In this course, the student will learn about continuous and discrete integral transforms enabling filtering, compression of signals (including multidimensional), and generation of their time-frequency spectra, including effective implementations of both forward and inverse transforms based on the orthogonality of the systems used, when the calculation of the image or the original reduces to the multiplication of the vector by the transformation matrix or its transposition.
Everything will be illustrated by Matlab's implementations.

Entry requirements for the course: Recommended knowledge of the basics of linear algebra, mathematical analysis, and functions of complex variables.

Requirements for course completion: Active participation in the sessions (80%) + final assignment. The deadline for completing the final assignment is May 16, 2025.

• reminder of orthogonality and FFT,
• window Fourier transform and its applications,
• multiresolution, wavelet transform, and its applications.

Available study materials: D. Horák, teaching texts and slides Discrete transformations