Course detail

Signals and Systems

FIT-ISS Acad. year: 2025/2026 Winter semester

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

Czech

Number of ECTS credits

5

Supervisor

prof. Dr. Ing. Jan Černocký

Department

Department of Computer Graphics and Multimedia

Entry knowledge

Basic maths and statistics.

Rules for evaluation and completion of the course

  • 6 tests in numerical exercises, each 2 pts, total 12 pts.
  • half-semester exam, written materials, computers and calculators prohibited, 19 pts.
  • submission of project report – 18 pts.
  • final exam – 51 pts., written materials, computers and calculators prohibited, list of basic equations will be at your disposal. The minimal number of points which can be obtained from the final exam is 17. Otherwise, no points will be assigned to the student.

 


  • participation in numerical exercises is not checked, but tests are conducted in them, each worth 2 points. 
  • Groups in numerical exercises are organized according to inscription into schedule frames.
  • Replacing missed exercises (and obtaining the points) is possible by (1) attending the exercise and the test with another group, (2) solving all tasks in given assignment and presenting them to the tutor, (3) examination by the tutor or course responsible after an appointment. Options (2) and (3) are valid max. 14 days after the missed exercises, not retroactively at the end of the course. 

 

Aims

To learn and understand the 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 – two basic building blocks of modern communication and machine learning systems.
Students will learn and understand the basis of the description and analysis of discrete and continuous-time signals and systems. They will also obtain practical skills in analysis and filtering in MATLAB/Octave. Students will deepen their knowledge in mathematics and statistics and apply it to real problems of signal processing.

The study programmes with the given course

Programme N-AAE-P: Advanced Automotiv Engineering, Master's, compulsory

Programme N-AIŘ-P: Applied Computer Science and Control, Master's, compulsory

Programme BIT: Information Technology, Bachelor's
specialization BITP: Information Technology, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Syllabus


  1. Introduction to the course, mathematical basics

  2. Introduction to projections and derivation of Discrete Fourier Transform (DFT)

  3. Practical use and properties of DFT

  4. Introduction to digital filtering, differential equation, implementation of filters, convolution

  5. Frequency characteristic and stability of digital filter. Applications of filtering.

  6. Random signals – introduction.

  7. Random signals II – correlation, spectra, white noise.

  8. Processing of 2D signals – images.

  9. Analog world – continuous time signal, Fourier transform, estimation using DFT. Sampling and quantization.

  10. Periodicity of signals with discrete and continuous time – definition, Fourier series, Discrete Fourier series.

  11. Fundamentals of systems – properties, impulse response.

  12. Continuous-time systems. – schematics, differential equation, frequency characteristic, stability.

  13. Conclusion – summary of frequency transformations and filtering.


 

Fundamentals seminar

12 hours, compulsory

Syllabus

  1. Complex numbers, cosines and complex exponentials and operations therewith 
  2. Basics, filtering, frequency analysis 
  3. Continuous time signals: energy, power, Fourier series, Fourier transform 
  4. Continuous time systems and sampling 
  5. Operations with discrete signals, convolutions, DTFT, DFT 
  6. Digital filtering and random signals

Project

14 hours, compulsory

Syllabus

The project aims at the practical experience with signals and systems in Matlab/Octave. Its study etap contains solved exercises on the following topics: 

  1. Introduction to MATLAB
  2. Projection onto basis, Fourier series
  3. Processing of sounds
  4. Image processing
  5. Random signals
  6. Sampling, quantization and aliasing
The project itself follows with an individual signal for each student, see http://www.fit.vutbr.cz/study/courses/ISS/public/#proj