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Discrete Harmonic Analysis

MA5911Elective Modules6 ECTSEnglishUnregelmäßigDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You deal with harmonic analysis in discrete, finite structures. The module covers Fourier transforms on finite (abelian and non-abelian) groups, discrete Fourier and fast Fourier transforms, and applications e.g. in signal processing, graph theory, and number theory. In the end you will be able to formulate the fundamental methods of discrete harmonic analysis and apply them to examples and applications.

What you will be able to do

  • Understand fundamentals of harmonic analysis on finite groups
  • Apply Fourier transformation on abelian and non-abelian finite groups
  • Apply discrete Fourier transform (DFT) and fast Fourier transform (FFT)
  • Recognize and utilize applications in signal processing, graph theory and number theory
  • Precise recitation of important definitions, main theorems and sketches of proofs

What the module consists of

  • VorlesungConveying the theoretical foundations and main theorems
  • ÜbungenDeepening through examples and exercises
  • HausaufgabenIndependent practice and application of the learned material

Teaching method

  • VorlesungenIntroduction and explanation of concepts and theorems
  • ÜbungsaufgabenApplication and deepening of the material
  • HausaufgabenIndependent work to consolidate and practice
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Official page in TUMonline · Details are not binding.