Noncommutative Geometry in Wireless Communication Applications
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The theory of time-frequency analysis is introduced, and basic results on modulation spaces are proved. We describe Gabor frames and prove results which are relevant to application in wireless communication. We outline a technique for transmitting data through a time-domain signal using time-frequency shifts, and show how pseudodifferential operators can be used to model a communication channel. The abstract structures of Hilbert $C^*$-modules are described and used to explain central aspects of Gabor theory, and we use a link to noncommutative geometry to prove the Balian-Low theorem.