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Some comments on Fourier analysis, uncertainty and modeling. (English) Zbl 0571.94004
Investigation of the problem of simultaneously concentrating a function and its Fourier transform has led to some interesting special functions that have widespread applications in engineering. They provide a means of proving a rigorous version of an engineering folk theorem called the 2WT- Theorem. Many generalizations of these ideas seem to possess a similar elegant mathematical structure. A brief descriptive review is given of these developments.
MSC:
94A11Application of orthogonal and other special functions in communication
42A38Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
94A12Signal theory (characterization, reconstruction, filtering, etc.)
94-02Research monographs (information and communication)