PřF:E5440 Time series - Course Information
E5440 Time series
Faculty of ScienceSpring 2025
- Extent and Intensity
- 2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
In-person direct teaching - Teacher(s)
- prof. Ing. Jiří Holčík, CSc. (lecturer)
Mgr. et Mgr. Jiří Kalina, Ph.D. (lecturer) - Guaranteed by
- prof. Ing. Jiří Holčík, CSc.
RECETOX – Faculty of Science
Contact Person: Mgr. et Mgr. Jiří Kalina, Ph.D.
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
- Mathematical Biology (programme PřF, B-EXB)
- Course objectives
- The aim of the course is to provide students with basic theoretical and methodological principles of description and analysis of time series and analysis of linear systems.
- 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
- Oppenheim, A.V. Willsky A.S. Nawab S.H. Signals & Systems. New Jersey, Prentice Hall 1997
- Lathi, B.P. Linear Systems and Signals, Oxford, Oxford University Press 2002
- 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.
- Enrolment Statistics (Spring 2025, recent)
- Permalink: https://is.muni.cz/course/sci/spring2025/E5440