Abstract
With a brief description of the origin, basic characteristics and major practical applications of Walsh functions, different forms of Walsh functions in one and two dimensions are systematically developed from the orthogonality considerations. Approximation of a continuous function over a given domain by a finite set of Walsh functions provides a piecewise constant approximation of the function. The latter has important consequences in tackling practical problems by way of opening up new techniques for analysis and synthesis. Highlights of these aspects are provided along with a brief description of Walsh Block functions and Hadamard matrices.
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References
Walsh JL (1923) A closed set of normal orthogonal functions. Am J Math 45(1):5–24
Hazra LN, Banerjee A (1976) Application of Walsh function in generation of optimum apodizers. J Opt (India) 5:19–26
Harmuth HF (1972) Transmission of information by orthogonal functions. Springer, Berlin, p 31
Beauchamp KG (1985) Walsh functions and their Applications. Academic Press, New York
Andrews HC (1970) Computer techniques in image processing. Academic, New York
De M, Hazra LN (1977) Walsh functions in problems of optical imagery. Opt Acta 24(3):221–234
Hazra LN (2007) Walsh filters in tailoring of resolution in microscopic imaging. Micron 38(2):129–135
Hazra LN, Guha A (1986) Farfield diffraction properties of radial Walsh filters. J Opt Soc Am A 3(6):843–846
Hazra LN, Purkait PK, De M (1979) Apodization of aberrated pupils. Can J Phys 57(9):1340–1346
Purkait PK (1983) Application of Walsh functions in problems of aberrated optical imagery, Ph.D. Dissertation, University of Calcutta, India
Hazra LN (1977) A new class of optimum amplitude filters. Opt Commun 21(2):232–236
Mukherjee P, Hazra, LN (2013) Farfield diffraction properties of annular Walsh filters. Adv Opt Tech 2013, ID 360450, 6 pages,
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Hazra, L., Mukherjee, P. (2018). Walsh Functions. In: Self-similarity in Walsh Functions and in the Farfield Diffraction Patterns of Radial Walsh Filters. SpringerBriefs in Applied Sciences and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-2809-0_1
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DOI: https://doi.org/10.1007/978-981-10-2809-0_1
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Publisher Name: Springer, Singapore
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