Course detail
Introduction to Signal Processing
FSI-RSZ Acad. year: 2027/2028 Winter semester
The course introduces the introduction to theory of digital processing of one-dimensional signals. Students apply this knowledge to practical tasks in MATLAB. Emphasis is placed on basic terminology and processing methods: signals, sampling, discretisation, quantisation, convolution, the Fourier transform, and IIR and FIR filtering. Part of the course is focused on estimation of dynamic systems states using Kalman filter and its nonlinear variants.
Language of instruction
Czech
Number of ECTS credits
5
Supervisor
Entry knowledge
Basic knowledge of MATLAB or Octave, particularly working with matrices and vectors, creating simple plots and programming.
Rules for evaluation and completion of the course
The course grade is based on a functional software project that uses selected method of signal processing. Students must submit a report describing the task together with the source code and present the project to their classmates in a short presentation.
The report, in PDF format, must be at least 5 pages long and include the rationale for the assignment, detailed instructions, a description of the procedure, and the results achieved. The source code must be executable on the instructor’s computer. The presentation must be in PowerPoint or a compatible format.
Assessment is based on the fulfillment of the project’s objectives, as well as the quality of the code and text, taking into account the difficulty of the assignment.
Attendance at lectures is recommended, attendance at exercises is compulsory. The teacher specifies how students can substitute missed exercises.
Aims
The course introduces the fundamentals of signal processing, particularly the digital processing of one-dimensional signals. Practical tasks in MATLAB form an essential part of the course.
After completing the course, students will understand basic signal-processing terminology, analyse a one-dimensional signal and design a filter for a given application using MATLAB.
The study programmes with the given course
Programme N-MET-P: Mechatronics, Master's, compulsory
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
specialization BIO: Biomechanics, compulsory-optional
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
specialization IME: Engineering Mechanics, compulsory
Type of course unit
Lecture
13 hours, optionally
Syllabus
1. Signal: definition, classification, why we need to process, applications.
2. Continuous / discrete signal, sampling, discretization, quantizing
3. Continuous systems and their description, discrete systems
4. Linear systems, superposition principle, decomposition
5. Convolution
6. Fourier transform
7. Fourier transform, properties
8. Digital filters, introduction, FIR filters
9. IIR filters
10. Kalman filtering
11. Extended Kalman filter
12 Unscented Kalman filter, particle filter
13. Laplace transform, Z-transform
Computer-assisted exercise
26 hours, compulsory
Syllabus
1. Matlab review. Signal Processing Toolbox.
2. Reading the signal, signal generation
3. Original (time) domain analysis
4. SPTool
5. Convolution
6. Correlation analysis
7. Spectral analysis – introduction
8. Discrete Fourier transform
9. Filtering – introduction
10. Filtering – using FDATool
11. Filtering, applications
12. Frequency analysis in time, spectrogram
13. Kalman filter, nonlinear versions of KF