Signal analysis 0800-ANSYG

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 analysis using independent component analysis (ICA)
12. and 13. Application of integral transforms and EMD and ICA decompositions to neuroinformatics
14. Signal processing exploiting sparsity of signal representation
15. Demo: application of signal analysis methods introduced during the course to full pipeline of neuroinformatics signal such as EEG.

Total student workload

Lecture: 30h Labs: 30h Student's self-teaching and preparations: 60h

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)

Expository teaching methods

- informative (conventional) lecture

Exploratory teaching methods

- project work

Type of course

compulsory course

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.

Additional information

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

Description of 0800-ANSYG in USOSweb