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PřF:Bi5440 Time series - Course Information

## Bi5440 Time series

**Faculty of Science**

Autumn 2020

**Extent and Intensity**- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
**Teacher(s)**- prof. Ing. Jiří Holčík, CSc. (lecturer)
**Guaranteed by**- prof. RNDr. Ladislav Dušek, Ph.D.

RECETOX - Faculty of Science

Contact Person: prof. Ing. Jiří Holčík, CSc.

Supplier department: RECETOX - Faculty of Science **Prerequisites**- Basic knowledge of differential and integral calculus, and complex numbers, resp.
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Epidemiology and modeling (programme PřF, B-MBB)
- Mathematical Biology (programme PřF, B-EXB)

**Course objectives**- At the end of the course, students should be able to:

- know fundamental theoretical and methodological principles of time series description and processing and linear system analysis

- explain consequences and relationships between characteristics of real processes and data and applied methods and algorithms;

- apply different practical approaches to data processing to obtain required analytic results;

- design modified algorithms to process time series data of given particular characteristics **Learning outcomes**- At the end of the course, students should be able to:

- know fundamental theoretical and methodological principles of time series description and processing and linear system analysis

- explain consequences and relationships between characteristics of real processes and data and applied methods and algorithms;

- apply different practical approaches to data processing to obtain required analytic results;

- design modified algorithms to process time series data of given particular characteristics **Syllabus**- 1. Systems and time series - basic vocabulary. Inspiration by practical tasks of biosignal processing and modelling biological systems.
- 2. Continuous variables. Basic types of continuous variables and their mathematical models - periodical and single-shot variables. Basic manipulations with mathematical models of continuous variables. Decomposition of the continuous periodical signals to harmonic components - Fourier series.
- 3. Decomposition of continuous aperiodic variables to harmonic components - Fourier transform. Examples and applications.
- 4. Time series. Sampling. Basic types of time series and operations with them. Decomposition of time series to harmonic components. Examples.
- 5. Discrete time Fourier transform. Discrete Fourier transform. FFT algorithm. Examples.
- 6. Convolution definition, practical meaning. Correlation function -autocorrelation, cross-correlation. - Definitions, practical meaning.
- 7. Linearní transforms – Laplace transform, z-transform. Definitions, properties, applications.
- 8. Systems. Basic attributes of systems. Linear and nonlinear systems. Examples in biology and medicine. Description of systems - input/output description, state space description.
- 9. Input/output description of linear continuous systems - differential equation, system transfer function, frequency responses, pole-zero plot, impulse and transient response.
- 10. Input/output description of linear discrete systems - difference equation, system transfer function, frequency responses, pole-zero plot, impulse and transient response. Differences between continuous and discrete systems
- 11. Stability. Definition. Basic relationships. Stability of linear and non-linear systems. Criteria of stability.
- 12. Connecting systems. Serial connection. Parallel connection. Feedback connection. Properties of the feedback connection

**Literature**- Kamen, E.W. Heck B.S. Fundamentals of Signals and Systems Using the Web and Matlab. London, Prentice Hall 2000
- Lathi, B.P. Linear Systems and Signals, Oxford, Oxford University Press 2002
- Oppenheim, A.V. Willsky A.S. Nawab S.H. Signals & Systems. New Jersey, Prentice Hall 1997

**Teaching methods**- Lectures supported by Power Point presentations. Understanding of principles, methods and algorithms is emphasized. Students are continuously encouraged to be in an interaction with a lecturer.
**Assessment methods**- oral examination
**Language of instruction**- Czech
**Further Comments**- The course is taught annually.

The course is taught: every week. **Listed among pre-requisites of other courses**

- Enrolment Statistics (Autumn 2020, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2020/Bi5440