Course syllabus

Stationary and Non-stationary Spectral Analysis
Stationär och icke-stationär spektralanalys

FMSN35, 7.5 credits, A (Second Cycle)

Valid for: 2024/25
Faculty: Faculty of Engineering LTH
Decided by: PLED I
Date of Decision: 2024-04-16
Effective: 2024-05-08

General Information

Depth of study relative to the degree requirements: Second cycle, in-depth level of the course cannot be classified
Elective for: BME4, C4, D4, E4-ss, F4, F4-ss, I4, Pi4-ssr
Language of instruction: The course will be given in English

Aim

This course is aimed at those who want wo broaden and deepen their knowledge in statistical signal processing and expand their toolkit with more advanced techniques. It lies on the border between statistics and signal processing and builds on the classical non-parametric methods that are wellknown and taught in, e.g. Stationary stochastic processes or Optimal signal processing. Since these methods are not always sufficient we need more advanced techniques in many application areas, e.g. communications or medicine.

Hence, the course covers more statistically robust methods that have become increasingly used in resent years, e.g. time-frequency analysis, which is a modern method for analysis of non-stationary signals and processes. The research in this area has expanded during the last 20 years, making this a commonly used tool.

Many applications will be presented in the course and the participants will work with real world data.

 

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must

Judgement and approach
For a passing grade the student must

Contents

Basic definitions. Extended studies of AR (auto regressive), MA (moving average) och ARMA-processes. Linespectra and parametric estimation methods. Noise-space based techniques. Non-parametric spectral estimators, data-adaptive techniques and multitaper methods. Non-uniform sampling. Orientation of circular and non-circular processes. Spatial spectral analysis. Non-stationary processes. Spectrogram. Wigner-Ville distribution. Cohen class. Ambiguity spectrum. Multitaper techniques for non-stationary signals. Orientation about bispectrum.

Examination details

Grading scale: TH - (U, 3, 4, 5) - (Fail, Three, Four, Five)
Assessment: Approved assignments and project report as well as participation in all compulsary parts. The final grade is given by a summary of the results on the assignments and the written and oral project report.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Modules
Code: 0116. Name: Computer Exercises.
Credits: 3.0. Grading scale: UG - (U, G). Assessment: Project with written and oral report
Code: 0216. Name: Assignments Part 1.
Credits: 1.0. Grading scale: UG - (U, G). Assessment: The first home assignment
Code: 0316. Name: Assignments Part 2.
Credits: 3.5. Grading scale: UG - (U, G). Assessment: The rest of the home assignments

Admission

Admission requirements:

Assumed prior knowledge: FMSN45 Time series analysis
The number of participants is limited to: No
Kursen överlappar följande kurser: MASM26

Reading list

Contact and other information

Course coordinator: Andreas Jakobsson, andreas.jakobsson@matstat.lu.se
Course coordinator: Maria Sandsten, maria.sandsten@matstat.lu.se
Director of studies: Johan Lindström, studierektor@matstat.lu.se
Course administrator: Susann Nordqvist, expedition@matstat.lu.se
Course homepage: https://www.maths.lu.se/utbildning/civilingenjoersutbildning/matematisk-statistik-paa-civilingenjoersprogram/
Further information: The course is also given at the Science faculty with the code MASM26