Numerical methods for software modeling of digital algorithms for difference filtering without algorithmic multiplication operations

The issues related to the study of the possibilities of virtual programming of digital counterparts of electronic equipment are considered. The relevance of the study is due to the need to reduce the computational complexity of digital signal processing algorithms for the virtualization of tests of aviation electronic equipment. The purpose of the study is to formalize numerical methods of difference digital filtering with difference coefficients of various orders of magnitude. The methods of mathematical and software modeling of numerical methods were used in the study. The results of the study showed and confirmed the possibility of modeling these filters by directional search and comparative analysis of their difference coefficients. The concept of difference digital filtering, the term «Difference digital filtering» and the concept of such filtering are defined and described. A mathematical model of a recursive difference digital filter is proposed. The numerical method of recursive difference digital filtering of different orders and different orders of difference is formalized. An example of using binary difference coefficients of a recursive RCF is given to replace convolutions of time samples of digital signals and difference coefficients of a digital filter with these reports in order to ensure the construction of a digital filtering algorithm without algorithmic multiplication operations. The results of modeling numerical methods of difference digital filtering with trivial difference coefficients of various difference orders are presented. Mathematical and software modeling of the proposed algorithm for convolution of the sequences of the time samples of the filtered digital signal and the integer coefficients of the difference digital filtering makes it possible to reduce the computational complexity of the hardware and software implementation of digital doubles of the difference digital filters with such coefficients.