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YouTube

Gabor Analysis and Its Mysteries

Hausdorff Center for Mathematics via YouTube

Overview

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The course aims to introduce learners to Gabor analysis, focusing on the construction and properties of series expansions of functions with respect to time-frequency shifts. The goal is to understand Gabor series and their applications in signal processing, speech and music signal analysis, wireless communications, quantum mechanics, and operator theory. The course covers the mathematical structure of Gabor frames and bases, including coarse duality structure, characterization, and concrete examples. The teaching method involves lectures discussing applications, basic concepts, mathematical structures, and recent progress in Gabor analysis. This course is intended for individuals interested in mathematics, signal processing, physics, and communication technologies.

Syllabus

Intro
What is Gabor Analysis
Uncertainty Principle
Gabor Analysis
Fourier Transform
Partition of Unity
Signal Processing
Time Frequency Shift
Filter Banks
Modulation
Data Transmission
axiomatic structure
time frequency space

Taught by

Hausdorff Center for Mathematics

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