Digital filters with hypercomplex coefficients

Digital filters with hypercomplex coefficients are considered. This filter can reduce the order of filters to 1/4 of a filter with real coefficients. The fact that digital filters with hypercomplex coefficients of the first order can realize any order of digital filters with real coefficients less than 4 is described in detail. Three different realizations of arbitrary higher-order digital filter with real coefficients are also considered. Stability criteria for digital filters with hypercomplex coefficients are suggested.<<ETX>>