By the end of the course, students are expected to have acquired the following knowledge and skills: • Signal characterization and classification, based on their fundamental properties and representations. • Continuous-time signal analysis, including time- and frequency-domain representations and associated analysis techniques. • Linear Time-Invariant (LTI) systems, with understanding of their behavior and representation in both the time and frequency domains. • Filtering theory, including the principles and characteristics of the main classes of analog and digital filters. • Stochastic processes and spectral analysis, with knowledge of their fundamental properties and spectral representations. • Sampling and signal conversion techniques, including methods for converting continuous-time signals into discrete-time signals and vice versa. • Discrete-time signal processing, encompassing time- and frequency-domain analysis techniques, discrete-time LTI systems, and the Z-transform. • Digital filtering techniques, including the analysis and design principles of Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters. • Practical analytical skills, including the ability to classify, transform, and analyze signals and systems in both the time and frequency domains, as well as to evaluate the behavior and performance of digital filters. • Stochastic processes and their analysis, including their fundamental properties, statistical characterization, and spectral representations.

For the proper understanding of the course contents, students are required to have basic knowledge of the following topics: • Analysis of real and complex functions of one or more variables. • Probability theory and random variables. • The Dirac delta distribution.

During the course, the following topics will be covered, with the corresponding credit allocation: • Signal classification; energy and power of signals (0.75 ECTS credits) • Fourier series and Fourier transform (0.75 ECTS credits) • Linear Time-Invariant (LTI) systems, impulse response and transfer function, convolution, filters (1.2 ECTS credits) • Energy spectrum and autocorrelation function; periodic signals and power spectrum (0.6 ECTS credits) • Sampling theorem (0.6 ECTS credits) • Discrete-time signals: basic operations, concepts of energy and power (0.7 ECTS credits) • Discrete-time Fourier transform, circular convolution, Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) (0.9 ECTS credits) • Z-transform (0.6 ECTS credits) • Discrete-time LTI systems: time-domain analysis, frequency-domain analysis, Z-transform analysis, FIR and IIR filters (0.9 ECTS credits) • Stochastic processes (1.0 ECTS credits) (ECTS credits are indicative – variations are possible.)

The course consists of lectures and classroom tutorial sessions. During the tutorial sessions, which account for approximately one third of the total teaching hours, problem-solving activities related to the topics covered in the lectures are presented and discussed. The tutorial material will be provided to students in advance.

1. [ENG] A. Papoulis e S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002. 3. [ENG] A.V.Oppenheim, R.W.Schafer: Discrete-Time Signal Processing, Prentice-Hall (any edition) 4. [ENG] Luca Mesin, Introduction to signal theory, CLUT. 5. [ITA] L. Lo Presti e F. Neri, L'analisi dei segnali, CLUT, 1992. 6. [ITA] L. Lo Presti e F. Neri, Introduzione ai processi casuali, CLUT, 1992. 7. [ITA] M. Laddomada e M. Mondin, Elaborazione numerica dei segnali, Pearson, 2007. For further (optional) reading and exercises: 8. [ITA] F. Dovis, E. Magli, Esercizi svolti di teoria dei segnali, CLUT, 2011 9. [ITA] M. Luise, G.M Vitetta, G. Bacci, Teoria dei segnali. Analogici, digitali, multimediali e dati, McGraw-Hill, 2025. 10. [ITA] Falaschi, A. (2023). Trasmissione dei segnali e sistemi di telecomunicazione ed. 2.0. TeoriadeiSegnali.it. https://teoriadeisegnali.it/libro/html/ Lecture slides used during lectures and classroom tutorial sessions will be made available to students through the teaching portal, together with additional complementary exercises.

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

You can take this exam before attending the course

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

The final examination aims to assess the acquisition of the knowledge and skills defined in the course learning outcomes (as described in the “Expected Learning Outcomes” section) through a written test and an optional oral examination (either chosen by the student or requested by the instructor when further clarification is deemed necessary). WRITTEN EXAM. The written exam lasts 90 minutes and consists of 10 multiple-choice questions covering all topics addressed in lectures and tutorials. During the exam, no teaching material, notes, or textbooks are allowed. Students may only use the formula sheet provided by the instructors and available on the teaching portal, a pen, blank paper, and a non-programmable calculator. The use of smartphones, smartwatches, smart glasses, or any other device enabling communication is not permitted. Examples of past exams will be made available through the teaching portal. All questions carry equal weight in the final assessment (3.4 points each), for a maximum theoretical score of 34 points. A correct answer is awarded 3.4 points. An incorrect answer results in a penalty of up to 1 point. Unanswered questions are not penalized. ORAL EXAM. The oral exam lasts approximately 10–15 minutes and consists of questions on the topics covered in class. Admission to the oral exam requires a written exam score of at least 15/30. The oral exam may result in an increase or decrease of the written exam grade (with a maximum adjustment of ±5 points). The evaluation criteria are: • correctness of the answers in the written test; • correctness in the use of technical terminology during the oral exam (if applicable); • promptness and clarity of responses 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.