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Presentation
Presentation
The main objective of the Signals and Systems course is to provide the students with the basics on the mathematical theory of signals and systems, sucha as: Concepts and properties of signals and systems, Linear time-invariant systems (LTI), Laplace transform, Fourier transform, Z transform, Discrete Fourier Transform, time-domain analysis, frequency-domain analysis and system transfer function. A parallel objective is to introduce the students to Matlab, which is the main tool for the laboratories. This course is a fundamental building block for more advanced subjects such as Telecommunictions, Computer Vision, Image Processing and System modeling.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 5
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Year | Nature | Language
Year | Nature | Language
2 | Mandatory | Português
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Code
Code
ULHT46-7339
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
Introduction and mathematical foundations. Imaginary numbers. Complex numbers. Operations with complex numbers. Sine and cosine. Euler equation. Inverse functions of sine, cosine and tangent. Exponential and logarithm. Derivatives and integrals. Signals. Continuous and discrete signals. Properties of signals. Periodic signals, even and odd signals. Singular signals. Systems. Modeling systems. Linear invariant time signals. Convolution. Laplace Transform. Initial value theorem. Inverse Laplace Transform. Z Transform. Initial and final value theorem. Inverse Z Transform. Fourier Transform. Fourier Transform of periodic signals. Fourier Transform of continuous and discrete signals
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Objectives
Objectives
Knowledge: Concepts and properties of signals and systems, focusing on linear time-invariant systems (LTI), Laplace Transform, Fourier Transform, Z Transform, Discrete Fourier Transform, time-domain system analysis, frequency-domain system analysis. Skills: Analysis of linear time-invariant (LIT) systems, using the tools provided by the Laplace Transform, Fourier Transform and Z Transform. From a theoretical point of view, the analysis is done using the mathematical tools, and from the practical point of view, using the software Matlab. Competences: Analysis and Synthesis of signals using the mathematical tools that transform signals and systems into space S, into frequency domain and analysis in the time-domain as well.
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Teaching methodologies
Teaching methodologies
Use of the questioning method, which aims to make questions to the students. These questions aim to understand the advantages and limitations of the subject of study.
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References
References
Discrete-Time Signal Processing - Pearson New International Edition. Alan Oppenheim, Ronald W. Schafer. Pearson Education Limited, 2014. Processamento Digital de Sinais. Projeto e Análise de Sistemas (2ª Edição). Paulo S. R. Diniz, Sergio L. Netto e Eduardo A. B. Da Silva, Bookman, 2014. Signals and Systems, Alan V. Oppenheim e Alan S. Willsky, Pearson New International Edition, 2013. Sinais e Sistemas (2aEd), Isabel Lourtie, Escolar Editora, 2007. Análise de Sistemas Lineares, Maria Isabel Ribeiro, IST Press, 2007.
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Assessment
Assessment
A nota de avaliação contínua corresponderá à média ponderada, arredondada para a decima, das notas dos testes escritos e dos trabalhos de acordo coma seguinte ponderação: 10% para cada trabalho prático (com um total de 2 trabalhos), 30,00% para o primeiro teste e 50% para o segundo teste. Caso o aluno não aprove nas frequências, haverá um Exame de recurso. Para obter aprovação na disciplina a nota mínima média dos testes é 9 valores e a nota mínima média dos trabalhos é 9 valores.
Na componente prática, os trabalhos laboratórios são os seguintes:
1º trabalho: Pretende introduzir os conceitos de amostragem e reconstrução, assim como verificar de forma prática a convolução de sinais, e como pode ser calculada a resposta de um sistema através da convolução.
2º Trabalho: Introduz a noção de filtros digitais para notas musicais e para sinais EEG, como forma de aplicação da transformada de Laplace e da Transformada Z.
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Mobility
Mobility
No
