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The book systematically explores the foundations of time-frequency analysis, a modern branch of harmonic analysis that examines functions and operators through translations and modulations. It covers essential topics such as the short-time Fourier transform, Wigner distribution, Gabor frames, and pseudodifferential operators. While motivated by applications in signal analysis and quantum mechanics, the focus remains on the mathematical structures of time-frequency analysis, tracing its origins to early quantum mechanics developments in the 1930s.
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Foundations of Time-Frequency Analysis, Karlheinz Gröchenig
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- 2013
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