Bi5440 Time series

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
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
Timetable
Mon 8:00–11:50 F01B1/709
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
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
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Spring 2021.
  • Enrolment Statistics (recent)
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