Calculus of Transforms 390-FM2-1RTR
A short introduction to the complex analysis: holomorphic functions, residues. Residue theorem.
Laplace transform and Z-transform. Fourier series, Fourier transform, Cosine transform.
Uncertainty principle. Discrete Fourier transform (DFT), fast Fourier transform (FFT).
Hilbert space. Bases. Operators. Scalar products. Dirac Delta. Wavelet transform. Low-pass and high-pass filters and their role in signal analysis.
Hough and Radon transforms.
Applications in tomography and image analysis.
Type of course
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
Student:
1. She/he knows methods and tools for computer supporting of a physical experiment*.
2. She/he has a further knowledge of mathematics in the field of mathematical methods of physics as well as transforms analysis and data analysis with particular emphasis on applications in medical physics*.
3. She/he knows professional computer computational tools, including tools for symbolic calculations*.
4. She/he knows mathematical tools for experimental data analysis, signal and image analysis, including medical diagnostic images*.
5. She/he knows methods for obtaining images and diagnostic signals in medical applications*.
6. She/he knows how to use the learned mathematical tools to formulate and solve selected problems in physics and its practical applications*.
7. She/he can understand and critically use professional literature and Internet resources - including sources in English - in relation to selected problems of mathematics and computer science.
8. She/he is able to use, with respect to intellectual property rights, computer tools available on the Internet.
9. She/he is able to supplement and expand her/his mathematical and computer knowledge by using the literature and resources of the Internet*.
10. She/he knows how to use computer tools for signal processing and signal analysis*.
11. She/he nderstands the need for continuous improvement of his knowledge and the need to provide society with reliable, evidence-based knowledge of physics and its applications, including medical applications*.
*- if the programm provides it.
Codes:
K_W08, K_W11, K_W12, K_W29, K_W32, K_U13,K_U16, K_U17, K_U42, K_U43, K_K02.
Assessment criteria
After completing the training, a written and oral exam takes place, which verifies the acquired knowledge.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: