Calculation of paired Haar spectra for systems of incompletely specified Boolean functions

A new algorithm is given that converts a reduced representation of Boolean functions in the form of disjoint cubes to unnormalized paired Haar spectra for systems of incompletely specified Boolean functions. Since the known algorithms that generate unnormalized Haar spectra always start from the truth table of Boolean functions the method presented computes faster with a smaller computer memory. The method is extremely efficient for such Boolean functions that are described by only few disjoint cubes and it allows the calculation of only selected spectral coefficients, or all the coefficients can be calculated in parallel.

[1]  Chip-Hong Chang,et al.  A novel paired Haar based transform: algorithms and interpretations in Boolean domain , 1993, Proceedings of 36th Midwest Symposium on Circuits and Systems.

[2]  Chip-Hong Chang,et al.  Generation of multi-polarity arithmetic transform from reduced representation of Boolean functions , 1995, Proceedings of ISCAS'95 - International Symposium on Circuits and Systems.

[3]  Bogdan J. Falkowski,et al.  Effective computer methods for the calculation of Rademacher-Walsh spectrum for completely and incompletely specified Boolean functions , 1992, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[4]  G. Rota Finite orthogonal series in the design of digital devices: M. G. Karpovsky, Wiley, 1976, 250 pp. , 1977 .

[5]  Bogdan J. Falkowski,et al.  An effective computer algorithm for the calculation of disjoint cube representation of Boolean functions , 1993, Proceedings of 36th Midwest Symposium on Circuits and Systems.

[6]  Chip-Hong Chang,et al.  Properties and applications of paired Haar transform , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[7]  Bogdan J. Falkowski,et al.  Efficient Algorithms for Forward and Inverse Transformations between Haar Spectrum and Binary Decisi , 1994, Proceeding of 13th IEEE Annual International Phoenix Conference on Computers and Communications.

[8]  Leonid P. Yaroslavsky,et al.  Digital Picture Processing , 1985 .

[9]  J.P. Hansen,et al.  Decision diagram based techniques for the Haar wavelet transform , 1997, Proceedings of ICICS, 1997 International Conference on Information, Communications and Signal Processing. Theme: Trends in Information Systems Engineering and Wireless Multimedia Communications (Cat..

[10]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[11]  K. R. Rao,et al.  Orthogonal Transforms for Digital Signal Processing , 1979, IEEE Transactions on Systems, Man, and Cybernetics.