Stochastic Systems


Recommended prerequisite for participation in the module

The module builds on basic knowledge of statistical and probabilistic quantities (stochastic variable, mean, variance, hypothesis test, etc.)

Content, progress and pedagogy of the module

The purpose is to introduce theory, models and tools for analysis of stochastic signals and systems. Stochastic signals and systems can loosely be described as anything random that changes in time and which we formally describe by stochastic processes. They are at the core of a number of disciplines in engineering, for example wireless communication, automation and control, and speech processing. While students are familiar that signals can change due to noise, a system can behave stochastic and not always produce the same output for a given input.

Students should become familiar with the description of stochastic signals and systems and learn about relevant theoretical models to describe them and understand the stochastic properties. Based on this the students learn how to analyze and simulate such processes using computer programming language.

Learning objectives


The student should have knowledge about:

  • Probability theory necessary to understand discrete time stochastic processes
  • Various types of stochastic process, such as WSS, Markov, Poisson, and Gaussian
  • Discrete time linear stochastic dynamical systems in transfer and state space form, including ARIMAX


  • Be able to analyze and simulate stochastic processes
  • Be able to apply stochastic processes in selected engineering disciplines e.g., within queuing systems, communication systems and control systems.


  • Attain appropriate “engineering” intuition of the basic concepts and results related to stochastic processes that allow to model, analyze and design solutions to engineering problems involving stochastic signals and systems

Type of instruction

As descript in §17



Name of examStochastic Systems
Type of exam
Written or oral exam
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Facts about the module

Danish titleStokastiske systemer
Module codeESNESK1K2
Module typeCourse
Duration1 semester
Language of instructionEnglish
Empty-place SchemeYes
Location of the lectureCampus Aalborg
Responsible for the module


Study BoardStudy Board of Electronics and IT
DepartmentDepartment of Electronic Systems
FacultyThe Technical Faculty of IT and Design