| 1. | Course Title | Frame Theory | |||||||||||
| 2. | Code | 4ФЕИТ08025 | |||||||||||
| 3. | Study program | 13-PMA | |||||||||||
| 4. | Organizer of the study program (unit, institute, department) | Faculty of Electrical Engineering and Information Technologies | |||||||||||
| 5. | Degree (first, second, third cycle) | Second cycle | |||||||||||
| 6. | Academic year/semester | I/1 | 7. | Number of ECTS credits | 6.00 | ||||||||
| 8. | Lecturer | Dr Sanja Atanasova | |||||||||||
| 9. | Course Prerequisites | ||||||||||||
| 10. | Course Goals (acquired competencies):
The aim of the course is for students to become familiar with the theory of frames and to become familiar with their application in engineering. Students will learn to use it as a tool for representing signals. They are distinguished into different frames according to the need for signal representation or the respective application. |
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| 11. | Course Syllabus:
Frames and their limits. Bases and frame systems. Orthonormal bases. Riesz bases. Wavelet bases. Frames in Hilbert spaces, frames in L2(R). Hilbert frames, Gabor frames, Wavelet frames, Fréchet frames, Frame localization, synthesis and analysis of frame operators, frame series |
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| 12. | Learning methods:
lectures and presentations |
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| 13. | Total number of course hours | 180 | |||||||||||
| 14. | Distribution of course hours | 3 + 3 | |||||||||||
| 15. | Forms of teaching | 15.1 | Lectures-theoretical teaching | 45 hours | |||||||||
| 15.2 | Exercises (laboratory, practice classes), seminars, teamwork | 45 hours | |||||||||||
| 16. | Other course activities | 16.1 | Projects, seminar papers | 30 hours | |||||||||
| 16.2 | Individual tasks | 30 hours | |||||||||||
| 16.3 | Homework and self-learning | 30 hours | |||||||||||
| 17. | Grading | ||||||||||||
| 17.1 | Exams | 15 points | |||||||||||
| 17.2 | Seminar work/project (presentation: written and oral) | 15 points | |||||||||||
| 17.3. | Activity and participation | 20 points | |||||||||||
| 17.4. | Final exam | 50 points | |||||||||||
| 18. | Grading criteria (points) | up to 50 points | 5 (five) (F) | ||||||||||
| from 51 to 60 points | 6 (six) (E) | ||||||||||||
| from 61 to 70 points | 7 (seven) (D) | ||||||||||||
| from 71 to 80 points | 8 (eight) (C) | ||||||||||||
| from 81 to 90 points | 9 (nine) (B) | ||||||||||||
| from 91 to 100 points | 10 (ten) (A) | ||||||||||||
| 19. | Conditions for acquiring teacher’s signature and for taking final exam | ||||||||||||
| 20. | Forms of assessment |
During the semester, tests and preparation of project tasks or seminar papers are planned. Project assignments or seminar assignments are defended in the scheduled sessions. The final grade includes the points from the tests, homework as well as the points from the defense of the project assignments or the seminar. |
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| 21. | Language | Macedonian and English | |||||||||||
| 22. | Method of monitoring of teaching quality | Self-evaluation | |||||||||||
| 23. | Literature | ||||||||||||
| 23.1. | Required Literature | ||||||||||||
| No. | Author | Title | Publisher | Year | |||||||||
| 1. | O. Christensen | Frames and Bases | Birkhäuser Basel | 2008 | |||||||||
| 2. | O. Christensen | An Introduction to Frames and Riesz Bases | Birkhäuser Basel | 2002 | |||||||||
