Course details

Signals and Systems (in English)

ISSe Acad. year 2023/2024 Winter semester 6 credits

Course is not open in this 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.


Language of instruction



Examination (written)

Time span

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

Assessment points

  • 55 pts final exam
  • 25 pts mid-term test
  • 20 pts projects


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.
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 knowledge 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.

Recommended prerequisites

Prerequisite knowledge and skills

Basic maths and statistics.

Study literature

  • Oppenheim A.V., Wilski A.S.: Signals and systems, Prentice Hall, 1997
  • Jan, J., Kozumplík, J.: Systémy, procesy a signály. Skriptum VUT v Brně, VUTIUM, 2000.
  • Jan J.: Číslicová filtrace, analýza a restaurace signálů, VUT v Brně, VUTIUM, 2002, ISBN 80-214-1558-4.

Syllabus of lectures

  1. Introduction, motivation, organization of the course. Examples of signal processing systems. Basic classification of signals - continuous/discrete time, periodic/non-periodic. Transformation of time.
  2. Continuous and discrete time periodic signals: sinusoids and complex exponentials. Overview of basic notions in complex numbers. Discrete and continuous time systems. Linear, time invariant systms (LTI). Representation of signals as series of pulses, convolution. Describing systems using differential and difference equations.
  3. Continuous time signals and their frequency analysis: periodic - Fourier series, coefficients. Non-periodic - Fourier transform, spectral function. Spectra of typical signals. Signal energy - Parseval's theorem.
  4. Continuous-time systems - Laplace transform, transfer function, frequency response, stability. Example of a simple analog circuit.
  5. Sampling and reconstruction - ideal sampling, aliasing, sampling theorem. Spectrum of sampled signal, ideal reconstruction. Normalized time and frequency. Quantization.
  6. Discrete-time signals and their frequency analysis - Discrete Fourier series, Discrete-time Fourier transform. Circular convolution, fast convolution.
  7. Discrete Fourier transform (DFT) and what it really computes. Fast Fourier transform.
  8. Discrete systems - z-transform, finite and infinite impulse response systems (FIR and IIR), transfer function, frequency response, stability. Example of a digital filter: MATLAB and C.
  9. Discrete systems cont'd: design of simple digital filters, sampling of frequency response, windowing. Links between continuous-time and discrete-time systems.
  10. Two-dimensional (2D) signals and systems: space frequency, spectral analysis (2D-Fourier transform), filtering using a mask. Example - JPEG.
  11. Random signals - random variable, realization, distribution function, probability density function (PDF). Stationarity and ergodicity. Parameters of a random signal: mean, etc. Estimation - ensemble and temporal.
  12. Random signals cont'd: correlation function, power spectral density (PSD). Processing of random signals by LTI systems.
  13. Summary of basic notions, systematic organization of signal processing knowledge. Examples.

Syllabus of computer exercises

  1. Generating and plotting of continuous and discrete-time signals in MATLAB.
  2. Sinusoids and complex exponentials. Convolution.
  3. Fourier analysis of continuous-time signal: 1) by hand, 2) semi-automatic (manual generation of e^(j2pift) functions, 3) using MATLAB functions (+their limitations).
  4. Simple LTI system, s-description, processing of signals. Comparison with theoretical frequency response.
  5. Discrete Fourier series and DTFT - by hand and using MATLAB-functions. Computing of spectrum of a continuous-time signal using DFT.
  6. Discrete-time systems - filtering. Design of a simple filter, frequency response, zeros and poles, stability. Influence of quantization of coefficients.

Syllabus - others, projects and individual work of students

Individual project - preparation:
  1. Sampling - aliasing. Generating of discrete signal with given frequency. Over- and under-sampling - - demonstration of aliasing.
  2. Random signals - generating, ensemble and temporal estimation of parameters, estimation of F(x) a p(x) using histogram.
  3. Random signals - correlation, power spectral density, processing by a filter.

The project will then consist in work with supplied and own signal, the results will be submitted using WIS.

Progress assessment

  • Mid-semester exam, all written material authorized, 20 pts.
  • Submission of project report - 20b.
  • Final exam - 60 pts., written materials prohibited, list of basic equations will be at your disposal.
  • Passing bounary for ECTS assessment - 50 points

  • 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.
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