Self-similarity in Walsh Functions and in the Farfield Diffraction Patterns of Radial Walsh Filters

  • Lakshminarayan Hazra
  • Pubali Mukherjee

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Lakshminarayan Hazra, Pubali Mukherjee
    Pages 1-15
  3. Lakshminarayan Hazra, Pubali Mukherjee
    Pages 17-24
  4. Lakshminarayan Hazra, Pubali Mukherjee
    Pages 59-71
  5. Lakshminarayan Hazra, Pubali Mukherjee
    Pages 81-82

About this book


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.


Walsh-functions Optical Imaging Pupil Plane Filtering Optical Tweezers Walsh Filters

Authors and affiliations

  • Lakshminarayan Hazra
    • 1
  • Pubali Mukherjee
    • 2
  1. 1.Department of Applied Optics and PhotonicsUniversity of CalcuttaKolkataIndia
  2. 2.Department of Electronics and Communication EngineeringMCKV Institute of EngineeringHowrahIndia

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering
  • Print ISBN 978-981-10-2808-3
  • Online ISBN 978-981-10-2809-0
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site