0 c0 c2.5 c0 c0 c0 c
0211 Examination 5 c
Grading: TH		0 c0 c5 c0 c0 c0 c

In programmes

Examiner

Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Basic knowledge in mathematical calculus and linear algebra (elementary functions, integral and differential calculus, differential equations, complex numbers, vectors and matrices, systems of linear equations).

Aim

The purpose of the course is to provide the foundation to solve engineering problems using mathematical modeling. Mathematical methods to describe and analyse linear and time-invariant systems (filters) are given special attention. A good understanding of such systems is necessary for continued studies in several areas, such as control, signal processing, communication systems, biomedical engineering and information theory.

Learning outcomes (after completion of the course the student should be able to)

  • understand the basic properties of signals and systems and be able to explain them to others.
  • determine if a system is linear and time invariant (LTI) as well as explain why these properties make systems more easily analyzed.
  • describe how and when one uses as well as the relation between the tools thought in this course, such as Fouriertransforms/series, Laplace and Z- transforms and convolution, to analyze signals and LTI-systems and apply these tools to transform between time and frequency domain and to determine the system behavior for arbitrary input signal.
  • from a mathematical description of a system, such as, a differential equation, zero-pole diagram, impuls response or system function, calculate and sketch the frequency response, as well as amplitud and phase characteristics of the LTI-system
  • demonstrate an understanding of the relationship between different descriptions of a LTI-system, such as, block diagram, diff-equations, impuls response, frequency response and transfer function, by showing how one can transform one description to the other and use them to draw conclusions regarding the properties of the system.
  • use digital tools, such as Discrete Fouriertransform, to analyze and process sampled continuos signals and discrete signals and understand important aspects to be able to do this, such as aliasing, the sampling theorem and the connection between the frequency content of the continuos signal and it sampled discrete counter-part.
  • combine the knowledge and skills listed above and apply it to solve new and unfamiliar problems.

Content

Fourier series, Laplace transform, Fourier transform, z-transform, distributions, impulse response, convolution, continuous- and discrete-time LTI filters, stability, frequency response, sampling theorem, difference equations. Properties of and classification of signals and systems. Connection between different ways to describe linear systems. Synthesis and realisation of analog and digital filters.

Organisation

Lectures, classroom exercises, computer exercises with Matlab. Written examination.

Literature

See the course homepage.

Examination including compulsory elements

Written examination and passed laboratory exercises.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.