Course: Integral Transformations

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Course title Integral Transformations
Course code KMA/IT
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Tomeček Jan, doc. RNDr. Ph.D.
  • Andres Jan, prof. RNDr. dr hab. DSc.
  • Fürst Tomáš, RNDr. Ph.D.
  • Rachůnková Irena, prof. RNDr. DrSc.
Course content
1. Fourier series 2. Classical Fourier transforms 3. Discrete Fourier transform and its fast version 4. Image and sound processing, ECG processing 5. Fourier transforms in the context of distributions 6. Laplace transform 7. RLC circuits

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
  • Attendace - 39 hours per semester
  • Preparation for the Course Credit - 20 hours per semester
  • Preparation for the Exam - 60 hours per semester
Learning outcomes
Understand classical and modern approach to Fourier and Laplace transforms, master the modern computer applications
Comprehension Comprehension of integral transforms, ability to use them in applications.
Integral and differential calculus, basic programming.

Assessment methods and criteria
Oral exam, Written exam

Credit: Implementation of a simple algorithm. Exam: Oral exam - the student has to understand the subject and be able to prove principal results.
Recommended literature
  • Beerends R.J. , Morsche H.G. , van den Berg J.C. , van de Vrie E.M. (2003). Fourier and Laplace Transforms. Cambridge University Press.
  • Benson D. (2006). Music: A Mathematical Offering.. Cambridge University Press.
  • Bracewell R. (1965). The Fourier transform and its applications. McGraw-Hill, New York.
  • Grafakos L. (2004). Classical and Modern Fourier Analysis. Pearson Education.
  • Howell K. B. (2001). Principles of Fourier Analysis. Chapman & Hall.
  • Chandrasekharan K. (1989). Classical Fourier Transforms. Springer.
  • Körner T. W. (1988). Fourier Analysis. Cambridge University Press.
  • Strichartz R.S. (1994). A Guide to Distribution Theory and Fourier Transforms. Scientific.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 1 Winter
Faculty of Science Applied Mathematics (2014) Mathematics courses 2 Winter