Course Unit Page

Academic Year 2021/2022

Learning outcomes

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.

Course contents

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

Office hours

See the website of Riccardo Rovatti

See the website of Mauro Mangia