LEADER 04578nam 22007575 450 001 9910299589203321 005 20220404231750.0 010 $a981-10-2809-5 024 7 $a10.1007/978-981-10-2809-0 035 $a(CKB)3710000001401306 035 $a(DE-He213)978-981-10-2809-0 035 $a(MiAaPQ)EBC4874800 035 $a(PPN)202992071 035 $a(EXLCZ)993710000001401306 100 $a20170609d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSelf-similarity in Walsh functions and in the Farfield diffraction patterns of radial Walsh filters /$fby Lakshminarayan Hazra, Pubali Mukherjee 205 $a1st ed. 2018. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018. 215 $a1 online resource (IX, 82 p. 44 illus.) 225 1 $aSpringerBriefs in Applied Sciences and Technology,$x2191-530X 311 $a981-10-2808-7 320 $aIncludes bibliographical references at the end of each chapters. 327 $aWalsh Functions -- Self-similarity in Walsh Functions -- Computation of Farfield Diffraction Characteristics of radial Walsh Filters on the pupil of axisymmetric imaging systems -- Self-similarity in Transverse Intensity Distributions on the Farfield plane of self-similar radial Walsh Filters -- Self-similarity in Axial Intensity Distributions around the Farfield plane of self-similar radial Walsh Filters -- Self-similarity in 3D Light Distributions near the focus of self-similar radial Walsh Filters. Conclusion. 330 $aThe book explains the classification of a set of Walsh functions into distinct self-similar groups and subgroups, where the members of each subgroup possess distinct self-similar structures. The observations on self-similarity presented provide valuable clues to tackling the inverse problem of synthesis of phase filters. Self-similarity is observed in the far-field diffraction patterns of the corresponding self-similar filters. Walsh functions form a closed set of orthogonal functions over a prespecified interval, each function taking merely one constant value (either +1 or ?1) in each of a finite number of subintervals into which the entire interval is divided. The order of a Walsh function is equal to the number of zero crossings within the interval. Walsh functions are extensively used in communication theory and microwave engineering, as well as in the field of digital signal processing. Walsh filters, derived from the Walsh functions, have opened up new vistas. They take on values, either 0 or ? phase, corresponding to +1 or -1 of the Walsh function value. 410 0$aSpringerBriefs in Applied Sciences and Technology,$x2191-530X 606 $aMicrowaves 606 $aOptical engineering 606 $aLasers 606 $aPhotonics 606 $aSignal processing 606 $aImage processing 606 $aSpeech processing systems 606 $aElectronics 606 $aMicroelectronics 606 $aMicrowaves, RF and Optical Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T24019 606 $aOptics, Lasers, Photonics, Optical Devices$3https://scigraph.springernature.com/ontologies/product-market-codes/P31030 606 $aSignal, Image and Speech Processing$3https://scigraph.springernature.com/ontologies/product-market-codes/T24051 606 $aElectronics and Microelectronics, Instrumentation$3https://scigraph.springernature.com/ontologies/product-market-codes/T24027 615 0$aMicrowaves. 615 0$aOptical engineering. 615 0$aLasers. 615 0$aPhotonics. 615 0$aSignal processing. 615 0$aImage processing. 615 0$aSpeech processing systems. 615 0$aElectronics. 615 0$aMicroelectronics. 615 14$aMicrowaves, RF and Optical Engineering. 615 24$aOptics, Lasers, Photonics, Optical Devices. 615 24$aSignal, Image and Speech Processing. 615 24$aElectronics and Microelectronics, Instrumentation. 676 $a515.2433 700 $aHazra$b Lakshminarayan$4aut$4http://id.loc.gov/vocabulary/relators/aut$01058122 702 $aMukherjee$b Pubali$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299589203321 996 $aSelf-similarity in Walsh Functions and in the Farfield Diffraction Patterns of Radial Walsh Filters$92497368 997 $aUNINA