At the end of the course, students should be able to:
- know fundamental theoretical and methodological principles of signal and 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 data of given particular characteristics
1. Systems and signals - basic vocabulary. Inspiration by practical tasks of biosignal processing and modelling biological systems.
2. Signals. Continuous signals. Basic types of continuous signals - periodical and single-shot signals. Basic manipulations with continuous signals. Decomposition of the continuous periodical signals to harmonic components - Fourier series.
3. Decomposition of continuous aperiodic signals to harmonic components - Fourier transform. Examples and applications.
4. Discrete signals. Sampling. Basic types of discrete signals and operations with them. Decomposition of discrete signals 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
Lathi, B.P. Linear Systems and Signals, Oxford, Oxford University Press 2002
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
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.