03212nam 22005655 450 991033825220332120200703191139.03-030-13423-710.1007/978-3-030-13423-5(CKB)4100000008280642(MiAaPQ)EBC5780114(DE-He213)978-3-030-13423-5(PPN)23652254X(EXLCZ)99410000000828064220190524d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe XFT Quadrature in Discrete Fourier Analysis /by Rafael G. Campos1st ed. 2019.Cham :Springer International Publishing :Imprint: Birkhäuser,2019.1 online resource (245 pages)Applied and Numerical Harmonic Analysis,2296-50093-030-13422-9 Introduction -- The ordinary discrete Fourier transform -- XFT: A discrete Fourier transform -- Applications of the XFT -- A discrete fractional Fourier transform.This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book’s second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.Applied and Numerical Harmonic Analysis,2296-5009Special functionsFunctions of real variablesIntegral transformsOperational calculusSpecial Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M1221XReal Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12171Integral Transforms, Operational Calculushttps://scigraph.springernature.com/ontologies/product-market-codes/M12112Special functions.Functions of real variables.Integral transforms.Operational calculus.Special Functions.Real Functions.Integral Transforms, Operational Calculus.515.96515.2433Campos Rafael Gauthttp://id.loc.gov/vocabulary/relators/aut781813BOOK9910338252203321XFT Quadrature in Discrete Fourier Analysis1733793UNINA