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Institutionernas kurser för doktorander

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Kursplan för

Läsår
MVE135 - Random processes with applications
 
Kursplanen fastställd 2009-02-23 av programansvarig (eller motsvarande)
Ägare: MPCOM
7,5 Poäng
Betygskala: TH - Fem, Fyra, Tre, Underkänt
Utbildningsnivå: Avancerad nivå
Huvudområde: Elektroteknik
Institution: 11 - MATEMATISKA VETENSKAPER


Undervisningsspråk: Engelska

Modul   Poängfördelning   Tentamensdatum
Lp1 Lp2 Lp3 Lp4 Sommarkurs
0107 Laboration 1,5 hp Betygskala: UG   1,5 hp    
0207 Tentamen 6,0 hp Betygskala: TH   6,0 hp   21 Okt 2010 em V,  10 Jan 2011 fm V,  15 Aug 2011 fm V

I program

MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Årskurs 2 
MPIES INTEGRATED ELECTRONIC SYSTEM DESIGN, MSC PROGR, Årskurs 2 (valbar)

Examinator:

Bitr professor Rossitza Dodunekova
Docent Patrik Albin  Ansvarig: PA Elektroteknik Beslutsdatum: 2010-04-13


Ersätter

TMS115   Probability and stochastic processes


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Behörighet:

För kurser inom Chalmers utbildningsprogram gäller samma behörighetskrav som till de(t) program kursen ingår i.

Kursspecifika förkunskaper

A first course in probability for engineering and science students. A first course in signals, systems, and transforms.

Syfte

The purpose of the course is to provide the students with the theoretical framework fundamental to the processing of signals with random variation. Starting from basic probability the course proceeds to a thorough study of models for stochastic processes which are relevant in processing of random signals, and gives techniques for manipulating and study of these signals. Practical methods for random signal analysis and filtering are also included. The level should be such that the student should be able to take an active part in designing and optimizing engineering systems involving random signals.

Lärandemål (efter fullgjord kurs ska studenten kunna)

-­ define and explain fundamental probability tools used in the design and analysis of communication systems, with emphases on multidimensional joint distributions, the Gaussian one in particular, conditional expectation and conditional variance, convergence of random variables and limit theorems for sums of independent and identically distributed random variables.
-­ describe the basic statistical principles involved in point and interval parameter estimation as well as in hypotheses testing.
­- identify basic models of random processes and explain their use for the designing of components in communication systems and analysis of their effect on system performance. These models include the Poisson process, Markov processes, Gaussian processes, white noise, and stationary stochastic processes.
-­ use wide-sense stationary processes for modeling systems involving random signals and noise. In particular the students should have got a firm grasp on the important class of ARMA processes.
- estimate second-order characteristics from data, including non-parametric estimation of the power spectral density, and understand the statistical properties of these estimates.
-­ explain the mathematical techniques for design of optimal linear systems for signal processing, with emphasis on match filtering and the Wiener filter.

Innehåll

    Basic Probability: Review and Extension.
  • Axioms of Probability. Conditional Probability. Independence of Events. Probability Distributions. Expectation and Variance.
  • Random Variables. Functions of Random Variables.
  • Multiple Random Variables. Conditional Distributions. Conditional Expectation and Conditional Variance.
  • Multidimensional Gaussian Distribution.
  • Convergence of Random Variables. Limit Theorems for Sums of Random Variables.
    Mathematical Statistics
  • Parameter Estimation. Maximum Likelihood.
    Random Processes with Application in Statistical Signal Processing
  • Definition of a Random Process. Autocorrelation Functions.
  • Wiener process, White Gaussian Noise, Poisson Process.
  • Wide-Sense Stationary Random Processes. Spectral Representation. Autoregressive Moving Average Processes.
  • Analysis and Processing of Random Signals Through a Linear System. Cross-Correlation and Cross-Spectrum.
    Statistical Signal Processing
  • Non-Parametric Spectrum Estimation. Windowing and Frequency Resolution. Welch and Blackman-Tukey Methods.
  • Optimum Linear Systems. Prediction, Filtering and Smoothing.
  • Wiener Filter.

Organisation

The course comprises lectures, classes with exercises and discussions, computer laborations, and home assignments.

Litteratur

Scott L. Miller, Donald G. Childers, Probability and Random Processes With application to signal Processing and Communications.

Examination

The course evaluation is based on the results from the computer laborations,
the home assignments, and the written final examination.


Sidansvarig Publicerad: må 13 jul 2020.