# Systems and Signals (2006/2007)

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Course code
4S00045
Credits
6
Coordinator
Paolo Fiorini
Teaching is organised as follows:
Modulo I 5 ING-INF/05-INFORMATION PROCESSING SYSTEMS 3° Q Paolo Fiorini
Modulo II 1 ING-INF/05-INFORMATION PROCESSING SYSTEMS 3° Q Paolo Fiorini

#### Learning outcomes

Module: Modulo I
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The objective of the course is to give students the mathmatical foundation to model, analyse and simulate, simple dynamical systems. The first part of the course deals with the introduction of transforms, which are then used to represent the model of a dynamic system in a domain different from the original time domain. The second part of the course aims at presenting the main methods for the analysis of the mathematical models of dynamic systems, and to study their main properties. The main concept that will be studied is stability.

Module: Modulo II
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The objective of this module is the allow the students to apply the concepts acquired in the course of Calculus and Physics to the study of dynamical systems. This module then consists of a first part in which students learn how to write the difeerential equations of a dynamical system, which are then studied in the second part of the module, with the mathematical tools develoed in Module I.

#### Syllabus

Module: Modulo I
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* Introduction: general structure of a dynamical system
* General properties of input/output maps and their representaiton with the convolution integral, and differential equations
* The Laplace Transform and its applications
* The Fourier Transofrm and its applications
* The Zeta Transform and its applications
* Bode diagrams
* Input/output stability of linear systems
* Introduction to the characterization and analysis of stability
* Discrete time systems
* Stability analysis in the discrete time domain

Module: Modulo II
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* Development of differential equations for mechanical systems
* Development of differential equations for electrical systems
* Exercises of stability analysis of dynamical systems

#### Assessment methods and criteria

Module: Modulo I
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The exam consists of two theory tests and a laboratory test. The theory tests are a midterm and a final, whreas the laboratory test is only done at the end of the period. The theory part consists of a closed book test with exercises and theory questions. The laboratory test requires the writing of differential equations of a simple system and their solution using MatLab. the average of the two test, weighted by the credits of each Module is the final grade of the course. The student is entitled to receive an oral examination which is decided on a case by case basis.

Module: Modulo II
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