Abstract
The paper considers calculation of autocorrelation functions on finite dyadic groups over decision diagrams. The methods exploit recursive structure of both autocorrelation matrices and decision diagrams. First, it is discussed calculation of the autocorrelation through the Wiener-Khinchin theorem implemented over decision diagrams. Then, it is proposed a method for calculation of separate autocorrelation coefficients over decision diagrams with permuted labels at the edges. For the case of restricted memory resources, a procedure with in-place calculations over the decision diagram for the function processed has been defined.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Agaian, S., Astola, J., Egiazarian, K.: Binary Polynomial Transforms and Nonlinear Digital Filters. Marcel Dekker, New York (1995)
Bracewell, R.: The Autocorrelation Function. In: The Fourier Transform and Its Applications, 3rd edn., pp. 40–45. McGraw-Hill, New York (1999)
Bryant, R.E.: Graph-based algorithms for Boolean functions manipulation. IEEE Trans. Comput. C-35(8), 667–691 (1986)
Clarke, E., Millan, M.M.C., Zhao, K.L., Fujita, X.,, M.: Spectral transforms for extremely large Boolean functions. In: Kebschull, U., Schubert, E., Rosenstiel, W. (eds.) Proc. IFIP WG 10.5 Workshop on Applications of the Reed-Muller Expression in circuit Design, Workshop Reed-Muller 1993, Hamburg, Germany, September 16-17, pp. 86–90 (1993)
Falkowski, B.J., Chang, C.H.: Properties and methods of calculating generalized arithmetic and adding transforms. IEE Proc. Circuits, Devices and Systems 144(5), 249–258 (1997)
Karpovsky, M.G.: Finite Orthogonal Series in the Design of Digital Devices. John Wiley, Chichester (1976)
Karpovsky, M.G. (ed.): Spectral Techniques and Fault Detection, pp. 35–90. Academic Press, London (1985)
Karpovsky, M.G., Moskalev, E.S.: Utilization of autocorrelation characteristics for the realization of systems of logical functions. Avtomatika i Telmekhanika 2, 83–90 (1970); English translation Automatic and Remote Control 31, 342–350 (1970)
Karpovsky, M.G., Stanković, R.S., Astola, J.T.: Spectral techniques for design and testing of computer hardware. In: Proc. Int. Worksop on Spectral Techniques in Logic Design, SPECLOG 2000, Tampere, Finland, June 2-3, pp. 1–34 (2000)
Meinel, C., Somenzi, F., Tehobald, T.: Linear shifting of decision diagrams and its application in synthesis. IEEE Trans. CAD 19(5), 521–533 (2000)
Pichler, F.: Walsh functions and linear system theory. In: Proc. Applic. Walsh Functions, Washington, D.C., pp. 175–182 (1970)
Pichler, F.: Some Aspects of a Theory of Correlation with respect to Walsh Harmonic Analysis, Techn. Report. Dept. of Electrical Engineering, University of Maryland, Washington, DC, Report R-70-11 (August 1970)
Pichler, F.: Walsh-Fourier Synthese optimaler Filter, AEÜ, Band 24, Heft 7/8, 350–360 (1970)
Pichler, F.: Realizations of Prigogine’s Λ-transform by dyadic convolution. In: Trappl, R., Horn, W. (eds.) Austrian Society for Cybernetic Studies (1992) ISBN 385206127X
Rice, J.E.: Autocorrelation Cefficients in Representation and Classification of Switching Functions, Ph.D. Disertation, University of Victoria, Victoria, B.C., Canada (2003)
Rice, J.E., Muzio, J.C.: Methods for calculating autocorrelation coefficients. In: Proc. 4th Int. Workshop on Boolean Problems (IWSBP 2000), pp. 69–76 (2000)
Rice, J.E., Muzio, J.C.: Use of autocorrelation function in the classification of switching functions. In: Euromicro Symposium on Digital System Design, pp. 244–251 (2002)
Rice, J.E., Muzio, J.C.: Properties of autocorrelation coefficients. In: Proc. IEEE Pacific Rim Conf. on Comunications, Computers and Signal Processing (2003)
Rice, J.E., Muzio, J.C.: On the use of autocorrelation coefficients in the identification of three-level decompositions. In: Proc. PAC 2003, pp. 577–580 (2003)
Rice, J.E., Muzio, J.C.: On the use of autocorrelation coefficients in the identification of three-level decompositions. In: Proc. Int. Workshop on Logic Synthesis, IWLS 2003 (2003)
Rice, J., Serra, M., Muzio, J.C.: The use of autocorrelation coefficients for variable ordering for ROBDDs. In: Proc. 4th Int. Workshop on Applications of Reed-Muller Expansion in Circuit Design, Victoria, Canada, August 20-21, pp. 185–196 (1999)
Sasao, T., Fujita, M. (eds.): Representations of Discrete Functions. Kluwer, Dordrecht (1996)
Stanković, R.S., Astola, J.T.: Spectral Interpretation of Decision Diagrams. Springer, Heidelberg (2003)
Stanković, R.S., Sasao, T., Moraga, C.: Spectral transform decision diagrams. In: Sasao, T., Fujita, M. (eds.) Representations of Discrete Functions, pp. 55–92. Kluwer Academic Publishers, Dordrecht (1996)
Tomczuk, R.: Autocorrelation and Decomposition Methods in Combinational Logic Design, PhD thesis, University of Victoria (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stanković, R.S., Karpovsky, M.G. (2005). Remarks on Calculation of Autocorrelation on Finite Dyadic Groups by Local Transformations of Decision Diagrams. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_40
Download citation
DOI: https://doi.org/10.1007/11556985_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29002-5
Online ISBN: 978-3-540-31829-3
eBook Packages: Computer ScienceComputer Science (R0)