Mathematics of Signal Analysis and applications 360-MS2-2SAMa
1. Signal Analysis: definitions and basic mathematics}
1.1 What is a signal? An image?
1.2 Hilbert spaces: the basics
1.3 Fourier analysis and reconstruction of signals
1.4 Gabor analysis and reconstruction of signals
1.5 Introduction to Distrbtions
1.6 Wavelet analysis (and beyond) and reconstruction of signals
2 Illustrations with MATLAB
2.1 Rapid introduction to MATLAB
2.2 1-D Transform: time-frequency, time-scale
2.3 2-D Transform: space parameters, angle-scale
3. Symmetry and functional analysis tools}
3.1 Group theory: the basics
3.2 Lie algebra: the basics
3.3 Operators in Hilbert spaces
3.4 Elements of group and algebra representation theory
3.5 Weyl-Heisenberg group
3.6 Affine group
Prerequisites (description)
Course coordinators
Type of course
Term 2024: elective monographs | Term 2025: elective monographs | General: elective courses |
Mode
Term 2024: Blended learning Self-reading | Term 2025: Self-reading Blended learning | General: (in Polish) w sali |
Learning outcomes
At the end of the course students should be able to implement analytically and numerically (MatLab) the taught mathematical and signal processing tools
KA7_UW02 abstract mathematical reasoning ability,
KA7_UW09 can use methods of functional analysis,
KA7_UW15 recognises mathematical structure in physical theories,
KA7_UK05 English proficiency,
KA7_UU02 can search mathematical literature for information, including in English,
KA7_WG06 understands relationship of the topic to other fields.
Assessment criteria
Each session consists of a ~ 90-minute theoretical presentation followed by ~ 90 minutes of applied learning through guided training exercises.
Midterm Exam : Tuesday April 8 2025
Final Exam : 13 June 2025.
Final mark: Max [final mark, (2times final mark + midterm mark)/3]
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: