Fourier- und Laplace-Transformation

What it is about

You learn the theory and applications of Fourier and Laplace transforms: Fourier series, Fourier analysis (integral transform), Gabor transform and Laplace transform. In the end you can understand the interaction between a function and its Fourier transform and use it for optimized approximations.

What you will be able to do

• Understanding of Fourier series and their convergence properties
• Application of approximation kernels and convergence results
• Knowledge of Fourier inversion and L2 theory
• Familiarity with sampling theorems
• Introduction to the Gabor transform
• Foundations of the Laplace transform

What the module consists of

• LectureConveying theoretical content with examples and discussion
• Übung/Practice sessionsDeepening through problem sheets and discussion of solutions

Teaching method

• Lecture with demonstrationsfor the introduction and illustration of the topics
• Discussion with studentsto foster own analysis and understanding
• Exercise sheets with solutionsfor self-check and deepening of the material