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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
MVE136 - Random signals analysis
Syllabus adopted 2015-02-11 by Head of Programme (or corresponding)
Owner: MPCOM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Electrical Engineering

Teaching language: English
Open for exchange students
Block schedule: D

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0111 Examination 6,0 c Grading: TH   6,0 c   28 Oct 2015 pm V,  05 Jan 2016 pm H,  15 Aug 2016 pm SB
0211 Laboratory 1,5 c Grading: UG   1,5 c    

In programs



Bitr professor  Lennart Svensson
Docent  Patrik Albin


MVE135   Random processes with applications TMS115   Probability and stochastic processes

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In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

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


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.

Learning outcomes (after completion of the course the student should be able to)

  • define and explain fundamental probabilistic tools used in the design and analysis of communication systems, with emphasis on multidimensional joint distributions, the Gaussian one in particular, and on conditional probabilities and expectations.
  • identify basic models of random processes and explain their use for the design 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 be familiar with the important classes of AR, MA and ARMA processes.
  • estimate second-order characteristics from data, including non-parametric and parametric estimation of the power spectral density, and understand the statistical properties of these estimates.
  • estimate linear filters from noisy measurements of the output by linear regression techniques.
  • explain the mathematical techniques for design of optimal linear systems for signal processing, with emphasis on matched filtering and the Wiener filter.


  • Review of Basic Probability and Random Variables
  • Multiple Random Variables. Conditional Distributions. Conditional Expectation.
  • Multidimensional Gaussian Distribution.

Random Processes
  • Definition of a Random Process. Autocorrelation Functions.
  • Wiener process, White Gaussian Noise, Poisson Process. Markov Process.
  • Wide-Sense Stationary Random Processes. Spectral Representation. AR, MA and ARMA Processes.
  • Analysis and Processing of Random Signals Through a Linear System. Cross-Correlation and Cross-Spectrum.

Statistical Signal Processing
  • Non-Parametric Spectral Estimation. Windowing and Frequency Resolution. Welch and Blackman-Tukey methods.
  • Parametric Spectral Estimation. Yule-Walker method.
  • Optimum Linear Systems: Matched Filtering and Wiener Filters.
  • Prediction, Filtering and Smoothing.
  • System Identification with Application to Channel Estimation.


Lectures, exercise classes and supervised laborations.


Scott Miller och Donald Childers (2012): Probability and Random Processes Second Edition, Academic Press. 

It is also quite possible to use the first edition of the book from 2004.åäö


The course is examined by means of two mandatory laborations and a written exam. The final grade on the course is the same as that on the written exam.evaluation is based on the results from the computer laborations, the home assignments, and the written final examination.

Page manager Published: Thu 04 Feb 2021.