The class describes the main fundamental analysis and processing techniques for deterministic and random continuous-time signals (first part), and for deterministic and random discrete-time signals (second part). The topics are quite multidisciplinary in the sense that these notions and techniques are used in many of the classes that follow.

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), and their design techniques.
- Ability to pass from discrete time to continuous time signals, and vice-versa.
- Ability to process signals and systems in the time and frequency domain.
- Ability to analyze and design discrete-time LTI systems.

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 class:

- Signal classification; energy and power (0.5 CFU)
- Linear and inner-product spaces, signal spaces, signal canonical representation and approximants (1 CFU)
- Fourier series and transform (1 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 (1.5 CFU)
- Sampling theorem (0.5 CFU)
- Discrete time signals: basic operations, energy and power (0.5 CFU)
- Discrete time Fourier transform, circular convolution, discrete time Fourier transform (1 CFU)
- Discrete time LTI systems: time and frequency analysis, Z transform based analysis (1 CFU)
- Digital filters with finite (FIR) and infinite (IIR) impulse response. Window-based design of FIR filters.
Bilinear transformation-based design of IIR filters. (1 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 lecture, or the students work independently on the suggested problems with guidance from the teacher.

Textbooks:
1. P. Poggiolini and M. Visintin, 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. Luca Mesin, Introduction to signal theory, CLUT.
4. L. Lo Presti e F. Neri, L'analisi dei segnali, CLUT, 1992.
5. L. Lo Presti e F. Neri, Introduzione ai processi casuali, CLUT, 1992.
6. M. Laddomada e M. Mondin, Elaborazione numerica dei segnali, Pearson, 2007.

The knowledge and the ability to apply it will be verified during the written and oral final examination. The oral examination will include an assessment of the students’ communication skills.

The final exam is both written and oral. The written part is composed of 1-2 problems, consisting each of 2-4 questions, along the lines of the exercises solved in class. The written part is approximately 45 to 60 minutes long, but duration may vary. The students with a grade of 15/30 or greater in the written part, are admitted to the oral exam, which is approximately 45 to 60 minutes long, and may deal with any of the topics presented in the class. The overall exam, both written and oral, is "closed books".
The grading criteria are as follows:
1) the correctness of the answer provided to the written problems and oral questions
2) the ability to appropriately use the technical terms
3) the autonomy and promptness of the student in providing the answers