Is there any relationship between Walsh functions and rationalized Haar functions?
Can we express a Walsh functions in terms of Haar functions?
I have found an expression in Wikipaedia for which any Walsh function can be expressed as a sum of odd and even Haar functions, I have some doubt about this, I think it is not true at all
The rationalized Haar functions (or wavelets) take only the values of 0, -1, and 1. Walsh functions take 1, and -1 as values !, so what is the difference?
The answer is yes. The difference is the total number of terms required for computation of the expansion of the fitness function f(x) for a given x using Haar is of order 2^l which is less than the order of Walsh which is 2^2l. This is from "Walsh and Haar Functions in Genetic Algorithms" by Sami Khuri
I thank you so much for this reply and specially for the reference paper
Dear Lakhdar Chiter . The answer yes, becous the Rademacher functions defined as some sums of Haar functions. More you can find in the book " Kaczmarz, S., Steinhaus H. Theorie der Orthogonalreihen "
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