Course syllabus for Transforms, signals and systems

Course syllabus adopted 2023-02-04 by Head of Programme (or corresponding).

Overview

  • Swedish nameTransformer, signaler och system
  • CodeSSY081
  • Credits7.5 Credits
  • OwnerTKDAT
  • Education cycleFirst-cycle
  • Main field of studyElectrical Engineering
  • DepartmentELECTRICAL ENGINEERING
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 49122
  • Block schedule
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0121 Examination 5 c
Grading: TH		5 c0 c0 c0 c0 c0 c
  • 28 Okt 2024 am J
  • 08 Jan 2025 pm J
  • 27 Aug 2025 pm J
0221 Laboratory 2.5 c
Grading: UG		2.5 c0 c0 c0 c0 c0 c

In programmes

Examiner

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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

Calculus in one variable, complex numbers and complex exponential functions. Electric circuits.

Aim

The course should provide fundamental knowledge about linear systems and how they can be used to describe physical phenomenons. Different mathematical tools which can be used to calculate the relationship between input- and output signals in linear systems will be presented.

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

  • identify and give examples of different signal types, such as periodic signals, absolutely summable/integrable signals, finite energy signals and band-limited signals.
  • identify important system properties, such as linearity, shift-invariance, causality and BIBO-stability, in examples.
  • select the appropriate transforms (Fourier series, Continuous and Discrete time Fourier transform, Laplace transform, Discrete Fourier transform and z-transform) for a given problem.
  • compute the transforms of commonly used signals in the course.
  • apply transform techniques to find the output of a LTI system, both in continuous and discrete time.
  • identify the Nyquist rate of a band-limited signal.
  • employ the Sampling Theorem to reconstruct band-limited signals from sampled data.
  • interpret plots of the DFT (Discrete Fourier Transform) of a sampled signal.
  • interpret the effect of filters on a given signal.

Content

Course content:
  • Continuous and discrete time signals. Signal models.
  • LTI-systems and their properties. Convolution.
  • Fourier representation of different kinds of signals and their properties.
  • Parseval's theorem.
  • Sampling and reconstruction of sampled signals.
  • The Discrete Fourier transform (DFT)
  • The Laplace- and z-transform.
  • Impulse and step response.
  • The system descriptions: Transfer function and Frequency response.
  • Filters.

Organisation

Lectures, tutorials and a laborative exercise.

Literature

See course web-page.

Examination including compulsory elements

The course is examined by an individual written exam for 5 ECTS points and laboratory project assignments 2.5 ECTS points. The Laboratory work is carried out in groups and graded with pass (P) or fail (F), while the exam is graded with (F), 3, 4, 5. 

To pass the course, the student needs to pass both modules and then the grade of the entire course is based on the grade of the exam.

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.