Метод генерації гіперкомплексних числових систем для моделювання цифрових реверсивних фільтрів 4-го порядку

Abstract

A digital filter is a digital system used to filter a discrete signal. It can be implemented either by software or by specialized equipment. The use of hypercomplex numbers for building digital filter structures can provide significant benefits. Digital filters with hypercomplex parameters have higher speed and better performance in terms of total parametric sensitivity. Although in previous works software filter of 3 th order structure synthesis algorithms were proposed, in this paper only software filter of 4 th order structure synthesis algorithms are considered. Studies have shown that the expression analysis method for the transfer function denominator norms of the hypercomplex filter allows you to effectively select the hypercomplex number system, which has all the necessary properties. It is shown that only quadriplex number system K and hypercomplex number system obtained by auto doubling of a double-number system W are suitable for the structures synthesis of fourth-order hypercomplex digital filters. These hypercomplex number systems allow to get a complete set of filter transfer function shift operator steps. On the other hand, they have isomorphic weakly filled hypercomplex number systems. Transition to such systems can significantly reduce the number of real operations during the filter operation time. In the work, all transformations and calculations in the hypercomplex domain were performed using the software module for hypercomplex calculations in the Maple computer algebra framework. This fact confirms the efficiency of this software module. Tabl.: 2. Refs: 17 titles.