- Knowledge of the classification of signals. Knowledge of frequency analysis for continuous-time signals. Knowledge of linear time-invariant (LTI) systems, as well as of their representation in the time and frequency domains. Knowledge of the basic types of filters. Knowledge of random processes and of their spectral representation. - Knowledge of the techniques for passing from a continuous time to a discrete time signal, and vice-versa. Knowledge of the techniques for processing a discrete-time signal in the frequency domain. Knowledge of the techniques for analysis of LTI systems, and of the Z-transform. Knowledge of digital filters structures (FIR, IIR). - Ability to classify signals with respect to their properties. Ability to transform and analyze a continuous or discrete time signal in the time and frequency domains. Ability to classify and analyze an LTI system in the time and frequency domains. Ability to analyze digital filters.

Real and complex analysis of functions in one or two variables. Probability theory. Gaussian random variables. First order linear differential equations. Dirac Delta distribution. Laplace transform.

Topics developed in the class: - Signal classification; energy and power (0.6 cfu) - Fourier series and transform (0.75 cfu) - Linear Time Invariant (LTI) systems, impulse response and transfer function, convolution, filters (0.9 cfu) - Energy spectrum and autocorrelation function. Periodic signals and power spectral density (0.6 cfu) - Random processes (0.75 cfu) - Sampling theorem (0.6 cfu) - Discrete time signals: basic operations, energy and power (0.65 cfu) - Discrete time Fourier transform, circular convolution, DFT, FFT (1.5 cfu) - Z transform (0.75 cfu) - Discrete time LTI systems: time and frequency analysis, Z transform based analysis, FIR and IIR filters (0.9 cfu)

The course consists of lectures and exercises. During the exercise sessions (corresponding to about one third of the total number of hours) the teacher will show the solution of problems related to the program carried out in class. The text of the exercises will be provided to students in advance.

Textbooks: 1. L. Lo Presti e F. Neri, L'analisi dei segnali, CLUT, 1992. 2. L. Lo Presti e F. Neri, Introduzione ai processi casuali, CLUT, 1992. 3. M. Laddomada e M. Mondin, Elaborazione numerica dei segnali, Pearson, 2007. Further references: 4. A. Papoulis e S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002. 5. F. Dovis, E. Magli, Esercizi svolti di teoria dei segnali, CLUT, 2011 The material (slides) used during the lectures will be uploaded on the portal, together with some supplementary exercises.

Lecture slides; Text book; Exercises; Exercise with solutions ; Video lectures (previous years);

Exam: Computer lab-based test; Optional oral exam;

The final exam is composed of a written part and an oral part (optional, or at the discretion of the instructor). The students with a grade equal or larger than 15/30 are admitted to the oral exam. The written exam is organized in two sections: - Multiple-choice quizzes: for each quiz, from 3 to 5 possible answers are shown, only one of which is correct. It’s also possible for the students to insert a few comments about the selected answer. The goal of this first part of the exam is to verify the understanding of the fundamental theoretical topics of the signal theory. - Problems: there are typically 2 or 3 problems, whose goal is to verify the knowledge and ability to classify and elaborate both analog and discrete-time signals. For each problem, the complete solution has to be reported on the sheets provided by the instructors (solutions written in any other piece of paper will not be considered). The written part is two hours long. The students are allowed to use only a calculator and a formula sheet provided by the instructor. Examples of previous years exams will be uploaded on the POLITO web portal (“Portale della Didattica”). During the oral exam, which is 10-15 minutes long, the students will have to answer a few questions on the topics addressed during the lessons and the computer room activities. After the oral exam, the grade obtained in the written part can be either incremented or decremented of a maximum of 3 points. The following evaluation criteria are used: - accuracy of quiz answers and problem solutions; - use of a proper technical terminology in the written exam (and oral exam); - accuracy in the drawing of the plots (labels, unit of measure, etc.); - ability to give prompt and proper answers during the oral exam.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.