Signal analysis 0800-OG-ANALSI

1. Basics of matrix algebra
2. Eigenvalue and singular value decompositions
3. Principal component analysis
4. Basics of tensor algebra
5. CANDECOMP/PARAFAC and Tucker tensor decompositions
6. Application of matrix and tensor decompositions in signal analysis
7. Time-,frequency- and spatial domains representations of signals
8. and 9. Integral transforms, focusing of Fourier and wavelet transforms
10. Signal analysis using empirical mode decomposition (EMD)
11. Signal decomposition using independent component analysis (ICA)
12. Example of using integral transforms, EMD and ICA decompositions on real data
13. Methods for selecting a sparse signal representation
14 and 15. Analysis of dynamic systems using the Koopman operator and dynamical mode decomposition (DMD)

Total student workload

Hours carried out with the participation of an acadamic teacher (70 hours): - participation in lectures – 30 hours - participation in laboratories – 30 hours - consultations with an academic teacher – 10 hours Time devoted to individual student work (50 hours): - preparation for the lecture - 10 - preparation for laboratories – 10 - reading literature- 10 - preparation for the exam - 10 - preparation for the project - 10 Total: 120 hours (4 ECTS)

Learning outcomes - knowledge

- has knowledge on mathematical basics of signal analysis and its relationship with other branches of mathematics and science; also, possesses both theoretical and applied knowledge of signal analysis methods, in particular time series analysis methods in time, frequency, and spatial domains (K_W01) - possesses insight into workings of basic signal processing algorithms and its implementations (K_W02)

Learning outcomes - skills

- understands aims, scope of applications and limitations of learned signal processing algorithms (K_U01) - possesses sufficient mathematical proficiency to formulate and solve signal processing problems using learned algorithms (K_U07) - has the ability to use learned signal processing methods in various applications, and to be able to assess usefulness of signal processing methods in applications (K_U01,K_U06)

Learning outcomes - social competencies

- may work in both industry and science and apply learned signal processing methods in various fields (K_K04,K_K05) - has the ability to improve his professional skills and increase his knowledge on his/her own (K_K01,K_K02)

Teaching methods

- informative (conventional) lecture - project work

Expository teaching methods

- programmed material
- participatory lecture
- informative (conventional) lecture
- description

Exploratory teaching methods

- laboratory
- practical

Prerequisites

Basics of linear algebra, mathematical analysis and statistics

Course coordinators

Tomasz Piotrowski

Assessment criteria

Assessment methods:
- labs: project, effects U01,U06,U07
- lectures: written exam consisting of theoretical and implementational parts: effects W01,W02,U01,U06,U07,K01,K02,K04,K05
Assessment criteria:
- labs: binary grade:
i) project not meeting its objectives or lack of project: grade 2
ii) project meeting its objectives: grade 5
- lectures: weighted grade of theoretical part (50%) and implementational part (50%) according to the following scale (jointly theoretical and implementational parts):
2 – below 50%
3 – 51%-60%
3.5 - 61%-70%
4 - 71%-80%
4.5 - 81%-90%
5 - 91%-100%

Practical placement

Not applicable.

Bibliography

1. R A Horn, C R Johnson, Matrix Analysis, Cambridge University Press, 2012.
2. A Cichocki, R Zdunek, A H Phan, S-I Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation, Wiley, 2009.
3. N E Huang, Z Shen, S R Long, M C Wu, H H Shih, Q Zheng, N-C Yen, C C Tung, H H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society A, 454(1971), pp. 903-995, 1998.
4. A Hyvarinen, J Karhunen, E Oja, Independent Component Analysis, Wiley, 2004.
5. Alexandre Mauroy, Igor Mezić, Yoshihiko Susuki (Eds.), The Koopman Operator in Systems and Control, Springer, 2020.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 0800-OG-ANALSI in USOSweb