Scientific Disciplinary Sector (SSD)
INF/01 - INFORMATICS
The teaching is organized as follows:
The course objective is to give students the mathematical tools required for the analysis and modeling of linear, time-invariant (LTI) systems, and of the input/output signals to an LTI system. The model will allow students to study the main system properties and to address the general concepts of controller and filters to perform simple control actions on the dynamic system and filter operations on the input/output signals.
The mathematical tools will be based on analysis methods in the time domain, as well as of the complex variables s, z and the frequency of the input/output signals. Analysis and synthesis will be carried out both for continuous and discrete time systems and signals. The theoretical concepts acquired during the course will be consolidated with exercise sessions addressing the solution of basic problems with analytical approach and with numerical simulations.
The theoretical aspects will be integrated with MATLAB code. The LTI systems described by differential equations will be analyzed with SIMULINK tool that is integrated in the MATLAB environment.
1. Review: complex numbers, functions of complex variables, series of complex powers, convergence, Euler's formula
2. Distributions: impulse, step, ramp. Sampling and reproducibility. Sinusoidal exponential functions, time translation. Discrete signals
3. Continuous time systems. Causal LTI systems. Stability.
4. Characteristic equation of a system, elementary modes, convergence.
5. Convolution, impulsive response, forced response, BIBO stability, asymptotic stability
6. Frequency response
7. The Laplace transform. Convergence region. Properties
8. Free response and forced response in the complex plane, transfer function, zeros and poles, stability.
9. The Laplace's antitrasform, poles, residues.
10. The Fourier series for periodic signals. Frequency, pulsation, linear combination of periodic signals, synthesis equation, analysis equation. The energy and power of a signal, the discrete spectrum.
11. The Fourier transform. Conditions of existence, discontinuities.
12. Convolution and modulation. Spectrum.
13. Fourier trasform of the ideal sampling train, replication and sampling, reconstruction filters, Nyquist frequency, Shannon forumula.
14. Bode diagrams
15. Block diagrams
16. Discrete-time LTI systems. ARMA model. Impulsive response, forced response.
16. z trasform. Properties
17. The antitransformed z. Frequency response. Discrete Fourier transform
The students can integrate the reference books (Valcher for theory and Di Stefano et al. for the laboratory part) with the free text at the link:
Office hours: after class
||Segnali e Sistemi
||Di Stefano, Stubberud, Williams
||Schaum -- Etas
The exam is written. The students that obtain more than 27 may take an oral test, on an appointment basis.
During the course two optional intermediate written tests will be offered, that can replace, in full or partially, the written test.
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2019_06_12_Esami degli anni precedenti
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Secondo parziale 2012
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Secondo parziale 2013
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