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Walsh Functions and Gray Code

IEEE Transactions on Electromagnetic Compatibility, 1971
Gray code is a natural way of ordering binary vectors in dyadic space, hence it appears frequently in connetion with Walsh functions. In Paley's definition of Walsh functions their sequencies are arranged in Gray code. Gray code also appears in a new Walsh function generation algorithm which obtains a function by locating all its sign changes.
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Walsh Functions and Their Generalizations

1991
Consider the function defined on the half open unit interval [0, 1) by $${{r}_{0}}(x) = \left\{ {\begin{array}{*{20}{c}} 1 & {for x \in [0, 1/2),} \\ { - 1} & {for x \in [1/2,1).} \\ \end{array} } \right.$$ Extend it to the real line by priodicity of period 1 and set r k (x) = r0(2 k x)for k = 0,1, … and real x.
B. Golubov, A. Efimov, V. Skvortsov
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Function Generation by Walsh Functions

IETE Journal of Research, 1973
S. S. R. Murthy, P. S. Ramakrishna
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Walsh Functions

2017
Lakshminarayan Hazra, Pubali Mukherjee
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Walsh–Hadamard Transform Kernel-Based Feature Vector for Shot Boundary Detection

IEEE Transactions on Image Processing, 2014
Lakshmi Priya G G
exaly  

A chaotic colour image encryption scheme combining Walsh–Hadamard transform and Arnold–Tent maps

Journal of Ambient Intelligence and Humanized Computing, 2019
Syam Sankar, Ashok S Kumar
exaly  

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