Stochastic signals 7.5 Credits

Stokastiska signaler
Second cycle, S7001E
Course syllabus valid: Autumn 2016 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Syllabus established
by the Department of Computer Science and Electrical Engineering 28 Feb 2007

Last revised
by Jonny Johansson, HUL SRT 15 Feb 2016

Education level
Second cycle
Grade scale
G U 3 4 5
Signal Processing
Subject group (SCB)
Computer Technology

Entry requirements

Upper secondary education and documented skills in English language, including the following knowledge/courses: S0001E, S0008M, or equivalent.

More information about English language requirements


The selection is based on 20-285 credits

Course Aim

After completion of the course, the students shall have knowledge and understanding concerning:

  • Random Variables, Functions of Random Variables, Cumulative Distribution Functions, Probability Density Functions
  • Expectations and Moments, Random Vectors, Central Limit Theorem
  • Parameter Estimation, Maximum Likelihood Estimation, Linear Estimation
  • Minimum Mean Squared Error (MMSE) Estimation, Linear MMSE Estimation,
    Statistical Orthogonality,
  • Random Sequences, Random Processes, Stationarity
  • Autocorrelation, Cross-correlation
  • Linear Time Invariant Systems and Wide Sense Stationary Sequences and Processes, Filtering
  • Power Spectral Density, White Noise
  • Ergodicity, Wiener Filter, Spectral Estimation


After completion of the course, the students shall be able to:

  • Use mathematical and statistical methods to process random signals, disturbances and noise. Applications are found in many areas, e.g., electrical engineering, signal processing, image analysis, communication theory, control theory, measurement systems, and economics
  • Estimate random parameters, estimate signals and parameters in noise, separate randomly composed signals, estimate the estimation error, calculate and estimate the spectral content in random signals
  • Present and demonstrate results in written reports



Review of probability theory, random variables, functions of random variables, expectation and moments, multidimensional stochastic variables, stochastic vectors, stochastic sequences- and processes, stationarity, spectral representation, linear processes and filtering, prediction, statistical theory and tools for random sequences and processes.


Lectures, mandatory laboratory assignments, problem solving.


Written exam with differentiated grades and successful completion of the laboratory assignments. All practical laboratory assignments must be completed to pass the course, but the grade is set by the result on the written exam.

Rickard Nilsson

Transition terms
The course S7001E is equal to SMS029

Literature. Valid from Spring 2013 Sp 3 (May change until 10 weeks before course start)
Probability and Random Processes with Applications to Signal Processing, 4/E (2012).
Henry Stark, John W Woods. Pearson Higher Education. ISBN 0273752286.

Course offered by
Department of Computer Science, Electrical and Space Engineering

0001Written exam6.0G U 3 4 5
0002Laboratory work1.5U G#

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.