Izmailov A. Methods and devices of symmetric ternary transforms for digital information processing

In this thesis, an actual task of reducing the amount of memory for storage of the correlated data by developing methods and devices of digital information processing based on symmetric ternary transforms was presented and solved. Application areas of orthogonal and wavelet transforms with advantages and disadvantages of existing bases of such transforms and corresponding devices of digital information processing are analyzed. System of orthogonalized products of symmetric ternary functions and discrete symmetric ternary orthogonal transform on its basis are proposed. Fast algorithm is developed for the introduced transform. Symmetric ternary mother wavelet and continuous symmetric ternary wavelet transform on its basis are proposed. The use of an auxiliary symmetric ternary mother wavelet is proposed for synthesis of the discrete symmetric ternary wavelet transform and its filter form. Device of the symmetric ternary orthogonal transform based on the FPGA is developed and simulated. Device of the discrete symmetric ternary wavelet transform based on the microcontroller is developed and implemented. It is proved that application of the introduced methods and devices for digital information processing provides reduction of memory required for storage of the correlated data in computerized technical systems.