Mathematics of Signal Analysis and applications [360-MS2-2SAMa] Rok akademicki 2024/25
Ćwiczenia, grupa nr 1

1. S. T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets, and Their Generalizations (Theoretical and Mathematical Physics), Springer, 2nd ed. 2014.

2. S.T. Ali, J.-P Antoine, and J.-P. Gazeau, Coherent States, Wavelets and their Generalizations 2d edition, Theoretical and Mathematical Physics, Springer, New York (2013), specially Chapter 11.

3. A. O. Barut and R. Rączka, Theory of Group Representations and Applications PWN, Warszawa, 1977.

4. I. Bengtsson and K. Życzkowski, Geometry of Quantum States, An Introduction to Quantum Entanglement, Cambridge University Press, 2017.

5. I. Daubechies, Ten Lectures on Wavelets, SIAM 1992.

6. T. A. Davis, K. Sigmon, MATLAB PRIMER, CHAPMAN & HALL/CRC, 2005.

7. J.-P. Gazeau, Coherent States in Quantum Physics, Wiley-VCH, Berlin, 2009.

8. A. Papoulis, Signal analysis, McGraw-Hill, New York, 1985.

9. S. Mallat A Wavelet Tour of Signal Processing Academic Press, 2nd edition, 1999.

10. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010.

11. M. Reed and B. Simon, Methods of Modern Mathematical Physics Academic Press, New York, 1975.

12. W. Rudin, Functional Analysis, McGraw-Hill, New York, 1991.

13. N. JA. Vilenkin, Special Functions and the Theory of Group Representations, Translations of Mathematical Monographs, 22, American Mathematical Society, 1988.

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

Lecture Slides: Course slides made available to students.

Exercises: Three sets of exercises provided for student practice.

Supplementary Materials: Additional resources, including documents on group theory and selected research papers, made accessible to students.

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

A set of exercises with specific scores. Totality of scores : 180

Final Exam : 13 June 2025.

Final mark: Max [final mark, (2times final mark + midterm mark)/3]