Course details

Signals and Systems

ISS Acad. year 2006/2007 Winter semester 6 credits

Current academic year

Signals with continuous time and their spectra. Systems with continuous time: I/O description, impulse response and convolution, transfer function, frequency response, stability. Signals with discrete time: sampling and reconstruction, spectral representation, discrete Fourier transform. Systems with discrete time: state- and I/O description, impulse response and discrete convolution, IIR and FIR systems, transfer function, frequency response, stability, quantisation errors. Relations between continuous-time and discrete-time systems, impulse invariance. Stochastic processes and signals: Random signal as a realisation of stochastic process, stationary and ergodic processes, correlation and covariance functions, power spectra, transfer of a random signal via a linear system. Basic concepts from information theory: information measure, entropy, redundancy, channel capacity, entropic coding.

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

Basic theoretical knowledge in the area of description and analysis of continuous and discrete signals and linear systems. Modelling of systems in the MATLAB - Simulink environment; signal processing in MATLAB - DSP Blockset environment.

Learning objectives

Introduction to the theory of signals and linear systems with continuous and discrete time, to the theory of random signals and to basic concepts of information theory. The obtained knowledge is a necessary base for understanding of information processing- and communication methods, and for description and modelling of technical systems.

Prerequisite knowledge and skills

Rudiments of discrete mathematics and mathematical analysis.

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.

Obtaining at least 7 points from the labs and minimum 7 points for the project.

Controlled instruction

Active participation in the computer-lab tutorials is checked, the minimum participation is 5 out of 7 tutorials, which cannot be substituted

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