Course details

Signals and Systems

ISS Acad. year 2024/2025 Winter semester 5 credits

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

Course coordinator

Language of instruction

Czech

Completion

Examination (written)

Time span

  • 26 hrs lectures
  • 12 hrs exercises
  • 14 hrs projects

Assessment points

  • 51 pts final exam (written part)
  • 19 pts mid-term test (written part)
  • 12 pts numeric exercises
  • 18 pts projects

Department

Lecturer

Instructor

Learning objectives

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. 

Recommended prerequisites

Prerequisite knowledge and skills

Basic maths and statistics.

Study literature

Syllabus of lectures

  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.

 

Syllabus of numerical exercises

  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

Syllabus - others, projects and individual work of students

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

Progress assessment

  • 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. 

 

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exercise 1., 3., 5., 9., 11., 13. of lectures O204 11:0012:5020 2BIA 2BIB 3BIT xx Kocour
Mon exercise 2., 4., 6., 8., 10., 12. of lectures O204 11:0012:5020 2BIA 2BIB 3BIT xx Kocour
Tue exercise 1., 3., 5., 7., 9., 11., 13. of lectures O204 08:0009:5020 2BIA 2BIB 3BIT xx Vendrame
Tue exercise 2., 4., 6., 8., 10., 12. of lectures O204 08:0009:5020 2BIA 2BIB 3BIT xx Vendrame
Tue exercise 1., 3., 5., 7., 9., 11., 13. of lectures O204 10:0011:5020 2BIA 2BIB 3BIT xx Vendrame
Tue exercise 2., 4., 6., 8., 10., 12. of lectures O204 10:0011:5020 2BIA 2BIB 3BIT xx Vendrame
Tue exercise 1., 3., 5., 7., 9., 11., 13. of lectures O204 12:0013:5020 2BIA 2BIB 3BIT xx Sedláček
Tue exercise 2., 4., 6., 8., 10., 12. of lectures O204 12:0013:5020 2BIA 2BIB 3BIT xx Sedláček
Tue exercise 1., 3., 5., 7., 9., 11., 13. of lectures O204 14:0015:5020 2BIA 2BIB 3BIT xx Sedláček
Tue exercise 2., 4., 6., 8., 10., 12. of lectures O204 14:0015:5020 2BIA 2BIB 3BIT xx Sedláček
Wed lecture 1., 3., 5., 6., 7., 8., 10., 11., 12., 13. of lectures D0206 D105 08:0009:50470 2BIB 3BIT 20 - 29 xx Černocký
Wed lecture 2., 4., 9. of lectures D0206 D105 08:0009:50470 2BIB 3BIT 20 - 29 xx
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures N203 10:0011:5020 2BIA 2BIB 3BIT xx Grézl
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures O204 10:0011:5020 2BIA 2BIB 3BIT xx Han in English
Thu exercise 2., 4., 6., 8., 10., 12. of lectures N203 10:0011:5020 2BIA 2BIB 3BIT xx Grézl
Thu exercise 2., 4., 6., 8., 10., 12. of lectures O204 10:0011:5020 2BIA 2BIB 3BIT xx Han in English
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures N203 12:0013:5020 2BIA 2BIB 3BIT xx Polok
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures O204 12:0013:5020 2BIA 2BIB 3BIT xx Han in English
Thu exercise 2., 4., 6., 8., 10., 12. of lectures N203 12:0013:5020 2BIA 2BIB 3BIT xx Polok
Thu exercise 2., 4., 6., 8., 10., 12. of lectures O204 12:0013:5020 2BIA 2BIB 3BIT xx Han in English
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures N203 14:0015:5020 2BIA 2BIB 3BIT xx Grézl
Thu exercise 2., 4., 6., 8., 10., 12. of lectures N203 14:0015:5020 2BIA 2BIB 3BIT xx Grézl
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures N203 16:0017:5020 2BIA 2BIB 3BIT xx Grézl
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures O204 16:0017:5020 2BIA 2BIB 3BIT xx Rohdin
Thu exercise 2., 4., 6., 8., 10., 12. of lectures N203 16:0017:5020 2BIA 2BIB 3BIT xx Grézl
Thu exercise 2., 4., 6., 8., 10., 12. of lectures O204 16:0017:5020 2BIA 2BIB 3BIT xx Rohdin in English
Thu exercise 1., 3., 5., 7., 9., 11., 13. of lectures N203 18:0019:5020 2BIA 2BIB 3BIT xx Grézl
Thu exercise 2., 4., 6., 8., 10., 12. of lectures N203 18:0019:5020 2BIA 2BIB 3BIT xx Grézl
Fri exercise 1., 3., 5., 7., 9., 11., 13. of lectures N203 09:0010:5020 2BIA 2BIB 3BIT xx Polok
Fri exercise 2., 4., 6., 8., 10., 12. of lectures N203 09:0010:5020 2BIA 2BIB 3BIT xx Polok
Fri exercise 1., 3., 5., 7., 9., 11., 13. of lectures N203 11:0012:5020 2BIA 2BIB 3BIT xx Grézl
Fri exercise 2., 4., 6., 8., 10., 12. of lectures N203 11:0012:5020 2BIA 2BIB 3BIT xx Grézl
Fri lecture lectures E112 13:0014:50154 2BIA 3BIT 10 - 19 xx Černocký

Course inclusion in study plans

  • Programme BIT, 2nd year of study, Compulsory
  • Programme BIT (in English), 2nd year of study, Compulsory
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