## 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
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
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