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On the Application of Haar Functions
IEEE Transactions on Communications, 1973Recent interest in the application of Walsh functions suggests that Haar functions, close relatives of Walsh functions, may also be useful. In this primarily tutorial paper, Haar functions are reviewed briefly and the computational and memory requirements of the Haar transform are analyzed; applications are then discussed. It is concluded that, whereas
J. Shore
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Discrepancy estimates based on Haar functions
Mathematics and Computers in Simulation, 2001The author presents a technique to estimate the star-discrepancy of \((t,m,s)\)-nets using generalized Haar function systems, and applies it to prove that the star-discrepancy of \({\mathcal P}_t\), the digital \((t,m,2)\)-nets in base \(b=2\), satisfies \[ D_N^*({\mathcal P}_t)\leq 1- \biggl(1- \frac{1}{2^{m-t}} \biggr)^2+ \frac 13 \frac{m-2t}{2^m ...
K. Entacher
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Walsh and Haar functions in genetic algorithms
Proceedings of the 1994 ACM symposium on Applied computing - SAC '94, 1994Theoretical analysis of fitness functions in genetic algorithms has included the use of Walsh functions [14]. They form a convenient basis for the expansion of fitness functions [3]. These orthogonal, rectangular functions have also been used to compute the average fitness values of schemata [5]. This work explores the use of Haar functions [7] for the
S. Khuri
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Mutual relations between arithmetic and Haar functions
ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187), 2002Mutual relations between arithmetic and unnormalized Haar functions are stated. The new relations allow one to calculate directly arithmetic spectrum from unnormalized Haar spectrum and vice versa without the necessity of obtaining the original function.
B. Falkowski
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