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## Syllabus for

SSY080 - Transforms, signals and systems
Transformer, signaler och system

Syllabus adopted 2019-02-08 by Head of Programme (or corresponding)
Owner: TKDAT
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Electrical Engineering
Department: 32 - ELECTRICAL ENGINEERING

Teaching language: Swedish
Application code: 49114
Open for exchange students: No
Block schedule: B+
Only students with the course round in the programme plan

 Module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0106 Examination 7,5c Grading: TH 7,5c 31 Oct 2019 am M 08 Jan 2020 pm SB_MU 26 Aug 2020 pm J

#### In programs

TKDAT COMPUTER SCIENCE AND ENGINEERING, Year 3 (compulsory)
MPBME BIOMEDICAL ENGINEERING, MSC PROGR, Year 1 (elective)

Ants Silberberg

#### Replaces

TMA780   Mathematics

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### 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 solve the LTI-equation y = h * x, both in continuous and discrete time, when two of the factors are known.
• 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.

#### 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.

#### Organisation

Lectures, tutorials and a laborative exercise.

#### Literature

See course web-page.

#### Examination including compulsory elements

• A written exam
• A laborative exercise

Published: Mon 28 Nov 2016.