Stochastic Processes and Signals

Subject description


  • definition of stochastic process and random signal. Introduction of some important issues from mathematical modeling in statistics and probability theory.

Random signals processing:

  • time and sample mean, random signals filtering (Wienner and Kalman filter), probability distribution evaluation (Expectation-Maximization (EM), Maximum A Posteriori (MAP) and »Maximum Likelihood Linear Regression« (MLLR) procedures)

Modeling of stationary and non-stationary stochastic processes:

  • Gauss process, Poisson process, Gauss-Markov process, non-stationary stochastic processes representation using Hidden Markov Models (HMM)

Examples from speech signals processing, modeling of speech perception and production:

source-filter model for speech production, speech perception model and deconvulution of speech signals, time-frequency representations of speech signals, speech detection, speech signal modeling using HMM

The subject is taught in programs

Objectives and competences

The aim of the course is to recognize and understand advanced methods for representations of stochastic processes and random signals processing with special attention to the examples on speech signals processing.

Teaching and learning methods

Lectures, individual consultations, project work

Expected study results

Learning outcomes and competences will be knowledge and understanding on:

  • stochastic processes modeling,
  • advanced methods for random signals processing.

Basic sources and literature

Robert MG, Lee DD (2004) An Introduction to Statistical Signal Processing. Cambridge University Press

Shlomo E (2007) Random signals and noise: a mathematical introduction. CRC Press

Rabiner L, Schafer R (2010) Theory and Applications of Digital Speech Processing. Prentince Hall

Pieraccini R (2012) The Voice in the Machine: Building Computers That Understand Speech. MIT Press

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University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana

E: T:  01 4768 411