Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

The Course requires the knowledge of the basic concepts of mathematical analysis.

To know and understand the basic elements for the description and characterization of signals, both deterministic and random, and the problems related with their processing. To be able to apply, in specific scenarios, the techniques learned, with special focus on the representation of signals in the frequency domain and the usage of basic instruments of the probabilistic calculus.

In order to correctly model the signals of interest (in particular, those of interest in telecommunication systems) the student shall be able to use properly the theoretical and software tools developed for signal analysis and processing. Such a capacity will become evident through some specific abilities that the student shall show, like: 1) the capacity to describe, in suitable domains, an assigned signal and to extract its fundamental features; 2) the capacity to evaluate quantitatively the changes that the signal suffers because of controlled or uncontrolled manipulations; 3) the capacity to use software tools, like Matlab, for the automatic description of the signal. The skills relative to the usage of Matlab will be acquired by the student through specific exercises in the classroom, complementary to the traditional lectures.

Capacity to use the tools of classic maths (Fourier transform, probabilistic calculus, etc.) in different application environments. Capacity to use software tools adaptable to different contexts (like Matlab). Capacity to discuss with criticism the results obtained on the basis of a comparison between the numerical data and the intuitive expectations. Capacity to present in a concise and clear way the results of his study and elaboration.

Contents (Frontal lectures, 36 hours) - Signal classification: deterministic signals and random signals. - Representation of signals in the frequency domain: continuous time periodic signals and continuous time aperiodic signals. - Linear continuous time monodimensional systems: impulse response, transfer function and linear non distortion conditions. Intersymbol interference. - Sampling theorem: ideal, natural and instantaneous sampling. - Other transforms. - Random variables theory. - Stationary and ergodic processes. Thermal noise. Classroom exercises (12 hours) - Software for the representation and characterization of signals.

The evaluation of the learning level is organized in two tests: - A written test, consisting in the solution of one numerical exercise, to be completed in approximately one hour (the exact time is determined by the difficulty level established for the exercise). - An oral test, consisting in the discussion of two or more topics of the course and the critical review of possible mistakes made in the written test. In the written test the student must face a problem of signal analysis or concerning the application of the probability calculus, by employing the methods, models and maths tools presented in the classes. In the oral test the student is asked to explain the basic elements for the description and characterization of signals, both deterministic and random, and the problems related with their processing. Moreover, he is asked to discuss the main concepts of the probability calculus. The written test is propaedeutic to the oral test, in the sense that the student is admitted to the oral test only if he has received a sufficient evaluation in the written test. The oral test should be stood, preferably, in the same session of the written test. Deviations from this rule are possible, but must be agreed with the teacher before starting the written test. In case of negative evaluation of the oral test, the student can decide to retain the result of the written test or to repeat it in the subsequent sessions. The chosen option must be communicated to the teacher before starting the new exam session the student wishes to attend.

Learning evaluation is based on the verification, through the tests, that the student has acquired a sufficient level of understanding and a suitable capacity of employing the topics presented throughout the course, as regards both the theoretical foundations and their application in order to solve specific numerical problems.

During the exam tests, the teacher evaluates the capacity of the student to model correctly the signals and to use properly the theoretical and software tools developed for signal analysis and processing. For the written test, the teacher assigns a mark that, as a function of the quality of the paper, can be: not sufficient, sufficient, fair, good, very good, excellent. The student is non admitted to the oral test if his mark is not sufficient. Any positive mark (sufficent or more), by which the student has been admitted to the oral test, permits the student to reach the maximum final mark (thirty, cum laude if applicable) if he is able to demonstrate that the gaps shown in the written test do not correspond to real deficiencies in the preparation. The final mark, in thirtieths, is the result of the global evluation on the oral and written tests.

In order to pass the exam, the student must reach at least a sufficient mark in the written test and show an adequate preparation in the oral test. The maximum mark is reached by showing a deep knowledge of the course topics throughout the tests. Laude is reserved to those students who are particularly brilliant in the oral test, even able to compensate in an excellent way possible gaps emerged in the written test.

1. Set of lectures provided by the teacher, that can be found in the university Moodle platform. 2. Marco Luise, Giorgio M. Vitetta, Teoria dei Segnali, Terza Edizione, McGraw-Hill, 2009.

- Ingegneria Elettronica (Corso di Laurea Triennale (DM 270/04))

**Università Politecnica delle Marche**

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