Course details

Signals and Systems

ISS Acad. year 2005/2006 Winter semester 6 credits

Current academic year

Continuous and discrete time signals and systems. Spectral analysis in continuous time - Fourier series and Fourier transform. Systems with continuous time. Sampling and reconstruction. Discrete-time signals and their frequency analysis: Discrete Fourier series and Discrete-time Fourier transform. Discrete systems. Two-dimensional signals and systems. Random signals.

Guarantor

Černocký Jan, prof. Dr. Ing. (DCGM)

Language of instruction

Czech

Completion

Examination

Time span

  • 39 hrs lectures
  • 12 hrs pc labs
  • 14 hrs projects

Department

Department of Computer Graphics and Multimedia (UPGM)

Subject specific learning outcomes and competences

Students will learn and understand basis of  description and analysis of discrete and continuous-time signals and systems. They will also obtain practical skills in analysis and filtering in MATLAB.

Students will deepen their knowldge in mathematics and statistics and apply it on real problems of signal processing. During the course, they will get acquainted with math- and visualization-SW Matlab.

Learning objectives

To learn and understand basic theory of signals and linear systems with continuous and discrete time. To introduce  to random signals. The emphasis of the course is on spectral analysis and linear filtering - 2 basic building blocks of modern communication systems.

Prerequisite knowledge and skills

basic maths and statistics

Study literature

  • http://www.fit.vutbr.cz/study/courses/ISS/public/
  • Jan, J., Kozumplík, J.: Systémy, procesy a signály. Skriptum VUT v Brně, VUTIUM, 2000.
  • Šebesta V.: Systémy, procesy a signály I., Skriptum VUT v Brně, VUTIUM, 1997.
  • Jan J., Číslicová filtrace, analýza a restaurace signálů, VUT v Brně, VUTIUM, 2002, ISBN 80-214-1558-4.

Fundamental literature

  • Oppenheim A.V., Wilski A.S.: Signals and systems, Prentice Hall, 1997

Syllabus of lectures

  • Continuous-time signals, properties and classification
  • Spectral representation of continuous time signals (Fourier series and transformation)
  • Continuous-time systems, I/O description
  • Transfer function and characteristic responses of continuous-time systems, stability
  • Sampling and reconstruction of signals. Discrete-time signals
  • Spectral representation of discrete-time signals (DTFT, DFT)
  • Discrete-time systems, recursive and non-recursive, input-output description
  • Transfer function and impulse response of discrete-time systems
  • Frequency-domain description of discrete-time systems, IIR and FIR systems
  • State description. Stability of discrete-time systems. Quantisation errors
  • Relations between continuous-time and discrete-time systems, impulse invariance
  • Discrete stochastic processes and signals, stationarity and ergodicity, correlation function, power spectra
  • Basic concepts from information theory: information measure, entropy, redundancy, channel capacity, entropic coding

Syllabus of computer exercises

  • Discrete deterministic and stochastic signal generation, basic operations with the signals, displaying results
  • Spectra of periodic and non-periodic deterministic signals. Filtering and sampling frequency conversion in frequency domain. Use of DFT
  • Introduction to Simulink. Analysis of continuous-time systems via responses. Construction and testing of integrator-based models
  • Convolution - aperiodic and cyclic, convolution via frequency domain. Correlation, applications on random signals
  • Analysis of discrete-time systems via responses. Examples of computer-based designs of discrete-time systems
  • Intuitive designs and testing of discrete-time systems.Signal filtering and sampling frequency conversion in time-domain
  • Stochastic signals, transfer via linear time-invariant systems. Power spectra of stochastic processes

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

  • participation in computer labs is not checked but active participation and presentation of results to the tutor is evaluated by 2 pts.
  • Groups in computer labs are organized according to inscription into schedule frames, the study groups are considered only as auxiliary information.
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