The course focuses on **Advanced Statistical Digital Signal Processing **and covers the following topics:

**Review of basics & fundamentals**(12h)**:**linear algebra & factorizations (Tel); z trasf. & filters, random processes (Mat); multivariate Gaussian (All); constrained optimization (Tel).**Block-processing**(6h)**:**regression, filtering, interpolation, direct & inverse problems**Estimation theory and performance limits**(24h): Min Var. & BLUE, MLE, Cramer Rao Bound, LS w/examples (regression, sinusoids & PLL, TOA, ch.estimation, MLSE)**Bayesian estimators**(14h): a-posteriori estimation (MAP, MMSE and LMMSE); Wiener filter; linear prediction, Yule-Walker equations and Levinson recursion; EM method (2h).**Sequential estimators & adaptive filters**(8h): iterative LMMSE, LMS, RLS methods; examples: adaptive identification and equalization**Bayesian sequential estimators**(8h): dynamic model and Kalman filter; examples: target localization & tracking.**Spectral analysis**(12h): periodogram; parametric methods (MA, AR, ARMA models); line spectra and high-resolution methods (HOYW, MUSIC).**2D****signal****processing**(20h): 2D signals & Fourier trasf., sampling & aliasing; 2D physical filters (diffusion, Poissonâ€™s equation, wavefield propagation); array processing and direction of arrivals (DOA) estimation, backpropagation and focusing (geophysical experiment). Estimation from projections and tomography.

Theory: 54h, Exercises&Examples: 38h, Review: 12h