# SF1635 Signals and Systems, part I 7.5 credits

Basics of continuous-time signals and their representation. Basics of ordinary differential equations and linear systems of differential equations.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus SF1635 (Autumn 2010–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

Signals and generalized functions. Fourier series. Fourier Transform of continuous-time signals. Sampling of continuous-time signals. LTI-system. Laplace transforms. Existence and unicity of solutions of ODEs and system of ODEs.

Methods to solve linear and separable ODEs of order 1 and for systems with constant coefficients.

### Intended learning outcomes

After passing the course you should

• be able to use generalized functions to describe signals,
• be able to represent periodic continuous-time signals with Fourier series,
• be able to determine the Fourier and Laplace Transforms of generalized functions,
• know about the most important properties of these transforms,
• be able to describe the frequence properties of signals,
• be able to describe the properties of sampled continuous-time signals,
• have some practice in using Matlab to analyse signals,
• be able to solve linear and systems of linear equations in case the coefficients are constant
• be able to solve separable and linear ODEs of order 1 with standard methods.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

SF1624, SF1625, SF1626 or equivalent. Some experience of Matlab.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

Zill-Cullen/Differential Equations with Boundary-Value Problems

Exempelsamling till Signaler och system I

Råde-Westergren/Mathematics Handbook for Science and Engineering.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• LABA - Assignment, 0,7 hp, betygsskala: P, F
• TENA - Examination, 6,8 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Other requirements for final grade

One written examination (TEN1; 6,8 cr)
One homework problem (LAB1; 0.7 cr).

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF1635

SCI/Mathematics

### Main field of study

Mathematics, Technology

First cycle