Course detail

# Signals and Systems

This module provides an introduction to the linear time-invariant continuous- and discrete-time signal and systems. Students are introduced with the various methods of description and analysis of the continuous- and discrete-time signals and systems: time domain, frequency domain, spectrum, Fourier series, sampling, transforms (Laplace, Fourier, Z) and differential equations. These methods are used to analyse signal and system properties and to determine basic characteristic: linearity, time-invariance, causality, stability, power, etc.

Learning outcomes of the course unit

By the end of the module, the student will be able to:
Describe continuous and discrete time signal in time and frequency domain.
Perform continuous and discrete time signal transform using the Fourier series, the Fourier transform, the Laplace transform and the Z-transform.
Discuss practical interpretations of these transforms and their properties.
Describe fundamental properties of LTI continuous-time systems.
Describe fundamental properties of LTI discrete-time systems.
Use the different methods to describe LTI systems.
Determine system response of an LTI system to standard and general signals.
Determine from the description of the LTI system its characteristics such as linearity, time-invariance, causality and stability.

Prerequisites

Student should have sufficient competences of the mathematical analysis for bachelors, mainly: differential and integral calculus, series, and complex numbers.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Oppenheim, A., V., Willsky, A., S. and Hamid, S., Signals and Systems. Prentice Hall; 2nd edition (August 16, 1996), ISBN: 0138147574 (EN)
Mandal, M., Asif, A., Continuous and Discrete Time Signals and Systems, Cambridge University Press; 1 edition, ISBN: 0521854555. (EN)

Planned learning activities and teaching methods

The module will be regularly lectured with laboratory exercises and consultations according to the paragraph 7 of BUT Rules for Studies and Examinations. Students have to write several tests during the semester.

Assesment methods and criteria linked to learning outcomes

In accordance with the paragraph 13 BUT Rules for Studies and Examinations, the point gain from different activities in this module is as follow:
30 points for individual projects,
70 points for final exam.
Only students with submitted individual projects with point gain greater than or equal 10 points are allowed to proceed to the final exam.

Language of instruction

Czech, English

Work placements

Not applicable.

Course curriculum

1. General introduction and motivation; continuous and discrete world, signals classification.
2. Continuous-time and discrete-time signals - basic operations and manipulations, discretization of continuous-time signals.
3. Frequency domain of the continuous-time signal, the Fourier series.
4. The Fourier transform, examples.
5. Time and frequency domain of the discrete-time signal, the discrete Fourier series, the discrete Fourier transform (DFT).
6. Systems – definition, classification, the examples of real systems.
7. Continuous-time LTI system – description using the differential equations, the Laplace transform.
8. Continuous-time LTI system – transfer function, poles and zeros, stability of LTI systems.
9. Continuous-time LTI system – response on the standard input signals, the relation to the BIBO stability.
10. Discrete-time LTI system - description using the difference equations, the Z-transform.
11. Discrete-time LTI system – transfer function, poles and zeros, stability of LTI systems.
12. Discrete-time LTI system – – response on the standard input signals, the relation to the BIBO stability.
13. Summary.

Aims

The purpose of this module is to provide students with the theory of the linear signals and systems with the continuous- and discrete- time and with the fundamental principles of their analysis.

Specification of controlled education, way of implementation and compensation for absences

Controlled tuition in this module is determined by the paragraph 7.5 of BUT Rules for Studies and Examinations and it is performed by a lecturer in accordance with the common sense in the academic sphere.

Classification of course in study plans

• Programme AJEI-H Bachelor's

branch H-AEI , 2. year of study, winter semester, 3 credits, compulsory

#### Type of course unit

Lecture

26 hours, compulsory

Teacher / Lecturer

eLearning