Digital information processing in dispersed control systems with application of the fast orthogonal transform based on symmetric ternary functions
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Abstract
The paper deals with orthogonal transform based on symmetric ternary functions and its efficiency due to the criterion of operational complexity. The purpose of the study is to synthesize a rapid transformation on the basis of an orthogonal, constructed with the use of a system of triple symmetric functions, and to evaluate the effectiveness of its application according to the criterion of operational complexity. Research results. 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-and-conquer principle. The described fast transform was successfully built and its efficiency was tested in comparison with Walsh-Hadamard and Haar transforms using the criterion of operational complexity. The scientific novelty of the results obtained is the synthesis of a fast orthogonal transformation based on triple symmetric functions and compares the effectiveness of its application with the criterion of operational complexity with the Walsh-Hadamard and Haar transformations. Further research is to develop and explore alternative ways to implement rapid conversion and to compare the efficiency of conversion to different from the operational complexity and the degree of decoupling of the coefficients of conversion to the criteria.
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References
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