Stochastic Processes and Signals

Introduction:

• 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 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.

Lectures, individual consultations, project work