Course syllabus for Probability and statistical signal processing

The course syllabus contains changes
See changes

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameSannolikhetsteori och statistisk signalbehandling
  • CodeESS012
  • Credits7.5 Credits
  • OwnerTKELT
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentELECTRICAL ENGINEERING
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 50126
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0120 Examination 7.5 c
Grading: TH		0 c0 c0 c7.5 c0 c0 c
  • 30 Maj 2022 pm J
  • 09 Okt 2021 pm J
  • 15 Aug 2022 am J

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Basic knowledge of elementary functions; linear algebra; calculus; differential equations; complex numbers; vectors and matrices; linear equation systems; Fourier, Laplace, and z transforms; discrete-time and continuous-time linear systems

Aim

To provide basic knowledge of probability theory and mathematical statistics, foremost from an application perspective, and to provide understanding of the underlying models and approaches. This will give the students insights into how to identify problems that are suitable to be handled with tools from probability and mathematical statistics. The course also aims to give insights into modern statistical signal processing, e.g., digital communication, machine learning, and artificial intelligence.

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

After completing the course, the student should be able to
  • explain fundamental probability theory concepts, e.g., probability space, events, probability measures, conditional probability, statistical independence, random variables, cumulative distribution function, probability mass and density functions, and to be able to use these concepts to solve problems
  • explain the difference between a frequentist and Bayesian approach
  • use Bayes theorem, the law of large numbers, and the central limit theorem in problem solving
  • perform point estimation and hypothesis test and assess the performance
  • design Matlab-programs to solve statistical signal processing problems

Content

Important basic concepts from probability, such as probability measures, random variables, mathematical expectation and variance. Some basic statistical distributions, for example the binomial, Poisson and normal distributions. Multidimensional distributions, sums of random variables and the central limit theorem. The three main inference problems are discussed: point estimation, confidence interval and hypothesis test. The least squares method and its distribution theory is studied with emphasis on linear regression. Application of hypothesis testing on signal detection and matched filter interpretation. Introduction to machine learning.

Organisation

Lectures and problem solving exercise sessions. Project. Written exam.

Literature

See the course homepage.

Examination including compulsory elements

Passing the course requires that both the project and written exam are passed. Credit from project and exam is used to assign the final grade.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

The course syllabus contains changes

  • Changes to examination:
    • 2021-09-21: Grade raising Changed to grade raising by GRULG