Abstract
Walsh functions Ψ0, Ψ1, … have many applications to information theory (see [3]), especially to problems of pattern recognition and image enhancement. The Walsh system shares many properties with other orthonormal systems but is distinguished by the fact that each Ψj is locally constant, takes on only the values ±1, and the intervals of constancy shrink uniformly to points as j → ∞.
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References
G. E. Albert and W. R. Wade, Haar systems for compact geometries, (preprint).
R. F. Gundy, Martingale theory and pointwise convergence of certain orthogonal series, Trans. Amer Math Soc. 124 (1966), 228–248.
H. F. Harmuth, “Transmission of Information by Orthogonal Functions,” Springer-Verlag, Berlin, 1972.
D. C. Harris, A.e. divergence of multiple Walsh-Fourier series, Proc. Amer. Math. Soc. (in print).
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© 1987 Springer-Verlag Berlin Heidelberg
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Wade, W.R. (1987). Walsh Series in Polar Coordinates. In: Meyer-Ebrecht, D. (eds) ASST ’87 6. Aachener Symposium für Signaltheorie. Informatik-Fachberichte, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73015-3_17
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DOI: https://doi.org/10.1007/978-3-642-73015-3_17
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