Stochastic Processes and Signals

Higher education teachers: Mihelič France
Credits: 5
Subject code: 64837

Subject description


  • Finished programme in technical or natural sciences disciplines.
  • Enrolment in corresponding year of third level (doctoral studies).

Content (Syllabus outline):


  • 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

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.

Intended learning outcomes:

Learning outcomes and competences will be knowledge and understanding on:

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

Learning and teaching methods:

  • lectures,
  • individual consultations,
  • project work.

Study materials

  1. Robert M. Gray, Lee D. Davisson: An Introduction to Statistical Signal Processing. Cambridge University Press, ISBN 0-521-83860-6, (2004), 463 pp.
  2. Shlomo Engelberg : Random signals and noise : a mathematical introduction. CRC Press, ISBN 978-0-8493-7554-5, (2007), 216 pp.
  3. Rabiner L., Schafer R., Theory and Applications of Digital Speech Processing, Prentince Hall, 1. Ed., 2010
  4. R. Pieraccini: The Voice in the Machine: Building Computers That Understand Speech, MIT Press, 2012.