84457 - Signal Acquisition and Processing M

Course Unit Page

Academic Year 2021/2022

Learning outcomes

The course aims to give students the appropriate techniques for the acquisition and processing of real world data and the implementation of efficient and robust signal processing structures. Knowledge about the modern theory and practice of sampling from an engineering perspective, and classical and modern signal processing tools will be acquired.

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