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By Karlheinz Gröchenig

Time-frequency research is a latest department of harmonic research. It com­ prises all these elements of arithmetic and its functions that use the struc­ ture of translations and modulations (or time-frequency shifts) for the anal­ ysis of services and operators. Time-frequency research is a sort of neighborhood Fourier research that treats time and frequency at the same time and sym­ metrically. My target is a scientific exposition of the principles of time-frequency research, whence the name of the ebook. the themes variety from the elemen­ tary concept of the short-time Fourier remodel and classical effects in regards to the Wigner distribution through the new thought of Gabor frames to quantita­ tive equipment in time-frequency research and the idea of pseudodifferential operators. This ebook is influenced via functions in sign research and quantum mechanics, however it isn't approximately those purposes. the most ori­ entation is towards the specific mathematical research of the wealthy and stylish constructions underlying time-frequency research. Time-frequency research originates within the early improvement of quantum mechanics by way of H. Weyl, E. Wigner, and J. von Neumann round 1930, and within the theoretical starting place of knowledge concept and sign research via D.

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