PřF:Bi5440 Signals & Systems in CompBiol - Course Information

Bi5440 Signals and systems in Mathematical Biology

Extent and Intensity

2/0/0. 2 credit(s) (plus extra credits for completion). 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.

Timetable

Wed 9:00–10:50 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

• Mathematical Biology (programme PřF, B-BI)

Course objectives

The course provides students with basic theoretical facts about signals and systems with respect to possible applications in biology and medicine. It deals with basic approaches for description of signals in time and frequency domain - both for cases of continuous and discrete time. It describes basic types of signals and operations with them, in particula convolution, and correlations. Further, it deals with basic attributes of systems and ways od description of their properties - input/output description, state space description, both for continuous and descrete time again. Finally, it describes basic phenomena in systems - impact of initial conditions and inputs. It treats problems of stability of systems and their connecting. At the end of the course students should understand all the mentioned facts and apply them for description of basic algorithms for biological data processing.

Syllabus

• 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 aperiodical signals to harmoniccomponents - Fourier transform. Examples and aplications. 4. Descrete 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. Limear and nonlinear systems. Examples in biology and medicine. Description of systems - input/output description, state space description. 9. Input/output descrition of linear continuous systems - differential equation, system transfer function, frequency responses, pole-zero plot, impuls and transient response. 10. Input/output descrition of linear discrete systems - difference equation, system transfer function, frequency responses, pole-zero plot, impuls 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. Feed-back connection. Properties of the feed-back 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

Assessment methods

oral examination

Language of instruction

Czech

Further Comments

Study Materials
The course is taught last offered.

• Enrolment Statistics (Autumn 2008, recent)
  
• Permalink: https://is.muni.cz/course/sci/autumn2008/Bi5440