Discrete-time signals and systems
Objectives and Contextualisation
The processing of sequences of numbers, also known as discrete signals, is a task present in virtually all information transmission, processing and storage systems, even when the source signals can be analog. The aim of the course is to provide the student with the fundamental knowledge to describe the discrete signals and the systems that deal with them, both in the temporal domain and in the frequency or transformed domains.
The specific goals are:
To understand the representation of discrete signals over time, as well as their properties.
To analyze the systems for the discrete signals processing over time and propose alternative ways of describing them.
To represent signals and systems in transformed domains: in the frequency domain and in the Z domain.
To design basic digital filters.
To relate discrete signals with the periodic sampling of analog signals and with their reconstruction.
To apply the Matlab programming environment to solve digital signal processing problems.
To characterize random discrete signals.
Competences
Electronic Engineering for Telecommunication
Communication
Develop personal attitude.
Develop personal work habits.
Develop thinking habits.
Draft, develop and sign projects in the field of telecommunications engineering designed to conceive, develop or exploit electronic systems
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Resolve problems with initiative and creativity. Make decisions. Communicate and transmit knowledge, skills and abilities, in awareness of the ethical and professional responsibilities involved in a telecommunications engineer's work.
Work in a multidisciplinary group and in a multilingual environment, and communicate, both in writing and orally, knowledge, procedures, results and ideas related with telecommunications and electronics
Work in a team.
Telecommunication Systems Engineering
Communication
Develop personal attitude.
Develop personal work habits.
Develop thinking habits.
Draft, develop and sign projects in the field of telecommunications engineering that, depending on the speciality, are aimed at the conception, development or exploitation of telecommunication and electronic networks, services and applications.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Resolve problems with initiative and creativity. Make decisions. Communicate and transmit knowledge, skills and abilities, in awareness of the ethical and professional responsibilities involved in a telecommunications engineer's work.
Work in a multidisciplinary group and in a multilingual environment, and communicate, both in writing and orally, knowledge, procedures, results and ideas related with telecommunications and electronics.
Work in a team.
Learning Outcomes
Analyse and design digital signal processing diagrams.
Communicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.
Develop and seek basic signal processing applications other than for communications.
Develop curiosity and creativity.
Develop independent learning strategies.
Develop systemic thinking.
Develop the capacity for analysis and synthesis.
Devise and seek basic applications for signal processing other than communications.
Efficiently use ICT for the communication and transmission of ideas and results.
Illustrate signal and communication processing algorithms using a basic mathematical formalism.
Illustrate the algorithms of signal processing and communications using a basic mathematical formalism.
Make basic use of computer applications in digital processing.
Make one's own decisions.
Transfer concepts of discreet mathematics to telecommunications, in the field of the processing of numerical series by means of digital filters.
Transfer concepts of discrete mathematics to telecommunications, in the area of numerical series processing using digital filters
Use computer applications for basic digital processing.
Work autonomously.
Work cooperatively.
Content
1. Signals and discrete systems
Signals: properties, transformations and basic signals
Systems: properties, basic systems
Convolution
Description of systems using finite difference equations
2. Frequency representation
Fourier transform (FT): definition, properties, convolution theorem
Discrete Fourier Transform (DFT): definition, properties, circular convolution
Correlation and spectrum
Decimation and interpolation
3. Sampling and reconstruction
Periodic sampling
Sampling representation in the frequency domain
Reconstruction of limited band signals: Nyquist Theorem
Modification of the sampling frequency
4. Representation of signals and systems in the Z domain
The Z-transform: definition and properties
The inverse Z-transform
Frequency response and transfer function
5. System analysis
Inverse, minimum-phase and all-pass systems
Linear phase systems
Introduction to the design of IR and IIR filters
Presential
TRUE
Discrete-time signals and systems
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or HaDEA. Neither the European Union nor the granting authority can be held responsible for them. The statements made herein do not necessarily have the consent or agreement of the ASTRAIOS Consortium. These represent the opinion and findings of the author(s).
