Digital Signal Processing (graduate)

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, Poisson’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