The specific knowledge and abilities that the student will acquire are: - 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 signal filters. - Knowledge of random signals (called random processes), of their statistical characterization and of their spectral representation. - Ability to classify signals with respect to their properties. - Ability to transform and analyze a signal in the time and frequency domains. - Ability to classify and analyze a LTI system in the time and frequency domains. - Ability to statistically describe a random process and to characterize its spectral properties, as well as its interactions with LTI systems. - Knowledge of the techniques for passing from a continuous-time to discrete-time signal, and vice-versa. - Knowledge of the techniques for digital processing of a signal in the frequency domain. - Knowledge of the techniques for discrete-time processing of digital signals in the frequency domain. - Knowledge of the techniques for analysis of LTI systems in discrete-time, and of the Z-transform. - Knowledge of digital filters structures (FIR, IIR) - Ability to pass from discrete time to continuous time signals, and vice-versa. - Ability to process discrete-time signals and systems in the time and z-domain. - Ability to analyze discrete-time LTI systems.

Fundamentals of Calculus (including trigonometric, exponential and logarithmic functions, with their properties). Fundamental notions of linear algebra, Euclidean spaces and the representation of their elements in terms of components vs. a basis. Complex analysis of functions in one or two variables. Fourier series, Fourier and Laplace transforms. First order linear differential equations. Probability theory: discrete and continuous random variables, probability density function, expectation operator. Geometric series and their convergence criteria.

Topics dealt with in the course: - Signal classification; energy and power (0.4 CFU) - Linear and inner-product spaces, signal spaces, signal canonical representation and approximants (0.8 CFU) - Fourier series and transform (0.8 CFU) - Linear Time Invariant (LTI) systems, impulse response and transfer function (1 CFU) - Energy spectrum and autocorrelation function. Periodic signals and power spectral density (1 CFU) - Random processes (2 CFU) - Sampling theorem (0.4 CFU) - Discrete time signals: basic operations, energy and power (0.3 CFU) - Discrete time Fourier transform: circular convolution, discrete time Fourier transform (0.7 CFU) - Discrete time LTI systems: Z transform based analysis (0.6 CFU) (CFUs are indicative – variations are possible.)

Theoretical topics are dealt with in regular lectures. Regarding problem-solving, either the teacher solves problems in class on the topics introduced during the lectures, or the students work independently on the suggested problems with guidance from the teacher. If teaching assistants are available, they will assist students in carrying out exercises.

1. P. Poggiolini, M. Visintin, A. Carena, Class Notes on Signal Analysis and Processing (downloadable from the course portal). For further (optional) reading: 2. A. Papoulis e S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002. 3. A.V.Oppenheim R.W.Schafer: Discrete-Time Signal Processing, Prentice-Hall (any edition). 4. Luca Mesin, Introduction to signal theory, CLUT.

Exam: Optional oral exam; Computer-based written test in class using POLITO platform;

The final exam consists of a mandatory written test and an optional oral test. The written test lasts approximately two hours and consists of questions that may involve theoretical aspects, proofs of results, and solving computational problems. In case of computational problems, the mathematical steps used to get to the solution may have to be submitted. The written test is "closed book". Students are given a standard "table of formulas" which they can consult. Students are allowed to use the scientific calculator embedded in the exam application software. The questions and problems of the written test deal with all three main sections of the course: deterministic time-continuous signals and linear systems, discrete-time signals and linear systems, random processes. The written test is meant to verify that students have acquired the knowledge of the fundamental concepts of signal theory and related systems and the skills and abilities needed to classify, manipulate and process them. The written test maximum grade is 30/30. Students can withdraw from the exam after learning about their written test grade. The optional oral exam can be taken by students whose written test is sufficient (18/30 or higher). Besides further probing the students’ knowledge, it will also focus on their ability to use the appropriate technical terms and their promptness in providing the answers. The oral test grade awards extra points in the range from -5 to +5 (thirtieths). The final exam grade is awarded by summing the following: - the written exam grade - the optional oral exam grade, from -5 to +5 (thirtieths) Particularly brilliant students may be awarded the grade 30/30 with “lode”.

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.