- Docente: Riccardo Rovatti
- Crediti formativi: 6
- SSD: ING-INF/01
- Lingua di insegnamento: Italiano
- Moduli: Riccardo Rovatti (Modulo 1) Mauro Mangia (Modulo 2)
- Modalità didattica: Convenzionale - Lezioni in presenza (Modulo 1) Convenzionale - Lezioni in presenza (Modulo 2)
- Campus: Bologna
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Corso:
Laurea Magistrale in
Advanced automotive electronic engineering (cod. 9238)
Valido anche per Laurea Magistrale in Ingegneria elettronica (cod. 0934)
Conoscenze e abilità da conseguire
The course aims at reviewing basic concepts of probability, operator theory and optimization and using them in the development of fundamental signal processing methods ranging from filtering to spectrum estimation, linear prediction, adaptive sampling and dimensionality reduction.
Contenuti
Mathematical tools:
- euclidean vector spaces of functions and random variables
- operators
- Optimization problme, Lagrange's multipliers
- pseudo-differentiation of functioncs of complex variables
Basics of probability and statistics
- random variable and their characterization (PDF, CDF, expectation, moments, characteristic function)
- covariance and linear prediction, orthogonality principle
- independence and unpredictability
- stochastic processes and their charcterization (joint probabilities, correlation/covariance functions, projections)
Processing of stochastic quantities
- linear algebraic processing (importance of pre-images, pseudo-inversion)
- linear dynamics processing (universal characterization of linear filters)
- scalar quantization of random variables (conditions ofr uniformity and incorrelation of quantization error)
Gaussian vectors and processes
- definitions and properties
- White Gaussian Noise
Power spectrum
- definition for continuous-time and discrete-time processes
- Wiener-Kinchine theorem
- estimation in general and its application to power spectrum
- periodogoram and modified periodogram
- minimum-variance estimation
- regular and predictable processes
- Wold theorem
- maximum-entropy estimator
Orario di ricevimento
Consulta il sito web di Riccardo Rovatti
Consulta il sito web di Mauro Mangia