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  5. Digital information processing in dispersed management systems with application of the fast orthogonal transform based on symmetric ternary functions

Digital information processing in dispersed management systems with application of the fast orthogonal transform based on symmetric ternary functions

A. Izmailov, L. Petryshyn
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Description: The paper deals with orthogonal transform based on symmetric ternary functions and its efficiency due to the criterion of operational complexity. Digital information processing (DIP) is an important part of most of the information technologies applied in different areas of economy, production, medicine, etc. Thus, effective solutions in DIP give efficiency increase in all its application areas. Orthogonal transforms play a significant role in DIP processes and therefore, the problem of synthesis of new efficient orthogonal transforms has high practical significance. The former efficiency analysis of orthogonal transform based on symmetric ternary functions due to the criterion of decorrelation degree of the transform coefficients proved its application efficiency for problems of data compression. However, implementation of this orthogonal transform straight in form of matrix multiplication has maximal possible operation complexity. At the same time transform matrices of the described transform give many opportunities for simplifying its calculation. From properties analysis of transform matrices it follows that it is possible to build a fast transform based on the given orthogonal transform using recursive calculation procedure known as divide-andconquer principle. The described fast transform was successfully built and its efficiency was tested in comparison with WalshHadamard and Haar transforms using the criterion of operational complexity.


Keywords: Digital information processing, symmetric ternary functions, fast orthogonal transform, divide-and-conquer

Reference:
Izmailov, A.V. and Petryshyn, L.B. (2018), “Tsyfrova obrobka informatsii v rozoseredzhenykh systemakh upravlinnia iz zastosuvanniam shvydkoho ortohonalnoho peretvorennia na osnovi triikovykh symetrychnykh funktsii” [Digital information processing in dispersed management systems with application of the fast orthogonal transform based on symmetric ternary functions], Information Processing Systems, Vol. 3(154), pp. 79-89. https://doi.org/10.30748/soi.2018.154.11.