11MAI / Mathematical Tools

Important note: I am away until September 19, 2022, then again from September 20 to September 23, 2022. The first lecture will therefore be offline, self-paced.

Mathematical Tools for ITS

Instructor: Dr.-techn. Ing. Jan Přikryl <prikryl@fd.cvut.cz>

Lectures: Monday 09:45-11:15 K304 (group 26), Monday 13:15-14:45 K304 (group 25)

Computer sessions: Monday 11:30-13:00 K104 (group 26), Monday 15:00-16:30 K104 (group 25)

Course description

The objective of this course is to establish the mathematical foundations necessary to understand general constructions useful for signal processing using Fourier Transform and the Short Time Fourier Transform, update and extend the knowledge about data processing and to provide an introduction to numerical methods for solving traffic flow equations. The course includes experimental and computer projects involving individual effort.

Prerequisites: Linear Algebra, Statistical Learning, MATLAB

Texts

M. Vetterli, J. Kovacevic, and V. K. Goyal. “Fourier and Wavelet Signal Processing”. With permission of authors the preprint is available from our webpage as PDF here.

Broughton, S. A., & Bryan, K. (2018). Discrete Fourier analysis and wavelets: applications to signal and image processing. 2nd edition. John Wiley & Sons.

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning. New York: Springer. Electronic version, errata, and supplementary material available from https://www.statlearning.com/.

Friedman, J., Hastie, T., & Tibshirani, R. (2009). The elements of statistical learning. Springer Series in Statistics. 2nd edition. New York: Springer. Electronic version, errata, and supplementary material available from https://web.stanford.edu/~hastie/ElemStatLearn/.

Heath, M. T. (2018). Scientific Computing: An Introductory Survey, Revised Second Edition. Society for Industrial and Applied Mathematics.

Li, J., & Chen, Y. T. (2019). Computational partial differential equations using MATLAB®. 2nd edition. CRC press.

Grading

The following table lists all possible scores that can be obtained:

Homeworks	21 points
- minimum homework points	9 points
Final project	14 points
- minimum from the project	7 points
Total	30(+5) points

Final grade is given by the total points obtained for homeworks and the final project. The grading scheme is as follows:

Total points	Grade	ECTS
27 to 30	excellent	A
24 to <27	very good	B
21 to <24	good	C
18 to <21	satisfactory	D
16 to <18	sufficient	E
less than 16	failed	F