General method of synthesis by PLIC/FPGA digital devices to perform discrete orthogonal transformations

Abstract

A general method is proposed to synthesize digital devices in order to perform discrete orthogonal transformations (DOT) on programmable logic integrated circuits (PLIC) of FPGA class. The basic and the most "slow" operation during DOT performance is the operation of multiplying by a constant factor (constant) - OMC. To perform DOT digital devices are implemented at the use of the same type of IP-cores, which allow to realize OMC. According to the proposed method, OMC is determined on the basis of picturing set over the elements of the Galois field. Due to the distributed computing of nonlinear polynomial function systems defined over the Galois field in PLIC/FPGA architecture, the reduction in the estimates of time complexity concerning OMC performance is achieved. Each non-linear polynomial function, like OMC, is realized on the basis of the same type of IP-cores according to one of the structural schemes in accordance with the requirements for the device to perform DOT. The use of IP cores significantly reduces the cost of designing a device that implements DOT in the PLIC/FPGA architecture.

Keywords: digital signal processing, discrete orthogonal transformations, distributed computing, nonlinear polynomial functions, Galois fields, FPGAs, digital devices