Objectives and Contextualisation
Introduce the student to the analysis and characterization of signals and systems, with emphasis on linear systems.
Learn the Laplace transform and its properties.
Learn how to apply the Laplace transform to circuit analysis.
Learn and apply the concept of transfer function of an LTI system.
Learn how to obtain the Bode diagram of a system.
Learn the Fourier transform and its properties.
Learn how to apply the Fourier transform to periodic signals (Fourier series) and the limitation in time (windowing) and frequency (Gibbs phenomenon).
Learn and apply the concepts of energy and power of a signal.
Learn and know how to apply the concepts of correlation and spectrum of signals
Competences
Electronic Engineering for Telecommunication
Communication
Develop personal attitude.
Develop personal work habits.
Develop thinking habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Telecommunication Systems Engineering
Communication
Develop personal attitude.
Develop personal work habits.
Develop thinking habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Learning Outcomes
Analyse and design analogue signal processing diagrams.
Apply the basic concepts of linear systems and the related functions and transforms, to resolve engineering problems.
Autonomously learn new and suitable knowledge and techniques for devising, developing or exploiting telecommunication systems, especially with regard to basic signal processing subsystems.
Communicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.
Describe the fundamental parameters of a communications system, in the functional aspect.
Develop curiosity and creativity.
Develop independent learning strategies.
Develop the capacity for analysis and synthesis.
Manage available time and resources.
Manage available time and resources. Work in an organised manner.
Use computer tools to research bibliographic resources or information on telecommunications and electronics.
Work autonomously.
Content
Introduction to the subject. Signals and systems.
Signals. Independent variable transforms and basic signals.
System properties: linearity, invariance, causality and stability.
Linear and time invariant systems (LTI). Convolution equation.
The Laplace transform.
Laplace transform. Definition. Properties.
Solution of differential equations using the Laplace transform.
Obtaining the inverse Laplace transform.
Applications of the Laplace transform.
Analysis of circuits with capacitors and inductors.
Transfer function of a system. Definition and obtention of the impulse response.
Pole and zero diagrams and system stability.
Permanent response of a system. Bode diagrams.
The Fourier transform.
Definition of the Fourier transform.
Transform of basic signals.
Properties of the Fourier transform.
Limitation in frequency (Gibbs phenomenon) and limitation in time (windowing).
Fourier transform of periodic signals. The Fourier series.
Correlation and spectrum of deterministic signals.
Energy and power
Correlation and energy spectrum.
Correlation and power spectrum
