LEADER 04556nam 22007095 450 001 9910254291903321 005 20200704200530.0 010 $a1-4939-7393-2 024 7 $a10.1007/978-1-4939-7393-4 035 $a(CKB)4340000000223148 035 $a(DE-He213)978-1-4939-7393-4 035 $a(MiAaPQ)EBC6315779 035 $a(MiAaPQ)EBC5576266 035 $a(Au-PeEL)EBL5576266 035 $a(OCoLC)1066196379 035 $a(PPN)221248641 035 $a(EXLCZ)994340000000223148 100 $a20171121d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aApplied Fourier Analysis $eFrom Signal Processing to Medical Imaging /$fby Tim Olson 205 $a1st ed. 2017. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (XVI, 302 p. 126 illus., 118 illus. in color.) 311 $a1-4939-7391-6 320 $aIncludes bibliographical references and index. 327 $aIntroduction: From Linear Algebra to Linear Analysis -- Basic Fourier Series -- The Discrete Fourier Transform -- The Fourier Transform -- Sampling and Interpolation -- Digital Communications -- Radar Processing -- Image Processing -- Medical Imaging -- Partial Differential Equations. 330 $aThe first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects.    The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis. 606 $aFourier analysis 606 $aSignal processing 606 $aImage processing 606 $aSpeech processing systems 606 $aDifferential equations, Partial 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aSignal, Image and Speech Processing$3https://scigraph.springernature.com/ontologies/product-market-codes/T24051 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aFourier analysis. 615 0$aSignal processing. 615 0$aImage processing. 615 0$aSpeech processing systems. 615 0$aDifferential equations, Partial. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aFourier Analysis. 615 24$aSignal, Image and Speech Processing. 615 24$aPartial Differential Equations. 615 24$aApplications of Mathematics. 676 $a515.2433 700 $aOlson$b Tim$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767505 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254291903321 996 $aApplied Fourier Analysis$91562551 997 $aUNINA