Методика вибору гіперкомплексних числових систем для моделювання цифрових реверсивних фільтрів

Abstract

Digital filter is a digital system, which is used for filtering a discrete signal. It can be implemented as a software method, and with the help of specialized equipment. In both cases, the digital filter can be used for filtering, both in real time and for a pre-stored signal value. In this paper, we consider only the algorithms for the synthesis of the software filter structure. However, it should be noted that on the basis of these structures, implementations and hardware solutions of digital filters can beat. The use of HNS for the synthesis of digital filter structures can give a tangible advantage. Digital filters with hyper complex parameters have greater momentum and better characteristics in integrated parametric sensitivity.The paper discusses the definition of hyper complex digital filter and the conversion of its transfer function to the form of hyper complex function. A technique for selecting a hyper complex number system has been developed for the equivalent of a hyper complex filter to a real analogue. It is shown that the main method for determining the expediency of using one or another HNS for the synthesis of the structure of a hyper complex digital filter is the general form of the normic denominator of the hyper complex transfer function of the filter. This turn should be a complete polynomial of the shift operator, and also contain all the components of the multiplier with the shift operator in the denominator.However, these conditions are only necessary in the synthesis of the hyper complex filter, since the system of equivalence equations may not have real solutions when fulfilling these conditions. In this case, it is necessary to switch to another HNS, if there is such an opportunity, or to switch to HNS of higher orders. The latter path needs further research.