Signals and Systems
Keywords |
Classification |
Keyword |
OFICIAL |
Physics |
Instance: 2020/2021 - 2S
Cycles of Study/Courses
Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
MI:EF |
70 |
study plan from 2017/18 |
2 |
- |
6 |
56 |
162 |
Teaching language
Portuguese
Objectives
- Understand the concept of information, the process that led to its quantification and coding in the form of a signal
- Understand what is meant by system and the universality of its characteristics;
- Know the methodologies and the physical/mathematical techniques to study the properties of signals and important systems in physics and engineering.
- Understand the central characteristics of linear and time invariant systems (SLIT);
- Master the behavior of SLIT systems actuated by continuous or discrete signals, including the actual situation in which signals are degraded by noise;
- Understand the fundamental principles of systems control and the techniques and procedures used for your study;
- Understand the wide domain of application of the principles, methodologies and techniques studied;
- Acquire skills to work effectively in applications involving systems, as well as proceed to further studies in this area;
- To internalize the level of complexity that a system may have considering two examples: the Earth System and the Biological Cell System.
Learning outcomes and competences
Working method
Presencial
Pre-requirements (prior knowledge) and co-requirements (common knowledge)
Program
PROGRAM SUMMARY
Concept of information, its quantification and its signal coding. Signal types and main characteristics. What are systems, essential characteristics and the importance of their interface with the outside world. Invariant linear system (SLI), examples. Laplace and Fourier Transforms, properties, applications in Physics and Engineering. Description and analysis of SLI in time and frequency. Examples of electrical and optical systems. Causal SLI and Hilbert Transform. Discreet SLI. Random signals and SLI's. Feedback and control systems, introduction to nonlinear systems. An integrated perspective on signals and systems considering the comparative analysis of a simple electrical system (RLC circuit), a complex macroscopic system (the Earth System) and a biological system (the cell).
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1. INTRODUCTION
Identification of the macros objectives of the curricular unit by the exposition and framing around the following questions: what is information? How is it quantified? What are signals? How can they encode information? How are signals transmitted? What are hardware and software? What is a system? What are its main features? Is the interface of a system important? Is the universe a system?
Introduction to the Earth System and a biological system (cell).
2. GENERAL CONCEPTS
Signals. Signal types. Continuous and discret signals. Systems. Types of systems. Importance of linear and time invariant systems (SLIT) and their analysis. Reference to SLIT systems outside the time domain. The case of optical SLIT systems.
3. LAPLACE AND FOURIER TRANSFORM
Importance of use of these mathematical tools in the context of studying SLIT systems. The formulation of eigenfunctions. Laplace transform. Convergence region, properties. Unilateral Laplace Transform and its importance in the context of causal systems. The fundamental principle of complex analysis. Circular integral involving singularities. Cauchy integrals and residual calculus. Inverse Laplace Transform. Calculation using the residual theorem and partial fraction expansion.
Fourier transform. The Fourier Transform as a particular case of the Laplace Transform. Fourier transform properties. Inverse Fourier Transform. Parseval's theorem. Passing band-time product. Reference to other transformations of interest in Physics and Engineering.
4. SLIT SYSTEM ANALYSIS IN THE TEMPORAL DOMAIN
Description by linear differential equations with constant coefficients. Using the Laplace Transform to solve the differential equation of systems with initial conditions. Important examples in physics.
State space description. System state variables. System matrix, input and output matrices. Determination of these matrices from the coefficients of the differential equation. State equation and output equation. Transformation matrices between equivalent representations in state space. Controllable and observable systems.
Description by impulse response. Convolution operation. System impulse response. Physical interpretation. Series and parallel systems.
5. SLIT SYSTEM ANALYSIS IN THE FREQUENCY DOMAIN
Eigenfunctions of SLIT systems. Transfer function. Determination of the transfer function from the system differential equation. Relationship between the transfer function and the SLIT description in state space. Impact of initial conditions. Transfer function and impulse response of the SLIT system. Frequency response; amplitude and phase. Physical interpretation. Goat diagrams.
Example of systems with non-temporal frequencies; optical systems and spatial frequencies.
6. CAUSALITY AND HILBERT'S TRANSFORM
Causal systems. Causal SLIT systems. Causal signals. Relationship between the real and imaginary parts of the causal signal Fourier transform. Hilbert transform. Consequences of this transform. Relationship between amplitude and phase of frequency response of a causal SLIT system.
7. DISCRET SLIT SYSTEMS
Fourier transform of periodic signals. Properties. Periodic convolution. Sampling. Sampling theorem. Frequency domain sampling. Discreet signs. Fourier transform of discrete signals. Properties. Transform Z. Convergence region of Transform Z. Relationship of Transform Z to Laplace and Fourier transforms. Z transform theorems. Inverse Z transform. Z and pole diagrams in the Z plane.
Discrete time SLIT systems. Equations to linear differences with constant coefficients. Characteristic sequences (self-sequences). Transfer function; determination from difference equations. Description of discrete state-space SLIT systems. Discreet convolution and impulsive response. Z Transform convolution theorem.
8. RANDOM SIGNS AND SLIT SYSTEMS
Random Signals. Expected and average value of a statistical set. Stationary and ergodic random processes. Real and complex signal correlation functions: autocorrelation, self-covariance, cross correlation, cross covariance. Power spectral densities. White noise.
SLIT systems response to random signals. Stationary and ergodicity. Linear average and autocorrelation of SLIT systems output. Cross correlation function between input and output of SLIT systems. Power spectral density and SLIT systems. SLIT systems output with white noise at input. Wiener filters.
9. FEEDBACK AND CONTROL SYSTEMS
Feedback theory. Open loop and closed loop systems. Transfer function. Control principle. On-off control systems, proportional control systems, differential and integral control systems. Analysis and design of frequency and state space control systems. Stability criteria. Bases of digital control systems.
Introduction to nonlinear control systems.
10. INFORMATION THEORY
General Aspects of Information Theory. Universe of messages. Message source entropy and connections to thermodynamic entropy. Flow of information. Scanning and coding. Shannon's theorem. Shannon-Hartley theorem for communication channels, consequences and applications.
11. SOME THOUGHS
Some thoughs about Information, Signals, Systems, Life and Universe
Mandatory literature
Isabel Lourtie; Sinais e Sistemas
Complementary Bibliography
B. Girod, R Rabenstein, A. Stenger; Sinais e Sistemas
J. L. Martins de Carvalho; Dynamical Systems and Automatic Control
E. Laszlo; The Systems View of the World
Teaching methods and learning activities
The best approach will be sought to achieve the desired learning objectives.
keywords
Technological sciences > Engineering > Systems engineering > Systems theory
Evaluation Type
Evaluation with final exam
Assessment Components
designation |
Weight (%) |
Exame |
100,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
designation |
Time (hours) |
Frequência das aulas |
56,00 |
Estudo autónomo |
106,00 |
Total: |
162,00 |
Eligibility for exams
Attendance in 2/3 of the practical classes.
Calculation formula of final grade
At the end of the semester students will have a Test. If the grade is equal to or higher than 9.5, the students have exemption from Exam. If the student under these conditions wishes to go to the Exam, the final grade will be the major of the Test/Exam grades.
Classification improvement
At the end of the semester students will have a Test. If the grade is equal to or higher than 9.5, the students have exemption from Exam. If the student under these conditions wishes to go to the Exam, the final grade will be the major of the Test/Exam grades.
Observations
The Jury of the curricular unit is constituted by:
- Jose Luis Campos Oliveira Santos
- Frederico André Branco dos Reis Francisco
- Pedro Alberto da Silva Jorge