Computationally efficient implementation of hypercomplex digital filters

Hypercomplex digital filters have an attractive advantage of order reduction; however, they also have a drawback that multiplication requires a large amount of computation. This paper proposes a novel implementation of hypercomplex digital filters. By decomposing hypercomplex number multiplication, we show that they can be realized as two parallel complex multiplications. Using this technique, any type of hypercomplex digital filter can be implemented with less than half the computation of the direct approach