# Statistical signal processing II

## Individual course

Max amount of FITech students: 20

Persons without a valid study right to a Finnish university have preference to this course.

Course contents

• Linear Bayesian estimators and filters
• Sequential Bayesian and least squares algorithms
• Wiener and Kalman filtering
• Iterative algorithms
• Statistical decision theory for signals with unknown parameters
• Application examples: equalization in communications engineering, array processing and beamforming, spectral analysis and estimation, delay estimation and positioning.

Learning outcomes

After successfully completing this course, the student

• understands the key design problems and constraints of the typical estimation problems in statistical signal processing.
• will have the skills to apply estimation, detection and other statistical signal processing methods to solve practical problems in signal processing applications.
• can use linear algebra, basics of optimisation and statistical signal processing to derive algorithms with statistical models.
• can use numerical analysis to approximate optimal algorithms with iterative solutions including adaptive algorithms.
• understands the basic requirements for the convergence of an iterative and adaptive algorithm.
• can model the operation of a transceiver using Matlab and other simulators to assess the performance of transceiver algorithms.
• can solve simple composite hypothesis testing problems with unknown parameters.

Course material

Lecture material etc. can be found on Moodle. Matlab software.

Teaching schedule

• Lectures are on campus (9.1.–27.2.), but there are lecture recordings available in Moodle.
• Exercises 13.1.–3.3. and computer exercises and simulations 17.1.–28.2.
• Exam is on campus (Oulu).
• Retake exam (later in the spring) is organised in University of Oulu’s EXAM room, so it may be possible to make the exam also in another university’s EXAM room. See instructions and limitations here.

Completion methods

Simulation project tasks, and minor exams during the course/a final exam later.

In the final grade of the course, the weight for the examination is 0.6 and that of project report 0.4.

Face-to-face teaching and e-learning tool usage:

• Face-to-face teaching and/or online teaching (lectures and exercises) 50h. Lectures available also as videos, online study is possible.
• Matlab simulation exercises in groups 30 h.
• Independent work & passed assignment 50 h.

More information about the prerequisites: Knowledge about Fourier analysis, analog and digital signal, fast Fourier transform, LTI system, Hilbert transform, AM, FM, and PM modulation. Random variable. Covariance matrix. Random signal. Stationarity, autocorrelation. Power spectral density. Random signal in LTI system, Probabilities, complex valued random variables and stochastic processes; eigenvalue decomposition, use of Matlab; estimation theory, minimum variance unbiased estimator, Cramer-Rao lower bound, linear models, the concept of general minimum variance unbiased estimation, best linear unbiased estimators, maximum likelihood estimation, least squares estimation, Bayesian estimation, linear Bayesian estimation; statistical decision theory, receiver operating characteristics, hypothesis testing, matched filter.

You can get a digital badge after completing this course.

### Responsible teacher

University of Oulu
Markku Juntti , Professor

### Further information about the course and studying

University of Oulu
FITech contact person Oulu

### Contact person for applications

FITech Network University
Fanny Qvickström, Student services specialist
Topics:
5G technology,
Wireless technology
Course code:
521324S
Study credits:
5 ECTS
Price:
0 €
Course level:
Teaching period:
8.1.–2.3.2024
Application start date:
07.11.2023
Application period has ended
Host university:
University of Oulu
Who can apply: