Gabor Analysis and Its Mysteries

Explore the fundamentals of Gabor analysis in this comprehensive lecture, the first in a series of four. Delve into the construction and properties of series expansions using time-frequency shifts, and discover their applications in signal processing, wireless communications, and quantum mechanics. Learn about the uncertainty principle, Fourier transform, partition of unity, and time-frequency shifts. Understand the role of Gabor series in analyzing speech and music signals, as well as their importance in orthogonal frequency division multiplexing (OFDM). Gain insights into the mathematical structure of Gabor frames and bases, and prepare for subsequent lectures covering advanced topics and recent developments in the field.