Self Similarity In Walsh Functions And In The Farfield Diffraction Patterns Of Radial Walsh Filters
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Self Similarity In Walsh Functions And In The Farfield Diffraction Patterns Of Radial Walsh Filters
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Author : Lakshminarayan Hazra
language : en
Publisher: Springer
Release Date : 2017-06-09
Self Similarity In Walsh Functions And In The Farfield Diffraction Patterns Of Radial Walsh Filters written by Lakshminarayan Hazra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-09 with Technology & Engineering categories.
The 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 π phase, corresponding to +1 or -1 of the Walsh function value.
Azimuthal Walsh Filters
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Author : Indrani Bhattacharya
language : en
Publisher: Springer Nature
Release Date : 2020-08-13
Azimuthal Walsh Filters written by Indrani Bhattacharya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-13 with Science categories.
This book explores the possibility of using azimuthal Walsh filters as an effective tool for manipulating far-field diffraction characteristics near the focal plane of rotationally symmetric imaging systems. It discusses the generation and synthesis of azimuthal Walsh filters, and explores the inherent self-similarity presented in various orders of these filters, classifying them into self-similar groups and sub-groups. Further, it demonstrates that azimuthal Walsh filters possess a unique rotational self-similarity exhibited among adjacent orders. Serving as an atlas of diffraction phenomena with pupil functions represented by azimuthal Walsh filters of different orders, this book describes how orthogonality and self-similarity of these filters could be harnessed to sculpture 2D and 3D light distributions near the focus.
Journal Of The Optical Society Of America
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Author :
language : en
Publisher:
Release Date : 1986
Journal Of The Optical Society Of America written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Imaging systems categories.
Science Citation Index
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Author :
language : en
Publisher:
Release Date : 1975
Science Citation Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Science categories.
Vols. for 1964- have guides and journal lists.